United States v. Michael Vallone

ROVNER, Circuit Judge. At the conclusion of an eleven-week trial, a jury convicted defendants Michael A. Vallone, William S. Cover, Michael T. Dowd, Robert W. Hopper, Timothy S. Dunn, and Edward Bartoli of conspiring to defraud the United States by impeding and impairing the functions of the Internal Revenue Service (“IRS”) and to commit offenses against the United States, along with related fraud and tax offenses. They were sentenced to prison terms ranging from 120 to 223 months. The defendants appeal their convictions and sentences. We affirm. *432 I This is the latest in a series of cases arising out of abusive trusts promoted by The Aegis Company (“Aegis”) and its sister company, Heritage Assurance Group (“Heritage”), both based in Palos Hills, Illinois. See United States v. Wasson, 679 F.3d 938 (7th Cir.2012); United States v. Hills, 618 F.3d 619 (7th Cir.2010), cert. denied, — U.S. -, 131 S.Ct. 2958, 180 L.Ed.2d 249, — U.S. -, 132 S.Ct. 130, 181 L.Ed.2d 51 (2011); United States v. Patridge, 507 F.3d 1092 (7th Cir.2007); United States v. Baxter, 217 Fed.Appx. 557 (7th Cir.2007); Muhich v. C.I.R., 238 F.3d 860 (7th Cir.2001); Bartoli v. Richmond, 215 F.3d 1329, 2000 WL 687155 (7th Cir.2000); see also United States v. Richardson, 681 F.3d 736 (6th Cir.2012); United States v. Welti, 446 Fed.Appx. 784 (6th Cir.2012); United States v. Ellefsen, 655 F.3d 769 (8th Cir.2011); Richardson v. C.I.R., 509 F.3d 736 (6th Cir.2007); United States v. Diesel, 238 Fed.Appx. 398 (10th Cir.2007); United States v. Tiner, 152 Fed. Appx. 891 (11th Cir.2005). Heritage was formed in 1990 by Michael Richmond as the Illinois offshoot of a like-named California firm. Defendants Michael Vallone and Robert Hopper joined the staff of Heritage shortly thereafter. Defendant Edward Bartoli, an attorney with degrees from both Notre Dame and Harvard, later became affiliated with Heritage as its legal counsel. Heritage was in the business of selling living trusts for estate planning purposes. These trusts were marketed to customers through a network of cooperating insurance agents. In 1993, Bartoli put forward the idea of a package of business, family, and charitable trusts that could be marketed to customers as a means of both estate planning and income tax minimization. Bartoli thought that such a package could command a price of $25,000 or more. Vallone and Hopper were amenable to the idea and joined Bartoli in bringing his idea to fruition. They began to promote the concept of a multi-trust system at training sessions that Heritage sponsored for its cooperating insurance agents, and eventually began to sell some trust packages to Heritage clients. By early 1994, however, Vallone and Hopper had fallen out with Richmond and forced him out of Heritage, accusing him of embezzlement. Along with Bartoli, they decided to form a new company, Aegis, to take over marketing of the multitrust system. Aegis was formed later that same year, and it began to sell multi-trust systems as a way for high-income individuals to minimize their income taxes. Aegis and Heritage continued to share the same building in Palos Hills, a Chicago suburb, as their headquarters. Although the Aegis system of trusts was portrayed as a legitimate, sophisticated means of tax minimization grounded in the common law, the system was in essence a sham, designed solely to conceal a trust purchaser’s assets and income from the IRS, thereby reducing his apparent tax liability and defrauding the United States of revenue to which it was entitled. Pursuant to the Aegis system, “customers appeared to sell their assets to several trusts when, in fact, customers never really ceded control of their assets.” Hills, 618 F.3d at 624. The trusts were marketed to and implemented for customers across the United States through a network of corrupt promoters, managers, attorneys, and accountants. Although prospective customers who bothered to seek independent advice as to the legitimacy of the Aegis system were routinely warned of its flaws, greed led many to overlook the system’s “too good to be true” attributes. Between 1994 and 2003, some 650 individuals purchased Aegis trust packages, at prices ranging *433 from $10,000 to $50,000 or more. The diverse clientele included real estate brokers, doctors, public officials, and a variety of small-business owners. Among the purchasers was a co-founder of the Hooters restaurants chain, Lynn “L.D.” Stewart, who himself was later charged with tax evasion, although the charges were dismissed after his trial resulted in a hung jury. (Others were not so lucky; some Aegis clients were convicted and sent to prison.) The thousands of false income tax returns that were filed based on the use of the Aegis trusts are estimated to have cost the federal government more than $60 million in tax revenue. The defendants in this ease include the progenitors of the Aegis trust along with some of its major promoters. Vallone was the executive director of Aegis; Bartoli, who came up with the idea of the trust system, was the firm’s first legal director until 1996, and continued to help manage Aegis thereafter; and Hopper served as the firm’s managing director. In 1995, these three, along with Timothy Shawn Dunn, created Aegis Management Company (“Aegis Management”) to provide trust management services and tax advice to individuals who purchased the Aegis trusts. Dunn, a certified financial planner, was a promoter as well as a manager of Aegis trusts; he became the executive director of Aegis Management. William Cover, like Dunn, was a promoter and manager of Aegis trusts. He served as the president of Sigma Resource Management, Inc. and later held the controlling interest in Sigma Resource Management, LLC (collectively, “Sigma”), which also provided management services to purchasers of Aegis trusts. Vallone and Michael Dowd served as directors and officers of Sigma. Dowd came to work at the Palos Hills offices of Heritage and Aegis in 1997, after earning a degree in business finance. In addition to assisting the Aegis principals, Dowd provided management services to trust purchasers through both Aegis and Sigma. David Parker, a New York attorney, served as the legal director of Aegis Management. He assisted in the promotion and management of Aegis trusts as well as the defense of the trust system from government inquiries. John Stambulis, an Illinois attorney, worked in the Palos Hills office of Aegis, and assisted with the creation and defense of Aegis trusts. Both Parker and Stambulis would later plead guilty and testify against the remaining defendants at trial. The Aegis trusts were typically marketed to wealthy, self-employed individuals whose income could not be easily traced through the W-2 forms that are issued to ordinary taxpayers. Aegis representatives, including the defendants, conducted seminars promoting the Aegis trusts in cities around the country. Attendance at these seminars was by invitation only, and guests were charged between $150 and $500 to participate. Attendees were told at such seminars that use of the Aegis trust system would reduce if not eliminate their federal income taxes. They were often given materials that purported to document the legitimacy of the system with seemingly thorough and impressive citations to the various legal authorities that supported the trusts. But as one lawyer wrote to a client who sought his advice as to the legitimacy of the system: This material is full of errors, irrelevancies and partial truths followed by non sequiturs. I know that I must resist the temptation to follow every line or I could spend the rest of my life on this. I will ■ concentrate on how, even if it were 99 percent correct, the claimed tax effects fail. In doing so, I’m not implying that that 99 percent is correct. I’m just skipping over the errors. *434 Gov’t Ex. Dunn Office 32, R. 962 Tr. 3395. Those persons who purchased packages of one or more trusts were also encouraged to purchase trust management services from Aegis Management or Sigma, for which they would pay thousands of dollars annually on top of the $10,000 to $50,000 they paid for the trusts themselves. These management services included advice and counsel on using the trusts to conceal income and assets from the IRS. The typical Aegis system comprised multiple domestic trusts, including a business trust, an asset management trust, and a charitable trust. (As we shall explain in a moment, foreign trusts were also used in many instances to further conceal an individual’s assets and income.) The centerpiece of the system was the business trust, also referred to as a “common law business organization” or “CBO.” The business trust was purportedly modeled after the Massachusetts Business Trust, a non-statutory arrangement by which ownership of a business is transferred to a trust in exchange for certificates of beneficial interest; the trustee then holds and manages the business on behalf of the holders of those, certificates. See Navarro Sav. Ass’n v. Lee, 446 U.S. 458, 468-69, 100 S.Ct. 1779, 1785-86, 64 L.Ed.2d 425 (1980) (quoting Hecht v. Malley, 265 U.S. 144, 146-47, 44 S.Ct. 462, 463, 68 L.Ed. 949 (1924)) (describing Massachusetts Business Trust). A key point distinguishing the Aegis business trust (along with the other trusts making up the Aegis system) is that an independent trustee never assumed any real control over the trust assets. With the aid of Aegis personnel, a purchaser nominally would transfer his assets—in-eluding his businesses and residence — to one or more trusts and formally cede control of those assets to the named trustee, typically Bartoli, Parker, or Stambulis. But routinely, within a few days after the trust was first established — and sometimes before the client had even transferred assets to the trust — the Aegis attorney would resign by means of a boilerplate letter citing “circumstances beyond [his] control,” and appoint the client as his replacement. E.g., R. 917 Tr. 3495-96; R. 921 Tr. 5408-09; R. 965 Tr. 306. Because the purchaser thus retained control over the assets assigned to the trusts, the transfer of those assets into the trust amounted to nothing more than a paper transaction with no economic substance. 1 Again, the sole purpose of the trust was to conceal the purchaser’s assets from the IRS in an effort to reduce his tax liability. As the defendants themselves put it to their clients, the clients would “own nothing but control everything.” R. 921 Tr. 5384, 5406; R. 943 Tr. 204. That the Aegis trust system was a fraudulent scheme was borne out in the manner in which the underlying documentation was prepared. We have noted, for example, that the purportedly independent trustee named in the creation of the trust routinely would resign shortly after the trust was created and be replaced by the client on whose behalf the trust was created. Typically the boilerplate resignation letter was prepared and signed at the same time as the paperwork creating the trust, although it was dated several days later, leaving no doubt that the resignation of the initial, “independent” trustee was *435 planned from the outset. Moreover, in many instances, the trust documents were backdated to make it appear that a client had (nominally) transferred his assets to the trusts long before he had even purchased the trusts — sometimes years earlier — in order to retroactively claim the tax advantages of the trusts. (False notarizations were routinely provided to give cover to the backdating.) An additional fee was sometimes charged for backdating documents in this way. Finally, false documents were created to make it appear that various legally important events had taken place — for example, minutes indicating that the directors of a trust had met— when in fact they never had. The income that Aegis clients derived from their businesses was also diverted to the trusts by means of management and consulting contracts between the clients’ businesses and their trusts, an arrangement that Aegis personnel suggested and helped to implement. Ostensibly, pursuant to such a contract, a trust would provide services to the client’s business, for which the business would in turn compensate the trust. In actuality, the trust would provide no services to the business, although the business would compensate the trust and write the payments off as an expense. The actual purpose of these contracts was thus to conceal the diversion of business profits to the trusts without the payment of taxes on that income. See Ellefsen, supra, 655 F.3d at 775, 779-80. The money that Aegis clients transferred to their trusts would be returned to the clients and their businesses in a variety of ways. In some instances, the trusts would make fictitious loans to the client or his business. In other instances, charitable trusts were used to pay for things that really had nothing to do with the stated aims of those trusts. For example, a charitable trust might pay hundreds of thousands of dollars to purchase a primary residence or vacation home for the Aegis customer, on the theory that the home would serve as the “world headquarters” of the trust. R. 943 Tr. 207, 222. Similarly, the charitable trust might pay for a family vacation trip on the theory that one of the purposes of the trip was to visit charitable enterprises to which the trust might make donations. Tax returns were prepared for the Aegis trust purchasers and for the trusts themselves, but these too were fraudulent in multiple respects. First, Aegis clients were advised by the defendants to assign their own income to the trusts despite the fact that the income was being earned and controlled by the clients just as it had been before the trusts were created. Second, clients were advised to report that assigned income on certain trust tax returns, but then to pass the income on to other trusts without taxes being paid on that income. The result was that the income remained in the clients’ hands, but the tax liability was transferred elsewhere. Third, the defendants encouraged clients to claim various deductions on the trusts’ federal tax returns that had no basis in law or fact. For example, clients were told to deduct their household utility and other expenses on the theory that their homes were the “world headquarters” of their trusts. College tuition for clients’ children was likewise posited as a trust expense based on the notion that the children would one day become directors of the trusts. The wealthiest Aegis clients were advised to participate in an offshore trust system employing foreign trusts and so-called “international business companies” (IBCs) in Belize. Belize was chosen as the locus for the offshore system because it was not particularly cooperative with the United States on issues related to asset- *436 hiding and tax evasion. David Jenkins, a citizen of Belize, assisted the defendants with this aspect of the Aegis system, which commenced in 1995. The use of offshore trusts and foreign bank accounts enabled clients to further conceal their income by nominally transferring that income to a foreign trust. Again, control of the money would in fact remain with the client, but the tax liability would be shifted to a foreign entity that would, in actuality, file no U.S. tax return and pay no tax. As with the domestic trusts, foreign trusts and IBCs were established in such a way as to create the illusion that they were not under the control of Aegis clients. Jenkins would designate certain foreign entities to serve as the nominal directors, trustees, and protectors of these trusts or IBCs. For example, Freedom Services Company, an entity directed by Yallone, was often named as a trust protector (whose job it was to oversee the trustee), and a second company controlled by Jenkins was typically named as trustee. Meanwhile, Aegis clients were given undated letters of resignation from Vallone and Jenkins so that control of the trusts and IBCs at all times remained with them. Offshore accounts in Antigua were established in the names of these Belizean trusts and IBCs, and these accounts too were in reality under the control of the Aegis clients. To effect the concealment of his income using the offshore trust system, an Aegis client was advised to first transfer his untaxed income to a trust bank account in the United States. From there, the money would be transferred to a bank account in Antigua that was held in the name of a foreign trust. The money was then transferred again to a second bank account, this one in the name of an IBC. The transfer of funds between domestic and foreign trusts often was characterized as a loan, evidenced by one or more promissory notes. Because the transfer of funds from one trust account to another was simply a means of hiding the client’s funds from the IRS, these notes were a fiction. But to give them a patina of legitimacy, Aegis clients were advised that periodic demands should be made on the notes and, in turn, relatively small repayments (say, $10,000) should be made on the outstanding “loans.” Once a client’s funds had been transferred to the IBC’s bank account, the money could be repatriated to the client in the United States in one of several ways. The client would be given a credit card linked to the IBC account in Antigua, which card he could use to access his money, either by making purchases using that card or by receiving cash advances through Automated Teller Machines (ATMs) in the United States. Because the card was linked to an offshore account, there would be no record of these transactions clearing in the United States. The IBC could also make fictitious “loans” or “gifts” of deposited funds to the client. No taxes were paid on income diverted through the offshore trust system. Aegis clients were assured that the IRS would not have access to offshore trust and bank records and would never be able to link the clients to the control of the IBCs or the bank accounts linked to those IBCs. The system worked to the benefit of the defendants as well: they could receive transaction fees equal to two or three percent of any funds funneled through the offshore trusts. The services that the defendants provided to Aegis clients did not end with the establishment of the various trusts. The defendants also provided clients with assistance on two fronts in an effort to ensure that the goal of tax evasion was accom *437 plished — preparation of tax returns, and defense of IRS audits. As the trusts were a sham, Aegis insisted that clients use pre-selected tax return preparers whom the defendants knew would both conceal the true nature of the tax-avoidance scheme and help to perpetuate it by preparing returns consistent with the purpose of that scheme. Vallone, Dunn, and Cover each assisted clients and their tax preparers in preparing their personal, business, and trust tax returns. Copies of the tax returns filed on behalf of many Aegis clients were later found in the defendants’ offices. By the mid-1990s, the IRS was aware that Aegis and other organizations were promoting various forms of trusts as a means of income tax evasion, and it began to step up its efforts to combat the abusé of trusts for this purpose. It formally signaled its focus on abusive trusts in April 1997, with the issuance of IRS Notice 97-24, available at 1997 WL 187852. The notice explained that it was “intended to alert taxpayers about certain trust arrangements that purport to reduce or eliminate federal taxes in ways that are not permitted by federal tax law.” Notice 97-24 at 1. The notice went on to cite five examples of potentially abusive tax arrangements, among them the business trust. Id. at 2. It explained that a common feature of an abusive trust is that the original owner of the assets nominally subject to the trust retains the .authority to cause the financial benefits of those assets to be returned to or made available to himself. Id. at 1-2. The notice also summarized the key legal principles applicable to trusts and tax liability, including firstly the - point that “[sjubstance — not form-— controls taxation,” such that abusive trust arrangements may be treated as shams for tax purposes. Id. at 3. It also noted: When used in accordance with the tax laws, trusts will not transform a taxpayer’s personal, living or educational expenses into deductible items, and will not seek to avoid tax liability by ignoring either the true ownership of income and assets or the true substance of transactions. Accordingly, the tax results that are promised by the promoters of abusive trust arrangements are not allowable under federal tax law.... Id. at 3. As we discuss in greater detail below, the Aegis principals were aware of Notice 97-24: Vallone, for example, acknowledged that Aegis received multiple copies of the notice (along with client inquiries) soon after it was issued by the IRS. R. 921 Tr. 5434. Yet, the notice did not cause, the firm to stop promoting Aegis trusts; instead, as we discuss below, it triggered efforts to avoid and/or obstruct IRS inquiry into the trusts. In fact, even before it issued Notice 97-24, the IRS was already quietly investigating Aegis. Michael Priess, then a Special Agent with the Criminal Investigation Division of the IRS, was among several agents who participated in an undercover investigation of Aegis that began in 1996. Priess posed as Mike Jordan, an investment adviser whose clients were mostly physicians. After attending an Aegis seminar in June 1996 at the Oak Lawn Hilton in suburban Chicago, Priess and another agent met with Dunn in 1997 to discuss the possibility of purchasing an Aegis package that would include an offshore trust. After attending two additional Aegis seminars — an October 1997 seminar in New York and a January 1998 seminar in Belize — Priess met again with Dunn in July 1998 to confirm-that he was interested in purchasing an offshore trust package. During that meeting, Dunn assured Priess that he would surrender control of the assets he.placed into the trust system for only about five minutes before the initial *438 trustee resigned. “In fact,” Dunn told Priess, “the resignation letter is completed before you’re actually signing up.” R. 965 Tr. 275. Two months later, Priess (as Jordan) agreed to purchase a trust package at a price of $38,000, and to engage Aegis Management to service the trusts at a cost of $11,500 per year. Priess told Dunn at that time that his accountant had told him the Aegis system was “bullshit” and that he should not go ahead with the purchase. R. 965 Tr. 288. Dunn was not surprised: “It’s not the first time we’ve heard those words, believe me.” Id. Tr. 288. The trust documents were ready for Priess’s (or rather Jordan’s) signature in November. The package that Priess had purchased included a CBO/business trust (the Jordan Business Company Trust), an asset management trust (the MJ Asset Management Trust), an offshore trust (the Fructus International Trust), and an IBC (the Pernour Services Company). Parker had already signed the paperwork as trustee of the MJ Asset Management Trust, and Jordan’s forthcoming signature had already been notarized. Dunn told Priess to date his signature August 26, 1998, although that date had come and gone more than eleven weeks earlier. (As it turned out, the dates on some of the documents had to be corrected later so that they matched the notarized dates.) Minutes had already been prepared showing .that the asset management trust’s board of directors (which included only one director— Parker) had met by telephone on August 26, 1998. Parker had signed a letter of resignation effective on September 28, 1998; and Priess was also given an undated letter of resignation from the trustee and protector of the Belizean trust, “[t]o give me [i.e., Jordan] assurances that I had control of the Fructus International Trust.” R. 965 Tr. 332. Bank accounts at the Swiss American Bank in Antigua were opened for both the offshore trust and the IBC. After the trust system was established, Priess (as Jordan) set about with Dunn’s help to use the system to divert profits from his (fictitious) business into the trusts. A contract was prepared between Jordan’s business (Cumberland Investment Group) and the CBO (Jordan Business Company Trust) pursuant to which the CBO purportedly would provide management services to the business. The fee that the CBO would charge for these services was pegged at the amount of money Jordan expected his business to realize in profits that year — initially $220,000 and later $290,000. In reality, the CBO would provide no services at all to Jordan’s investment business, but the business would pay the fee to the business trust as a cover for the diversion of the business’s profits; the business trust would then transfer the fee to the asset management trust, which would in turn convey the fee to the offshore trust, which would then transfer the fee to the IBC. Priess posed a wrinkle to Dunn: he (Jordan) did not have $290,000 on hand to pay the CBO its “fee.” Dunn helped Priess come up with a “Plan B”: Jordan’s business would make an initial payment of $185,000 to the CBO; that money would then be transferred among the various trusts into the bank account of the IBC in Antigua; then $105,000 of that money would be repatriated to Jordan from the IBC account to Jordan as a “gift”; Jordan would then send that $105,000 back into the trust system by writing a check for $106,400 to Fructus International Trust in purported repayment (with interest) of a $105,000 “loan” that Fructus had made previously. These machinations added a new level of deceit to the charade of the management fee, making it appear as though Jordan’s business ultimately paid the entire “fee” of $290,000, when in fact part of that total *439 was simply a recycling of the initial down-payment of $185,000. The net effect was that Jordan’s business gained a $290,000 deduction for its books, for which it paid only $185,000; the income tax liability that would have been due on the business’s profits was effectively shipped offshore to the IBC (which was beyond the reach of the IRS); and Jordan at all times retained control over the money. Priess subsequently had conversations with both Cover and Vallone at a February 1999 Aegis seminar in Cleveland about the way in which he had repatriated the $105,000 from the Belizean IBC to himself as a “gift.” Cover, who told Priess that he was managing trusts from some fifty Aegis clients, warned Priess that bringing money back into the United States as a gift from the IBC was risky, as he would owe tax on the portion of any gift in excess of $10,000. Cover suggested to Priess that he bring back the remainder of the $290,000 sent abroad as a “loan.” Cover also mentioned to Priess that he (Cover) used a credit card linked to his own offshore IBC account to obtain cash from that account. “I go to the Cash Station every week and pull out $400,” he told the agent. Priess Tr. 42; R. 944 Tr. 409; R. 966 Tr. 688. When Priess raised the same subject with Val-lone over lunch, Vallone had a different idea. Vallone suggested that Priess could still use a “gift” as the means of repatriating money from the Belizean entities, so long as he named a nominee director to the offshore bank accounts linked to the international trust and the IBC. That way, Vallone explained, Priess could say he had nothing to do with the “gift” if ever questioned by the IRS. Priess’s experience with the Aegis system documented most of the tax-evasive aspects of the Aegis scheme: a chain of connected trusts that, on paper, accomplished the transfer of client income abroad and assigned the income tax liability to an IBC, where it would effectively disappear; the designation of nominally independent trustees whose immediate resignation was planned for before the client signed the trust paperwork; the backdating of documents; the preparation of minutes to reflect fictitious meetings of the trusts’ boards of directors (e.g., Parker’s telephonic meeting with himself); the use of bogus management services contracts to facilitate the transfer of a client’s business profits into the trust system; the repatriation of funds diverted to the offshore trust and IBC back to the client in the United States through fictitious loans and gifts; and the reality that for the Aegis client, all of these transactions and events occurred on paper only, without altering the operation of their businesses, control of their assets, or access to their money. After the IRS signaled its interest in abusive trust arrangements with the issuance of Notice 97-24 in 1997, the defendants created what they referred to as the “Aegis Audit Arsenal.” This so-called arsenal was basically a series of obstructionist measures that the defendants encouraged Aegis clients to use, and in some instances aided their clients in using, to thwart IRS inquiries into the use of Aegis trusts. For example, the defendants encouraged clients to withhold information from IRS agents, to respond to IRS inquiries and requests for the production of financial records with non-responsive letters and questionnaires drafted by defendants, and to file frivolous motions to quash summonses issued by the IRS. In some instances, attorneys Parker and Stambulis sent letters drafted by Vallone to the IRS on behalf of Aegis clients. A nine-page letter that Parker sent to the IRS in November 1999 on behalf of Aegis client Genevieve Riccordino, a real estate broker, exemplifies the nature of this cor *440 respondenee. The letter is a font of evasion and obfuscation, posing a multitude of questions as to the IRS’s purposes in seeking information related to Riccordino’s trusts, voicing doubt as to the IRS’s authority to investigate the trusts, making frivolous document requests, and threatening to seek sanctions if the IRS did not comply with Parker’s demands. Gov’t Ex. Dunn Office 25 (Gov’t Supp. App. -189-97). Parker later confessed on - the witness stand that he issued letters such as this one with little or no forethought as to whether they had any arguable basis in the law. “I was more concerned about sending these letters' out pursuant to the Aegis Audit Arsenal than determining át the time whether they were legally defensible or not,” he testified. R. 947 Tr. 2040. Early in 2000, the defendants also created the Washington, D.C., law firm of Parker & Associates, which was owned by Parker and Hopper, to represent Aegis clients during IRS audits and examinations. The law firm served the dual function of helping to implement the Audit Arsenal’s goal of obstruction and to generate additional fees from Aegis clients. In a particularly brazen move, several of the defendants filed lawsuits against both the IRS and a number of its revenue and special agents, among others. Bartoli, Vallone, Hopper, and Dunn filed one such suit on May 8, 1997, in the Northern District of Illinois against (among others) IRS Revenue Agent James Pogue and the Illinois Attorney Registration and Disciplinary Commission (“ARDC”), which had initiated disciplinary proceedings against Bartoli based on his involvement with the trusts sold by both Heritage and Aegis. (We shall have more to say about the ARDC proceeding below.) That .suit was assigned to Judge Plunkett who, after dismissing most of the defendants and granting summary judgment to Pogue, imposed Rule 11 sanctions on the four plaintiffs for filing a frivolous lawsuit. See Fed.R.Civ.P. 11. His sanctions opinion, which we later affirmed and adopted on appeal, observed: ■ At base, the plaintiffs filed this claim because they believe the trusts they promote should be a legal means to avoid paying taxes. They are not. Plaintiffs may disagree with the state of the law, but Rule 11 prohibits them from filing fictional claims to protest it.... Bartoli v. A.R.D.C. of Ill. 1999 WL 1045210, at *3 (N.D.Ill. Nov. 12, 1999) (citations omitted), ajfd sub nom. Bartoli v. Richmond, supra, 2000 WL 687155. In May 2001, Vallone, Aegis, and Heritage also filed a class-action suit against the IRS and three of its agents (among other defendants) in the Southern District of Illinois, seeking damages of $556 billion for purported violations of the plaintiffs’ civil rights. That action was dismissed as devoid of merit in June 2003. Judge Plunkett’s November 1999 ruling in the Bartoli case was an unmistakable rejection of the legitimacy of the Aegis trusts, but in fact the defendants were on notice long before his ruling that the Aegis system was contrary to longstanding rules governing trusts and taxation. Prospective clients of Aegis who received warnings as to the legitimacy of the system from their own lawyers and' accountants frequently forwarded the negative opinions to Aegis personnel; copies of such opinions were later discovered in the files at Aegis headquarters. We' quoted earlier from one such opinion letter, which noted that the Aegis materials distributed at promotional seminars purporting to document the legality of the system were “full of errors, irrelevancies and partial truths followed by non sequiturs.” Gov’t Ex. Dunn Office 32, R. 962 Tr. 3395. We also noted that when Priess (posing as Mike Jordan) reported his own accountant’s description *441 of the Aegis system as “bullshit,” Dunn assured him it was not the first time he had heard such language used in reference to Aegis. IRS Notice 97-24, issued in April 1997, reiterated the ways in which abusive trusts akin to those promoted by Aegis violated longstanding and well-known legal principles. This notice, as we have discussed was well-known to the Aegis principals, and copies of the notice were found in the Aegis headquarters. Then in June 1999, the United States Tax Court issued its decision in Muhich v. C.I.R., 1999 WL 390695 (U.S. Tax Court June 14, 1999), holding that a multi-trust system that Bartoli had sold to Frank and Virginia Muhich through Heritage was a sham lacking in economic substance that should be disregarded for tax purposes. Mr. and Mrs. Muhich owned a family photography business. They purchased a trust package from Heritage in 1994 after meeting with Bartoli; they subsequently engaged Aegis to help operate the trusts. The Muhichs’ system ultimately comprised five trusts, including an asset management trust, a business trust, a charitable trust, an equity trust, and a vehicle trust. Bartoli served as the initial trustee of the asset management trust, which was formed first, and following Bartoli’s resignation as the initial trustee, the Muhichs became the sole trustees and beneficiaries of that and the other four trusts. Most of the Muhich’s assets were assigned to the asset management trust, including Mr. Muhich’s right to receive compensation for his services. Once the trusts were in place, Mr. Muhich ran the family business just as he did before. In lieu of paying a salary to him, however, the business paid the asset management trust for his services, calling the payments “consulting fees.” The Muhichs, as officers of the asset management trust, assumed responsibility for managing the trust’s affairs, and as compensation for their services, the trust “agreed” to pay the family’s housing, transportation, health care, and other expenses. The asset management trust, of course, claimed deductions for those expenses; and any net income remaining after the deduction of those expenses was transferred to the charitable trust. The asset management trust thus reported zero taxable income, and the charitable trust (which made only modest charitable contributions) claimed exemption from taxation. The other trusts reported no income whatsoever. On the returns that the Muhichs themselves filed for 1994 and 1995, they reported no income in the form of compensation. The IRS determined that the trust arrangement was an abusive one that should be disregarded for tax purposes, and the Tax Court agreed. The court found that the trusts lacked any economic substance apart from tax considerations. The court pointed out that (1) the Muhichs’ relationship with their property did not change (“the Muhichs could manipulate, distribute, or otherwise use trust property at their whim”) (2) the trusts lacked an independent trustee (“[t]he fact that Bartoli served as a trustee for a limited time is meaningless; it was a paper appointment solely for the purpose of facilitating the creation of the trust scheme”); (3) “no economic interest in the trusts ever passed to anyone other than the Muhichs”; and (4) the Muhichs were not bound by any restrictions as to the use of trust property. Id., at *6-*7. The court noted that, overall, “the tangled web” of trusts did little more than conceal who really owned the assets and who earned the income assigned to the trusts. Id., at *7. In sum, petitioners established the trusts with an aim to avoid, improperly, Federal income tax. None of the trusts *442 ever reported taxable income, and none of them conducted a legitimate business activity. Petitioners’ purpose for the trust scheme was to take untaxed money out of Midwest [the family business] and circulate it around the trusts to pay for the Muhichs’ personal expenses. The Muhichs admitted as much at trial. Although the Muhichs attempted to identify other nontax reasons for the trusts, we find these reasons incredible. Because the trusts lacked economic reality, the Court will ignore them for tax purposes. Id. (footnotes omitted). This decision to treat the trusts as a sham meant that the business income that had been diverted to the trusts would instead be treated as income to the Muhichs on which they would owe tax. The court went on to hold the Muhichs liable for a penalty equal to twenty percent of the amount of income they had underpaid in the relevant tax years based on their negligence in under-reporting their income. Id., at *10 — *11; see 26 U.S.C. § 6662(a) and (b)(1). In imposing that penalty, the court rejected the Muhichs’ contention that they had reasonably relied on the advice of Bartoli, among others, as to the legitimacy of the trusts. “Bartoli’s bias was obvious, and his ability to benefit financially by luring individuals into the scheme should have sent up a red flag. Petitioner is an experienced businessman who should have been suspicious of Bartoli’s claims.” Id., at *11. The court opted not to impose an additional penalty on the Muhichs under 26 U.S.C. § 6673(a)(1) for asserting a frivolous or groundless position in response to the IRS’s claims. The court agreed that the Muhichs’ contention that the trusts had economic substance indeed was frivolous; it rejected the penalty only because the Muhichs had prevailed on the distinct question whether the “consulting fees” paid by the Muhichs’ business to the asset management trust should be included in the Muhichs’ income as compensation or constructive dividends. Id. The Muhichs appealed the Tax Court’s decision to this court. We affirmed the Tax Court’s holding in January 2001, noting that it was wholly consistent with prior cases rejecting efforts to assign a taxpayer’s income and other assets to a trust, treat his personal expenses as deductible costs of trust administration, and avoid paying income taxes on his income. The Muhichs transferred their assets to the trusts and attempted to have their trusts pay all their personal expenses. As detailed above, courts have uniformly held that such transactions are a sham and that the Commissioner [of Internal Revenue] may disregard these sham trusts for tax purposes. This is what the Commissioner did and we can see no reason to overturn the decision of the Tax Court. 238 F.3d at 864 (footnote omitted). The executives of Aegis were keenly aware of the Tax Court’s decision in Muhich. The Muhichs may have purchased an early version of a trust system from Heritage (where Bartoli, Vallone, and Hopper developed the concept of a multitrust package aimed at tax avoidance), but their package of trusts was similar in essential respects to the Aegis system of trusts, and the Muhichs had in fact engaged Aegis to help them operate their trusts. Frank Muhich was spotted in the audience at the first Aegis seminar that Agent Priess attended in 1996, and in the wake of the Tax Court’s decision three years later, Hopper remarked to Priess that Muhich “was one of our CBO clients.” Priess Tr. 48; R. 944 Tr. 419. There was extensive discussion and correspondence both within Aegis and between Aegis representatives and existing and prospective *443 clients regarding the Muhich decision. Publicly, Aegis officials put on a brave face when referencing the decision, attempting to distinguish the Aegis trusts from the Heritage system that the Muhichs had purchased and criticizing the Muhichs’ implementation and use of the system. Privately, some at Aegis feared that the Tax Court’s decision marked the beginning of the end of Aegis. As we discuss in greater detail later in this opinion, the adverse decision led to a schism between Hopper and Vallone: Hopper believed that Muhich’s description of the trusts as a sham exposed the Aegis principals to criminal liability for promoting the Aegis trusts; he thought that Aegis clients should be encouraged to seek out independent advice as to how they should proceed in the wake of Muhich. Vallone, on the other hand, thought that Aegis should increase its efforts to avoid and obstruct IRS inquiries into the Aegis trusts. The other red flag that signaled official disapproval of the Aegis system came in the form of the disciplinary complaint that the Illinois ARDC filed against Bartoli in November 1996. By this time, Bartoli had resigned as Aegis’s legal counsel, assumed inactive status with the Illinois bar, and relocated to Myrtle Beach, South Carolina; but he remained involved in the management of Aegis. The ARDC began investigating Bartoli after Richmond, who had been forced out of Heritage in 1994, complained to the ARDC about Bartoli. The complaint that the ARDC ultimately filed against Bartoli was premised primarily on the assertion that Bartoli had engaged in dishonesty, fraud, and deceit in promoting CBOs as a means of tax avoidance, because the applicable principles of trust, tax, and common law did not recognize the CBO as employed by Heritage, Aegis, and Bartoli as a viable entity. R. 916 Tr. 2652-53. Much like the Muhich litigation, then, the ARDC proceeding directly implicated the legitimacy of the Aegis system of trusts. We shall have more to say about the ARDC proceeding later in this opinion as we discuss an issue with respect to the evidence that the government offered at trial regarding that proceeding. For now it is enough to note that although only Bartoli was named as a respondent in the ARDC proceeding, the defendants were well aware of the proceeding. Vallone and Hopper, in addition to Bartoli, were deposed in the course of that proceeding. Copies of the ARDC documents were later discovered in the Aegis headquarters. And, as we have already noted, four of the defendants filed suit against the ARDC based on its conduct in investigating and charging Bartoli. Ultimately, a Hearing Board of the ARDC issued a Report and Recommendation in February 2000 proposing that Bartoli be disbarred in Illinois based on his conduct in connection with promoting and selling the CBOs. That proposal was adopted by the ARDC’s Review Board in December 2001, and Bartoli was formally disbarred by the Illinois Supreme Court in May 2002. By early 2000, it was apparent to all that the government had both Aegis and the firm’s clientele in its sights. Vallone would report in an April 2000 letter to Aegis clients that as of January 2000, some 150 Aegis members had received audit requests from the IRS, although he assured clients that the IRS dropped half of these “after one or two letters from us.” Gov’t Ex. Priess 26; R. 944 Tr. 435. On March 31, 2000, search warrants were executed at the Aegis headquarters in Palos Hills, Illinois, at Dunn’s office in Indiana, and at the offices of other individuals working with the defendants. Both documents and computers were seized during the search, making plain that the government was not only building a case against Aegis and its officials but attempting to identify the firm’s *444 clients as well. Vallone would later testify that “new business was practically completely finished” at that point. R. 921 Tr. 5356. It would be another four years, however, before Aegis finally closed its doors. Aegis continued to service existing clients of the trust system; and Vallone led an ultimately unsuccessful effort to prevent the government from identifying those clients. Vallone initiated changes in the trust system in an ongoing effort to keep Aegis clients “off the radar screen” of the IRS. Kg., R. 944 Tr. 452-53, 455; R. 954 Tr. 5501-02. Vallone learned that the government had been able to identify some Aegis clients from the Schedule C forms (used to report income from sole proprietorships) that those clients had attached to their trust tax returns. R. 944 Tr. 438-39. Val-lone adopted a new business name — “The Fortress Trust” (which had the same address as the Aegis headquarters) — and under that name promoted a new “Tax Minimization Plan,” which employed a different type of trust and a limited liability company, so as to eliminate the type of tax return that called for a Schedule C. Existing Aegis clients were encouraged to switch to the new system — at a cost of several thousand dollars — in order to avoid scrutiny from the IRS. Dunn, in fact, had such a conversation with Agent Priess. Priess, in his role as Aegis client Mike Jordan, had a June 2000 meeting with Dunn in which Priess voiced skepticism whether he had an ongoing need for the services of Aegis Management. Dunn responded that Priess (Jordan) needed those services more than ever “[i]n light of the increased scrutiny and them [the IRS] now having the records” from the March 2000 search. Gov’t Ex. Priess Tr. 59; R. 944 Tr. 452. “There are ways to get those same benefits without having to be on the radar screen,” Dunn told Priess. Id. Tr. 452. In the meantime, changes were occurring within Aegis. Hopper resigned as the managing director of the firm in January 2000, although he remained on hand to provide assistance through April. Parker ceased his involvement as counsel in May 2000, after the Muhich decision caused him to seek independent advice as to the legitimacy of the Aegis trusts from three different tax attorneys, who informed him that the trusts were not valid. In May 2000, the same month as Parker’s departure, Dowd was named by Vallone to be the operations manager of both Heritage and Aegis. In a letter to Aegis clients announcing (among other events) Harper’s departure and Dowd’s promotion, Vallone described Dowd’s new role as a “purely administrative position, not managerial,” but added that Dowd “will greatly help me in carrying on with our operations.” Gov’t Ex. 27; R. 944 Tr. 450. In June 2000, Dowd, Cover and others joined what was known as the Aegis Advisory Board to counsel Vallone in his management of Aegis and the Fortress Trust. A discussion of the facts would not be complete without mention of the ways in which the defendants themselves used the Aegis trusts. The defendants not only promoted the Aegis trust system but used that system to hide the substantial income they reaped from sales of trust packages. (From 1997 through 2000, the total incomes earned by each defendant ranged from a low of $142,000 in Dowd’s case to a high of $1.5 million in Dunn’s case. Collectively, the defendants earned more than $6 million from the sale and management of Aegis trusts over the life of the scheme.) In some cases, the defendants failed to file tax returns at all: Vallone, Bartoli, and Hopper filed no individual tax returns for the years 1997 to 2000, for example. To hide the income they earned from Aegis and other sources, their paychecks were *445 made payable to the trusts they controlled and were deposited into the bank accounts held by those trusts; the defendants then withdrew cash and paid for personal expenditures out of the trust accounts. None of the income funneled through the trusts was reported as income and thus no tax was paid on it. Vallone failed to report gross income of $700,000 from 1997 through 1999 (he was not charged for the 2000 tax year), on which he owed federal income taxes of $182,000. Bartoli failed to report gross income of over $600,000 in 1997 through 2000, on which he owed tax of $192,000. Hopper failed to report gross income of more than $814,0000 in those four years, on which his tax liability was more than $220,000. Like Vallone, Bartoli, and Hopper, Dunn did not file a federal income tax for 1999, although his gross income exceeded $438,000 that year. He did file tax returns for 1997 and 1998, but he reported only modest income of approximately $16,000 and $9,000 for those years, when his actual income exceeded $434,000 and $604,000 respectively. On the income that he failed to report in these three years, Dunn owed taxes totaling more than $315,000. Dowd and Cover both filed federal income tax returns in 1997 through 2000, but as with Dunn the returns they filed substantially under-reported their actual income. Dowd, for example, reported income of only $3,000 to $6,000 annually, although his gross income in those four years amounted to more than $211,000. He owed $55,000 on the income that he failed to report, while Cover owed an additional $84,000 on the income that he did not report for 1997 through 1999. Although the doors of Aegis did not close until 2004, the scheme was largely at an end by 2003. By that time, people were being summoned to testify about Aegis to a grand jury. In March 2003, the government conducted a second round of searches which included, among other locations, the Aegis headquarters and Val-lone’s homes in Illinois and Florida. The defendants were indicted in April 2004. Count One of the superseding indictment charged all of the defendants with conspiring to defraud the United States by impairing and impeding the functions of the IRS and to commit tax offenses against the United States. Í8 U.S.C. § 371. The defendants were also charged with multiple counts of mail fraud, 18 U.S.C. § 1341; wire fraud, 18 U.S.C. § 1343; aiding and assisting the filing of false tax returns by others, 26 U.S.C. § 7206(2); filing their own false tax returns, 26 U.S.C. § 7206(1); and tax evasion, 26 U.S.C. § 7201. After multiple continuances were granted at the requests of one or more of the defendants, an eleven-week trial commenced in February 2008 and concluded in May 2008. The jury convicted Vallone, Bartoli, Hopper, and Cover on all counts in which they were charged. Dunn was convicted on the conspiracy charge and fourteen tax-offense charges, but he was acquitted on nine counts of mail and wire fraud. Dowd was convicted on the conspiracy count, one count of mail fraud, and four counts of filing false tax returns but was acquitted on four mail and wire fraud counts and four counts alleging that he aided and assisted the filing of false tax returns by others. Each of the defendants was sentenced to a substantial term of imprisonment: Val-lone was ordered to serve a prison term of 223 months; Bartoli, 120 months; Hopper, 200 months; Dunn, 210 months; Cover, 160 months; and Dowd, 120 months. All six defendants appeal, raising a multitude of joint and individual issues that we resolve in turn below. *446 II. JOINT ISSUES A. Speedy Trial Act Claim The trial in this case was originally set for June 29, 2004, R. 31, but was continued on multiple occasions thereafter at the request of various defendants. In a number of instances, these continuances were granted over the objection of the government, but at no time did any defense counsel voice an objection to the delays. However, in February 2008, shortly before the trial commenced, defendant Vallone moved to dismiss the indictment, contending that the multiple postponements of the trial date had violated his right to an expeditious trial under the Speedy Trial Act, 18 U.S.C. § 3161, et seq. (the “STA” or the “Act”). R. 408, 411. 2 That Act grants a defendant the right to a trial commencing within seventy days after he is charged or makes an initial appearance, § 3161(c)(1), subject to certain authorized exceptions that permit time to be excluded from the seventy-day period, § 3161(h). See Zedner v. United States, 547 U.S. 489, 492, 126 S.Ct. 1976, 1981, 164 L.Ed.2d 749 (2006); United States v. O’Connor, 656 F.3d 630, 636 (7th Cir.2011), cert. denied, — U.S. -, 132 S.Ct. 2373, 182 L.Ed.2d 1024 (2012). On the defendant’s motion, the district court must dismiss the indictment if the trial does not commence within seventy non-excluded days. § 3162(a)(2). Principally, Vallone contended that from February 7 to May 3, 2007, the court had failed to enter an order properly tolling the running of the speedy-trial clock, so that by April 18, 2007, seventy days had elapsed and because the trial had not yet commenced, his right to a speedy trial had been violated. (Secondarily, Vallone suggested that “other time periods” were problematic because the court’s findings as to the excludability of these time periods were inadequate. But Vallone never identified which time periods he was relying upon.) At the hearing on Vallone’s motion, the government responded that the lack of an order entered between February 7 and May 3, 2007, was immaterial, because the court in December 2006 had continued the trial date at the request of the defendants until October 23, 2007, and had excluded time through that new trial date from the STA’s seventy-day mandate with the agreement of the parties. R. 1051 at 54-57; see R. 1057 at 6. The government presented the court with a transcript of the December 7, 2006 hearing at which this had occurred. R. 1051 at 58-59. After reading a portion of that transcript into the record, the court denied Vallone’s motion. R. 1051 at 64. Vallone, now joined by the other defendants, contends that the court erred in denying his motion. As the defendants acknowledge, “certain specified periods of delay are not counted” toward the STA’s seventy-day limit. Defendants’ Joint Br. 23 (quoting Zedner, 547 U.S. at 492, 126 S.Ct. at 1981); United States v. Wasson, supra, 679 F.3d at 944. One such exception, and the one most on point here, is a continuance of the trial date granted based on the court’s finding that “the ends of justice served by taking such action outweigh the best interest of the public and the defendant in a speedy trial.” § 3161(h)(7)(A) (formerly § 3161(h)(8)(A) as noted in O’Connor, 656 F.3d at 636 n. 2). The statute identifies a number of factors that the court must consider in deciding whether such a continuance is warranted. § 3161(h)(7)(B); see *447 Wasson, 679 F.3d at 944. The district judge has broad discretion in weighing the pertinent factors and in determining whether a continuance is warranted. United States v. Rojas-Contreras, 474 U.S. 231, 236, 106 S.Ct. 555, 558, 88 L.Ed.2d 537 (1985); see also United States v. Broadnax, 536 F.3d 695, 698 (7th Cir.2008); United States v. Taylor, 196 F.3d 854, 860 (7th Cir.1999) (citing United States v. Blandina, 895 F.2d 293, 296 (7th Cir.1989)). Counterbalancing that open-ended discretion, however, is “procedural strictness”: The judge must set forth in the record, either orally or in writing, his reasons for concluding that a continuance is warranted by the ends of justice. § 3161(h)(7); Zedner, 547 U.S. at 509, 126 S.Ct. at 1990; see O’Connor, 656 F.3d at 639-40; United States v. Adams, 625 F.3d 371, 378-79 (7th Cir.2010). The defendants’ lead and principal argument on appeal, as it was below, is that the district court did not order the exclusion of time during the time period commencing on February 7, 2007, and ending on May 3, 2007. As the speedy trial clock consequently was running during that period, the defendants reason, the district court was obliged to start the trial no later than April 18, 2007 (seventy days after February 7). The fact that it did not shows that they were deprived of their right to a speedy trial and compelled the district court to grant Vallone’s request that the indictment be dismissed. § 3162(a)(2). We conclude that the defendants have waived this argument. The argument, as we have said, assumes that there was no order at all excluding time between February 7, 2007, and May 3, 2007, such that the speedy trial clock expired in April. This argument overlooks the fact that the court on December 7, 2006, had already continued the trial date from February 7, 2007, on motion of defendants, to October 23, 2007, and had orally excluded time, by agreement. The government relied on the December 7 continuance, and the surrounding context, as adequate to support the exclusion of time under the STA’s ends-of-justice provision. It is clear that the court itself relied on what had transpired on December 7 to deny Vallone’s motion: the court, after all, read the relevant portion of the December 7 transcript into the record in ruling on the motion. R. 416; R. 1051 at 64. It made the point even more explicitly in its order denying the defendants’ post-trial motions for judgments of acquittal, where it noted that it had granted the continuances based on defense counsels’ representations regarding the complexity of the case and the length of time needed to prepare for trial. R. 650 at 7-8. So the threshold question presented by the appeal on this issue is whether, as the government and the district court concluded, the December 2006 continuance of the trial date and the accompanying exclusion of time complied with the STA’s ends-of-justice provision. (To the extent the defendants presume that exclusion must take the form of a written order, they are mistaken. Our decision in United States v. Napadow, 596 F.3d 398, 405 (7th Cir.2010), leaves no doubt that a written order is not required so long as the district court’s oral remarks make clear its intent to exclude time. See also O’Connor, 656 F.3d at 639-40; Adams, 625 F.3d at 380.) Yet, in their lead brief, the defendants make no mention at all of what took place on December 7, 2006, let alone any argument as to why the court’s oral directive that time would be excluded from December 7, 2006, to October 23, 2007, was insufficient to comply with the STA. There can be no reasonable excuse for this omission. The December continuance and exclusion of time was the centerpiece of the govern- *448 merit’s response to the motion to dismiss below and was repeated when the defendants reasserted the speedy trial issue in their post-judgment motions for acquittal. The record leaves no doubt that the district court itself relied on the events of December 7, 2006, as the basis for its decision to deny Vallone’s motion to dismiss and likewise to deny the defendants’ post-judgment motions for acquittal as to this issue. But the defendants’ lead brief is altogether silent as to December 7. They belatedly address the subject in their reply brief, but this is too late. E.g., United States v. Stevenson, 656 F.3d 747, 753 (7th Cir.2011) (citing United States v. Boisture, 563 F.3d 295, 299 n. 3 (7th Cir.2009)). Having altogether ignored the rationale for the district court’s ruling in presenting the issue and making their initial argument on appeal, the defendants have waived this aspect of their challenge. See Bonte v. U.S. Bank, N.A., 624 F.3d 461, 466 (7th Cir.2010) (failure to grapple with basis for district court’s decision to dismiss case, and to respond to defendant’s arguments in support of dismissal, results in waiver of appeal); In re Snyder, 152 F.3d 596, 599-600 (7th Cir.1998) (although, in bankruptcy appeal, appellate court’s review is not confined to district court’s findings but extends to findings- of bankruptcy court as well, it is nonetheless “unacceptable” for appellant to ignore basis for district court’s ruling); United States v. Fuchs, 635 F.3d 929, 933-34 (7th Cir.2011) (failure to address district court’s alternative holding on an issue waives any challenge to that holding) (coll, cases); Fin. Inv. Co. (Bermuda) Ltd. v. Geberit A.G., 165 F.3d 526, 531 (7th Cir.1998) (failure to address alternative ground for district court’s decision until reply brief constitutes waiver of challenge to that ground). The defendants argue secondarily that many of the district court’s other orders excluding time based on the ends of justice were not supported by adequate findings; but this argument was waived in the district court. We noted above that although Vallone’s motion to dismiss primarily focused on the period from February 7 to May 3, 2007, he also suggested that the district court had not properly excluded other periods of time in the case. The entirety of Vallone’s argument in that regard reads as follows: In addition, other time periods in these proceedings are also not excludable for speedy-trial purposes, because the record does not reflect that the requisite “findings” were “made” in support of the “ends-of-justice” continuances that were nominally entered. R. 411 at 6 (citations omitted). Vallone did not cite any particular order as defective, and the sole documentation he provided to the court in support of his motion was the transcript of the February 7, 2007 hearing, which obviously had to do with his primary argument concerning the February 7 to May 3, 2007, period rather than any other period. At the hearing on Vallone’s motion, the government’s counsel asserted that this second argument was “undeveloped and, therefore, waived.” R. 1051 at 57. When Vallone’s counsel was given the opportunity to reply to the government’s arguments, counsel said nothing to amplify on this second argument nor to contest the government’s assertion that it was waived for lack of development. The district court, having been given no grist in support of the argument, never addressed it. Because this was Vallone’s motion, because the secondary argument was never fleshed out, and because Vallone’s counsel remained silent in the district court in response to the government’s contention that the argument had been waived, we find that Vallone indeed did waive it. *449 We add that the defendants have barely expanded on the basis for their secondary contention in their lead brief on appeal: they have cited roughly a dozen of the district court’s orders continuing the trial date, but have not bothered to address any individual orders and explain why, in light of the requirements of the STA and case law applying the Act, the district court’s exclusion of time was inadequate. To the extent that the defendants mean to suggest that time was not properly excluded because the court’s written orders granting the various continuances do not on their face reflect findings sufficient to satisfy the statute’s requirements as to ends-of-justice exclusions of time, we reiterate that the defendants are operating on a mistaken premise. As we have already said, the court need not put its findings justifying such an exclusion in a written order, so long as the record otherwise makes clear the reasons why the court found that the ends of justice warranted the exclusion of time. The defendants have not bothered to address whether the court’s oral remarks in granting the continuances, and the context surrounding the continuances, otherwise satisfy the statute. See Wasson, 679 F.3d at 946^18; O’Connor, 656 F.3d at 639-40; Adams, 625 F.3d at 380; Napadow, 596 F.3d at 405. B. Cheek Defense All six of the defendants before us were charged, inter alia, with the willful attempt to evade or defeat the federal income taxes owed on their income, either by filing tax returns that substantially understated their income or by filing no tax return at all. R. 103, Counts 35-55; see 26 U.S.C. § 7201. Four of the defendants— Yallone, Bartoli, Hopper, and Dunn — also were charged with willfully aiding and assisting, procuring, counseling, and advising the preparation and presentation of the false and fraudulent income tax returns filed by multiple Aegis clients. R. 103, Counts 11-34; see 26 U.S.C. § 7206(2). In Cheek v. United States, 498 U.S. 192, 201, 111 S.Ct. 604, 610, 112 L.Ed.2d 617 (1991), the Supreme Court noted that the mental state of willfulness, for purposes of section 7201 and other criminal tax laws, demands proof that the defendant knew of a duty imposed on Mm by the law and that he voluntarily and intentionally violated that duty. The court went on to hold that a defendant’s genuine belief that he is not legally required to do a particular act — to report his wages as income to the IRS, for example — is inconsistent with actual knowledge of that obligation, even if his understanding is objectively unreasonable. [I]f the Government proves actual knowledge of the pertinent legal duty, the prosecution, without more, has satisfied the knowledge component of the willfulness requirement. But carrying this burden requires negating a defendant’s claim of ignorance of the law or a claim that because of a misunderstanding of the law, he had a good-faith belief that he was not violating any of the provisions of the tax laws. This is so because one cannot be aware that the law imposes a duty upon him and yet be ignorant of it, misunderstand the Jaw, or believe that the duty does not exist. In the end, the issue is whether, based on all the evidence, the Government has proved that the defendant was aware of the duty at issue, which cannot be true if the jury credits a good faith misunderstanding and belief submission, whether or not the claimed belief or misunderstanding is objectively reasonable. Id. at 202, 111 S.Ct. at 610-11. The over-arching premise of the government’s case was that the Aegis trust system was a sham and that the defendants knew as much. The defendants disputed this premise, contending that they in fact *450 had a good-faith belief that the Aegis trust system was consistent with the relevant provisions of the Internal Revenue Code and thus a legitimate means of income tax minimization. Under Cheek, this required the government to negate their claim of good faith and to prove that they in fact realized that the Aegis system was not legitimate. Only if the defendants knew that the Aegis trusts were ineffective in reducing the income tax owed by those who used the trusts could the jury find that the defendants acted willfully with respect to their own income tax obligations and those of Aegis clients. But the defendants contend that the district court undermined their Cheek defense by precluding them from demonstrating to the jury that they had a good-faith belief in the legality of their actions. The problem, as they see it, began with the court’s pretrial ruling barring any attempt to show that the trusts were, in fact, a legal means of tax avoidance. By relieving the government of the burden of presenting testimony showing that the trusts violated the law, the court eliminated an opportunity for the defense to question whatever witnesses the government would have called on that subject as to potential ambiguities in the law that might have supported the defendants’ purported good faith belief in the legitimacy of the Aegis trusts. The defendants argue that the court later compounded the problem in two ways. First, the court would not allow the defendants to question any government witnesses about purported ambiguities with respect to the tax code and its application to entities like the Aegis trusts. Second, relying on the charge that the defendants had engaged in a conspiracy with one another, the court indicated to counsel that notice to one member of the conspiracy that the trusts were a sham would constitute notice of the same to all other members of the conspiracy. The defendants assert that, collectively, these rulings both prevented the defendants from showing that ambiguities in federal tax law made room for their good-faith belief that the trusts were legitimate and eliminated the government’s burden of negating that good faith belief. We take each aspect of this argument in turn, beginning with the court’s pretrial ruling as to the legality of the Aegis trust system. In advance of trial, the government moved in limine to bar the defendants from presenting to the jury any evidence or argument suggesting that the Aegis trust system was a lawful means of tax avoidance. The government noted that this court in a series of decisions had already determined that the Aegis trust system and others like it constituted unlawful tax shelters. R. 314 at 2-3, citing United States v. Patridge, supra, 507 F.3d at 1093-94; Muhich v. C.I.R., supra, 238 F.3d at 861-63; Bartoli v. Richmond, supra, 2000 WL 687155, at *1, *4; Pfluger v. C.I.R., 840 F.2d 1379, 1385-86 (7th Cir.1988); and Schulz v. C.I.R., 686 F.2d 490, 493-94 (7th Cir.1982). Because defendants’ trust system “clearly [is] not” a “legal means to avoid paying taxes” (Bartoli, 2000 WL 687155, at *1), any evidence or argument that they are lawful tax-avoidance schemes would be contrary to law, and the “probative value [of the evidence would be] substantially outweighed by the danger of ... unfair prejudice, confusion of the issues, or misleading the jury” (Fed. R.Evid.403). R. 314 at 3^4 (emphasis in original). The district court granted the motion. The court acknowledged that the Supreme Court’s decision in Cheek required proof that the defendants knew what the Internal Revenue Code required of them. R. 1046 at 90. Nonetheless, “once the Court *451 has decided that a particular trust or plan is unlawful, it cannot be relitigated to the jury.” R. 1046 at 90. Thus: You cannot argue to the jury that Aegis was a lawful plan and therefore because it was or is lawful that somehow the defendants are not guilty in this case. You certainly can require the government to prove that each defendant may be convicted of tax offenses only if he knows that the code requires him to pay. That’s the government’s burden here, they must show that the actions were willful, that they were done with knowledge, and the government concedes that. But you will not be permitted to reargue the lawfulness of the Aegis plan itself. R. 1046 at 90-91. The defendants contend that this ruling, while paying lip service to Cheek, actually precluded them from establishing that they had a good-faith belief in the legality of the Aegis trust system. They maintain that the court’s order barred them not only from asserting the legality of the Aegis trusts, but also from “raising the statutes, regulations and case law on which they relied in formulating what they subjectively believed was a lawful means of income tax reduction through the use of the Aegis CBO system.” Defendants’ Joint Brief at 38 (emphasis in original). We do not construe the court’s order as the defendants do. The district court was correct in holding that the legality of the Aegis trust system was not a matter for the jury to resolve. This was, instead, a question of law for the court to resolve, e.g., United States v. Caputo, 517 F.3d 935, 942 (7th Cir.2008) (“The only legal expert in a federal courtroom is the judge.”), and one which this court, indeed, had already resolved, see Muhich, 238 F.3d at 864; Bartoli, 2000 WL 687155, at *1. It was therefore appropriate to preclude the defendants from attempting to show that the Aegis trust system was legal. See United States v. Cheek, 3 F.3d 1057, 1063 (7th Cir.1993) (sustaining instructions advising jury that certain of defendant’s beliefs as to the tax laws were erroneous) (citing United States v. Powell, 955 F.2d 1206, 1213 (9th Cir.1992) (because jury cannot decide legality of particular conduct under tax code, district court must instruct jury that conduct was unlawful)). The district court’s order in no way blocked an appropriate Cheek defense, however. The court explicitly recognized that it was the government’s burden to prove that the defendants knew what their obligations were under the law. And nothing the court said suggested that it would preclude the defendants from attempting to show why they in good faith believed that the Aegis trust system was a lawful means of tax avoidance under the relevant statutes, regulations, and case law. To the contrary, the testimony that some of the defendants themselves went on to give demonstrates that they remained free to pursue such a defense, as the government points out. Dowd’s testimony is a good example. Dowd explained that his employment with Heritage was his first job after graduating from college. Although he would later assume more significant responsibilities with Aegis, in the beginning Dowd was something of a Man Friday whose responsibilities included a number of menial tasks: I changed light bulbs. I cleaned up. I brought my own vacuum a couple times and vacuumed the place, cleaned the windows, shoveled the walk. I made— whatever it took. We would have clients, they would have clients come in, and so I tried to make it look neat. R. 938 Tr. 6377. Dowd was given an asset management trust when he started work with Heritage, which his father (who was familiar with Heritage) told him was “a *452 great idea.” Id. Tr. 6358. Dowd himself had only a rudimentary familiarity with trusts and emphasized repeatedly during his testimony that he relied on what Aegis officers such as Vallone and Bartoli told him about the legitimacy of the Aegis system. “I believed in what I was doing, and I believed in The Aegis Company. They were very convincing,” Dowd testified. R. 922 Tr. 6415. Over time Dowd did become aware that the IRS was looking into the use of sham trusts, that Aegis clients were being audited, and that doubts were being raised in the media and other quarters about the use of trusts to minimize or avoid income taxes. He kept his own file (labeled “Trusts — Attacks On”) collecting negative opinions, rulings, and news articles. Yet, whenever he discussed such negative authorities or expressed concern to others at Aegis, he was assured either that the Aegis system was materially different from the trust systems that the IRS was finding to be invalid or that the IRS itself was acting improperly. See, e.g., id. Tr. 6402 (Vallone told him that Muhich did not know how to use the trust system); 6409 (Cover told him that the Aegis system did not operate like the sham trusts referred to in a Wall Street Journal article); 6414 (Vallone told him that other trust companies that the IRS had shut down were “doing it wrong”); 6417 (when he asked Vallone about IRS Notice 97-24, Vallone told him that Aegis was not abusing business trusts in the way described by that ruling and that Vallone was working on a line-by-line rebuttal to the ruling); 6418 (Vallone in multiple conversations cited various provisions of the Internal Revenue Code or pointed him to the Aegis Directors’ Manual in support of the validity of Aegis trusts); 6431 (Vallone cited a specific Code section that said use of a foreign credit card was acceptable. “So I believed him.”). Dowd also found reassurance in the professionals who spoke at Aegis seminars. He recalled attorney Parker saying at one of the seminars that Aegis’s attorneys were “the best,” that the Aegis trust was “kosher,” and that were it otherwise he (Parker) would not be promoting the trust. Id. Tr. 6424-25. Even when the Aegis offices were searched in March 2000 and the company’s computers and files seized, Vallone assured Dowd that the IRS was “just trying to impede Aegis.” Id. Tr. 6412. Not until Dowd learned later that Vallone and other Aegis officers were filing statements with the IRS claiming that they were not “citizens” subject to income taxes did Dowd conclude that something was wrong. Id. Tr. 6440-41. At that point, he decided to leave the company. Dowd’s testimony, during which he was permitted to both recount what others told him about the legitimacy of the Aegis system and to identify and discuss the various Aegis materials and favorable authorities on which his belief in the system was based, illustrates that nothing in the district court’s ruling prevented him from pursuing a Cheek defense. See also infra at 455 n.4; R. 974 Tr. 5142-5220 (on direct examination, Vallone’s counsel walks him through multiple legal authorities which purportedly formed basis for Val-lone’s good-faith belief in legality of Aegis system); e.g., id. Tr. 5158-65 (court overrules government objection to admission of Vallone Ex. Aegis School Book Second Ed. 1998 — which collected authorities Vallone believed supported Aegis trust system and which was given to participants at Aegis seminars — reasoning that exhibit was admissible as evidence of Vallone’s belief in legality of Aegis system; jury apprised that exhibit was admitted for purposes of establishing Vallone’s state of mind); id. Tr. 5189 (Vallone testifies that he understood Parker’s comment at March 1999 seminar regarding lack of legal precedent on business trusts “to mean that there were certain issues that related to business *453 trusts and their operation that simply had not been settled in the law”). The defendants posit, and we may assume arguendo, that expert testimony would be one way in which a defendant charged with tax evasion can establish that he had a good faith, albeit mistaken, belief that his conduct was lawful. Our own decision in United States v. Harris, 942 F.2d 1125, 1132 n. 6 (7th Cir.1991), explicitly recognizes this possibility. 3 Again, however, we see nothing in the district court’s ruling that preemptively rejected the possibility of a defense expert testifying about the legal precedents on which defendants purported to have based their belief that the Aegis trusts were effective tax-avoidance vehicles. The defendants’ real contention seems to be that the district court’s ruling somehow relieved the government of presenting its own expert testimony as to the relevant provisions of the law, which would have presented the defendants with an opportunity to cross-examine the experts about potential good-faith misinterpretations of those provisions. Defendants’ Joint Brief at 47-48. *454 Yet, although the government bore the burden under Cheek of negating the defendants’ good-faith defense and proving their actual knowledge of what the law required of them, it was not obliged to do so in any particular way. As we noted earlier in our summary of the facts, there was ample evidence that the defendants were on notice of the illegality of the Aegis trust system, and the defendants do not suggest that the government failed to carry its burden on this point. And because the legality of the Aegis trusts presented a question of law that had already been resolved by this court, there was no need for the government to present expert testimony as to what the law provided. The district court instead properly instructed the jury on the relevant provisions of the law. Finally, to the extent the defendants are suggesting that the government’s motion and the district court’s ruling somehow prevented them from showing that the relevant provisions of the law were ambiguous, see Defendants’ Joint Brief at 45^6, they are blurring the distinctions between objective ambiguity in the law and their own purportedly good-faith misinterpretation of the law. As our decision in Harris makes clear, objective ambiguity is a question for the court; and if the court were to find the law objectively ambiguous, that finding would require dismissal of the indictment, as the defendants would not have had appropriate notice that their conduct was illegal. 942 F.2d at 1132 n. 6. Defendants make no argument that the provisions of the Internal Revenue Code and regulations governing trusts are objectively ambiguous. The defendants next contend that the district court, in a series of evidentiary rulings during the government’s case, “eviscerated the government’s burden regarding the Cheek defense.” Defendants’ Joint Br. 48. They point out that the government was allowed to establish, through various exhibits seized during searches of Aegis’s office, Vallone’s home, Dunn’s office, and the offices of certain accountants not charged in this case, that the defendants had notice that the Aegis trust system was not lawful and thus lacked a good faith belief in its legality. By contrast, the defendants argue, when they attempted to establish on cross-examination of the government’s witnesses that there was other evidence indicating that the defendants in fact harbored a subjective belief that the Aegis system was lawful, the court barred them from doing so. They posit that the government in effect was allowed to present a one-sided case as to their own subjective understanding of the tax laws. Our own review of the record convinces us that although the district court prohibited certain questions and the introduction, during the government’s case, of exhibits that the defendants believed were favorable to them, it by no means precluded the defendants from presenting a Cheek defense. In virtually all of the cited instances in which the defendants complain that they were not allowed to ask particular questions of a government witness, the court appears to have sustained government objections not on the ground that the questions were not relevant and permissible with respect to the Cheek defense, but on the basis of some wholly independent, and valid, ground. For example, while cross-examining Revenue Agent Paul Ponzo as to why, in calculating the income that a defendant had earned but failed to report, the agent had disallowed reliance on an asset management trust to reduce the defendant’s income, Bartoli’s counsel sought to question Ponzo about a particular revenue ruling (No. 75-258) and the *455 circumstances under which a business trust might be lawful as opposed to a sham. R. 971, Tr. 4581-86. But the government had called Ponzo not to offer expert testimony as to the meaning of a particular revenue ruling or why the Aegis trust system violated the law, but solely to establish what income taxes three of the defendants (Hopper, Cover, and Dowd) would have owed had they properly reported their income. So it was perfectly reasonable to sustain the objections Bartoli’s attorney was attempting to pose. When comparable questions were posed of Agent Priess, who in his undercover capacity helped expose the Aegis fraud, they too were properly sustained because that agent had been called as a fact witness rather than an expert witness. See, e.g., R. 966 Tr. 678-88 (court precludes questions of agent about whether particular IRS regulations exist, but permits defense to inquire whether defendant Cover cited regulations to the agent); id. Tr. 712-14 (sustaining objection to question about what agent understood was meant by citation in Aegis trust package to Internal Revenue regulation). Nothing that the court said in sustaining these objections suggested that it would not allow questions legitimately aimed at establishing the defendants’ subjective understanding of the relevant tax laws at an appropriate time. As for the court’s unwillingness to allow the defense to introduce documents during the government’s case which supported their Cheek defense, this is explained by the court’s decision to confíne defense exhibits to the defense case. See, e.g., R. 947 Tr. 2106-08, 2113-17; R. 969 Tr. 3772-75; R. 935 Tr. 4086-89, 4222-29. As the defendants do not contend that they were prevented from introducing these exhibits in their own case, 4 the objection boils down to one of timing rather than of exclusion. This implicates the court’s discretion over the method and order of introducing evidence. Fed.R.Evid. 611(a); see, e.g., United States v. Smith, 26 F.3d 739, 744 (7th Cir.1994); see generally United States v. Wilson, 985 F.2d 348, 351 (7th Cir.1993) (district court has wide discretion in managing cross-examination and ruling on admissibility of evidence). The defendants have not actually addressed the merits of the district court’s preference for reserving defense exhibits to the defense case, nor have they shown how they were harmed by having to wait to bring those exhibits before the jury. See United States v. Hall, 165 F.3d 1095, 1117 (7th Cir.1999) (district court did not abuse discretion in refusing admission of defense photo during cross-examination of government witness, when defendant could have introduced photograph during his own case); United States v. Ellison, 557 F.2d 128, 135 (7th Cir.1977) (“even if we assume that the records would have been relevant rebuttal evidence if offered during the presentation of Ellison’s own case, we need not thereby conclude that the district court erred in excluding the evidence at the time it was offered” in the government’s case); United States v. Lambert, 580 F.2d 740, *456 747-48 & n. 7 (5th Cir.1978) (“Our review of the record, which discloses proffers of voluminous documentary evidence, leads us to the conclusion that the district judge properly controlled the flow of the trial under” Rule 611 by requiring defendant to introduce defense evidence during his own case). Next, the defendants complain that the district court improperly allowed the jury to construe notice to one defendant of the illegality of the Aegis trust system as notice to all of them. The government, as we have noted, relied on various documents— including adverse court rulings as to the legality of the Aegis system — that were found in the offices either of Aegis or one of its officers or employees (or their homes) to show that each of the defendants was aware that the Aegis trusts were not lawful means of tax avoidance and thus was willfully participating in a criminal tax evasion scheme. In a colloquy concerning the notice evidence that occurred fairly early on in the trial, the district court made the following remarks: THE COURT: What is it exactly that you want to say? MR. SCHINDLER: That this document is offered solely for the purpose of — that the defendants were on notice as of this date. MR. KOMIE: Some defendants. MR. SCHINDLER: Some defendants were on notice as of that date. MR. MECYZK: Otherwise I would object. THE COURT: Some defendants is not the issue, because if the conspiracy is on notice, the conspiracy has knowledge if these documents are found in the premises of the conspiracy. It is like finding the scales and the drug paraphernalia and the ledgers in the place that the conspirators congregate from time to time or place their materials. So now it goes to notice but also goes to that this was found in the premises. It is direct evidence in that sense. MR. SALTZMAN: Judge, if I may just add one thing. It’s my view that this is not like drug paraphernalia found which has only one purpose. These are documents that pertain to legal opinions that can be agreed with, disagreed with, and the fact that they’re found there doesn’t have the same significance, and there’s a knowledge issue. THE COURT: It’s not conclusive of the issue, of course not. But it’s evidence of knowledge, it is evidence of willfulness, it is evidence of notice. MR. SALTZMAN: Judge, with all due — in my view it’s not evidence of knowledge when it’s a few pages out of 1.2 million pages. R. 949 Tr. 2806-08 (emphasis ours). 5 The defendants read the district court’s remarks regarding notice to the conspiracy *457 as endorsing a theory that their individual willfulness could be inferred from evidence indicating that the conspiracy generally, or one member of the conspiracy, had knowledge that the Aegis trust system was unlawful. The court’s view, they reason, improperly relieved the government of its burden to show that each of them, individually, knew that the Aegis trust system was illegal and thus willfully participated in and promoted an illegal means of tax avoidance. Assuming that this was the court’s theory, any error in the court’s remarks was harmless, because the theory was not communicated to the jury. Certainly we agree that it would be error to instruct the jury that notice to one conspirator that his conduct is illegal — or notice to the conspiracy generally — is, in itself, notice to all members of the conspiracy sufficient to overcome everyone’s Cheek defense. See Jefferson v. United States, 340 F.2d 193, 197-98 (9th Cir.1965) (where statute required proof of defendant’s specific knowledge that drug was illegally imported, it was plain error to instruct jury that knowledge of any alleged co-conspirator was imputed to all members of conspiracy, thus permitting jury to impute one conspirator’s knowledge regarding illegal importation to his co-conspirators, without proof that other conspirators actually knew drug was imported illegally); see also Cheek, 498 U.S. at 202, 111 S.Ct. at 610 (“if the Government proves actual knowledge of the pertinent legal duty, the prosecution, without more, has satisfied the knowledge requirement of the wilfulness requirement”) (emphasis ours). But the jury in this case was never so instructed, nor does the record reveal that such a theory was otherwise communicated to the jury at any point in the trial — either by the court or by the government. The remarks on which the defendants rely were voiced outside the presence of the jury, and despite our invitation at oral argument, the defendants were not able to cite any instance in which comparable remarks were made in the jury’s presence. Certainly the government invited the jury to infer, from the various documents found in the possession of one or more of the defendants, that each defendant had actual knowledge that the Aegis trust system was not legal. It was entirely plausible for the government to urge that inference be drawn and for the jury to draw it, for the evidence showed that Aegis officers were actively tracking court decisions and legal opinions as to the validity of the Aegis trusts and had received unequivocal notice, from multiple sources and on multiple occasions, that the Aegis system was illegal. Evidence reflecting that notice was found in Aegis’s offices, for example. In Hills, we found comparable documentation discovered in the defendant’s office sufficient to support a finding of a defendant’s actual notice of the illegality of the Aegis trust system and her criminal willfulness, notwithstanding the absence of any direct evidence that she had seen these documents. 618 F.3d at 638. The plausibility of such an inference may have been all that the district court in this case meant to convey during the colloquy we have recounted above, as the court’s subsequent remarks suggest. See R. 916 Tr. 2666 (“[I]f your client [Hopper] or others say that they were not on notice [as to the ARDC proceedings], they can certainly make that claim.”); id. Tr. 2668 (“Whether your client [Dunn] was put on notice as a result of these [ARDC] proceedings is an issue for the jury to determine.”); R. 910 Tr. 6298 (“[I]f the government establishes that this ... was a seized document [from Aegis headquarters], it will be up to the jury to determine which one [of the defendants] or how many saw it. But in terms of the law itself, it is at least admissible as notice to the conspira *458 tors.”). In any case, the government never argued anything more than this sort of inference to the jury; on the contrary, its attorneys addressed notice, knowledge, and willfulness on an individualized basis in their closing arguments. See R. 923 Tr. 6808-24; R. 911 Tr. 6827-71. And certainly the court never advised the jury that it could deem all co-conspirators to have culpable knowledge of the illegality of the Aegis system if just one of them had such knowledge. Finally, the defendants object to the district court’s decision to admit evidence from the Illinois Attorney Registration and Disciplinary Commission proceeding that ultimately resulted in Bartoli’s disbarment in Illinois. The defendants hold up the ARDC evidence as a “glaring” example of the court’s willingness to permit the government to cite third-party documents as evidence that the defendants had notice of the illegality of the Aegis system, without proof that any defendant saw or knew about such documents. Defendants’ Joint Br. 53. In the defendant’s view, the admission of such evidence contravened Cheek’s mandate that the government prove that each defendant had actual knowledge that his conduct was illegal. The ARDC filed a complaint against Bartoli in 1996 based on his alleged misconduct in connection with both Heritage and Aegis. As amended, the complaint was based in part on trust packages that Bartoli had sold to (and prepared for) two couples: William and Mary DiSomma, who purchased a Heritage multi-trust system in March 1994 for $12,000, and Max and Linda Alumbaugh, who purchased an Aegis or Aegis-like CBO in August 1996 for $25,000. 6 The DiSommas were later told by an independent attorney that the trust system would not withstand scrutiny by the IRS and would not reduce their income tax liability as Bartoli had said it would, causing them to dissolve the trusts. Their request for a refund of the $12,000 they had paid to Heritage for the trust system was ignored. The Alumbaughs were audited by the IRS and informed that the CBO would not achieve the tax benefits that Bartoli had told them it would; they then dissolved the CBO. The ARDC’s complaint alleged, inter alia, that Bartoli had represented clients when the representation might be limited by his responsibility to his own interests; that he had engaged in conduct involving dishonesty, deceit, or misrepresentation; that he had engaged in the unauthorized practice of law following his transfer to inactive status in 1995; and that he had engaged in conduct that was prejudicial to the administration of justice. As we have noted Bartoli, Hopper, and Vallone were deposed in the course of the ARDC proceeding. A three member Hearing Board conducted an evidentiary hearing on the complaint in July and August 1999. Bartoli was represented by counsel during the hearing, but he did not appear in person at the hearing. He did participate by telephone during some portions of the hearing. Among the witnesses whose testimony was presented to the Hearing Board was William Marutzky, a certified public accountant and attorney with a background in both trusts and taxa *459 tion. Essentially, Marutzky opined that the trusts purveyed by Heritage and Athens were not effective means of income and estate tax minimization: he concluded that the system purchased by the DiSommas would be disregarded in an IRS audit, and that the CBO purchased by the Alumbaughs provided no value whatsoever to them. On February 17, 2000, the Hearing Board filed a Report and Recommendation proposing that Bartoli be disbarred. After summarizing the evidence, the Hearing Board set forth a series of findings. The Hearing Board found, inter alia, that Bartoli had labored under a conflict of interest in representing both Heritage (which was interested in selling as many trust packages as possible, and which paid Bartoli for each trust he prepared) and Heritage members (i.e., clients like the DiSommas), who were relying on Bartoli’s judgment and advice as a lawyer that a trust was appropriate for their needs. Report & Recommendation at 54-55, available atwww.iardc.org. Bartoli labored under a similar conflict of interest when he sold the CBO to the Alumbaughs on behalf of Athens. Id. at 72-73. It found further that Bartoli’s conduct was prejudicial to the administration of justice in that he had “created a situation where his professional judgment could have been clouded by the business interests of others and his own interests.” Id. at 56, 69-70. It also found that Bartoli had misrepresented the benefits of the trust system to the DiSommas and the benefits of the CBO to the Alumbaughs. Id. at 61-69, 74, 78. On December 27, 2001, a Review Board rejected Bartoli’s challenge to the Hearing Board’s Report and Recommendation and affirmed the Hearing Board’s findings and sustained .the recommendation that Bartoli be disbarred. The Illinois Supreme Court ordered Bartoli disbarred on May 24, 2002. Mary Robinson, who was the Administrator of the ARDC throughout the time period during which the proceeding against Bartoli was pending and who participated in the evidentiary hearing before the Hearing Board, testified as a witness for the government in this case. Robinson identified a variety of documents connected with the ARDC proceeding which the court admitted into evidence over the defendants’ objections, including the ARDC’s complaint against Bartoli, the Hearing Board’s Report and Recommendation, and the Review Board’s own Report and Recommendation. She also read various excerpts from these documents, including portions of the Review Board’s summary of Marutzky’s testimony. 7 These included Marutzky’s testimony (as summarized by the Hearing Board) that (a) the trust documents that Bartoli provided to clients would not reduce significantly the clients’ income tax liability as had been promised to them; (b) the tax laws would not permit the client to assign his future income to a trust; (c) nor would they permit the client to deduct the expenses incurred for his own housing and to educate his children; and (d) in an audit, the IRS would disregard the sort of trusts that Bartoli was providing to clients pursuant to the Tax Court’s decision in Muhich, which involved a trust system that had been created by Bartoli and Heritage. The Hearing Board had relied on Marutzky’s testimony in concluding that the trusts that Bartoli had sold to the DiSommas and the Alumbaughs were ineffective as a means of substantially reducing their income tax liability, and that Bartoli, in creating the trusts and *460 promoting them to his clients, had engaged in conduct involving dishonesty, deceit, and misrepresentation that was prejudicial to the administration of justice. Robinson also read excerpts from other testimony and evidence presented during the ARDC proceeding, but it is the excerpts from the Hearing Board’s summary of Marutzky’s testimony to which the defendants have given particular emphasis. The district court admitted the ARDC documents, and permitted Robinson to read excerpts from them during her testimony, for the purpose of showing that the ARDC proceeding against Bartoli placed him and other defendants on notice that the Aegis trust system was not a legitimate means of tax avoidance; and we conclude that the district court did not abuse its discretion in so ruling. The ARDC proceeding was relevant because it represented a direct challenge to the legitimacy of the Aegis CBO and its predecessor, the Heritage trust. See supra at 458 n.6. The Hearing Board’s reasoning in finding Bartoli guilty of misconduct, including the aspects of Marutzky’s testimony that it relied upon, was particularly probative in that it illustrated the ways in which the CBO system as promoted by Bartoli was irreconcilable with basic trust and tax principles. Bartoli himself was the respondent in the ARDC proceeding, was given notice of the proceeding and its outcome, and was represented by counsel throughout the proceeding. It is an entirely plausible and permissible inference that he was aware of the proceeding and what occurred in that proceeding despite the fact that he did not appear in person before the Hearing Board. Indeed, although Bartoli had assumed inactive status with the Illinois bar by the time the ARDC filed the complaint in 1996, Bartoli had an incentive to both monitor the proceeding and to deny the ARDC’s allegations, as the complaint called into question the legitimacy of the trust system promoted by Aegis, with which Bartoli remained involved long after the ARDC filed its complaint in 1996. See supra at 458 n.6. His co-defendants had similar reasons to be interested in the outcome of the proceeding, and there were multiple indicia that they were, in fact, aware of and following the proceeding. Hopper and Vallone, as we have noted, were both deposed in the course of the proceeding, and Robinson recalled that she also took a statement from Dunn. Bartoli, Vallone, Hopper, and Dunn were also plaintiffs in the May 1997 suit filed against the ARDC, Robinson, and others alleging that the ARDC was violating Bartoli’s First Amendment and due process rights and was conspiring to deprive all four plaintiffs of their Fourteenth Amendment liberty interest in their business reputation. To say the least, that suit displays an interest in the outcome of the ARDC proceeding. Moreover, a copy of Marutzky’s testimony was found in the Aegis office along with Hopper’s critique of the testimony. Several volumes of additional ARDC documents were also found in Aegis’s office. Similar documents were found in Dunn’s office as well. The district court advised the jury that the ARDC evidence was admitted solely for notice purposes, R. 916 Tr. 2673, and the jury was obviously free to give the evidence what weight it deemed appropriate as to the state of mind of each defendant. Indeed, the court noted that the defendants were free to question Robinson in an effort to show that they were not necessarily aware of the ARDC proceeding, and they exercised that prerogative: Bartoli’s counsel established on cross-examination of Robinson that he was not present before the Hearing Board, R. 916 Tr. 2727; and Dunn’s counsel established that only Bartoli, as the sole named respondent, would have been given formal *461 notice of what occurred during the ARDC proceeding, R. 916, Tr. 2757, 2764, 2769-70. In our view, however, given the multiple indicia that Bartoli, Vallone, Hopper, and Dunn were following the proceeding, this was highly probative evidence that these four defendants, if not all six, had reason to know as a result of the ARDC’s actions that the Aegis trust system was illegitimate. C. Count One Count One of the superseding indictment charged that the defendants violated 18 U.S.C. § 371 by conspiring to (a) defraud the United States by impeding, impairing, obstructing and defeating the lawful government functions of the IRS of the Department of the Treasury, an agency of the United States, in the ascertainment, computation, assessment, and collection of revenues, namely income taxes; and (b) commit offenses against the United States, namely: to willfully aid and assist in, and procure, counsel, and advise the preparation and presentation, to the IRS, of returns and claims on behalf of others which were fraudulent and false as to various matters, in violation of Title 26, United States Code, Section 7206(2). R. 103 ¶ 2. The defendants moved to dismiss this count as duplicitous, reasoning that it alleged two distinct conspiracies and therefore two different crimes; but the district court denied the motion. The defendants contend that this was error, renewing their contention that Count One on its faces alleges two different crimes. We review the district court’s ruling on this point de novo. E.g., United States v. Pansier, 576 F.3d 726, 734 (7th Cir.2009). We agree with the district court that Count One is not duplicitous. A duplicitous charge is not one that simply alleges a single offense committed by multiple means, e.g., United States v. Cephus, 684 F.3d 703, 706 (7th Cir.2012); United States v. Davis, 471 F.3d 783, 790 (7th Cir.2006), but rather one that joins two or more distinct crimes in a single count, e.g., United States v. Starks, 472 F.3d 466, 470-71 (7th Cir.2006); see also Worthington v. United States, 64 F.2d 936, 938-39 (7th Cir.1933). Count One does not allege two different crimes. Instead, it alleges a conspiracy with two goals — (1) to defraud the United States by impeding the IRS’s efforts to collect income taxes, and (2) to commit tax offenses, namely the preparation of fraudulent tax returns. Such a charge is permissible. As the Supreme Court explained in Braverman v. United States, 317 U.S. 49, 54, 63 S.Ct. 99, 102, 87 L.Ed. 23 (1942), “A conspiracy is not the commission of the crime which it contemplates, and neither violates nor ‘arises under’ the statute whose violation is its object____The single agreement is the prohibited conspiracy, and however diverse its objects it violates but a single statute.” Following that reasoning, this court concluded in United States v. Hughes, 310 F.3d 557, 560-61 (7th Cir.2002), that a charge alleging a conspiracy with two illicit objectives was not duplicitous. See also United States v. Bradfield, 376 Fed.Appx. 620, 623-24 (7th Cir.2010) (non-precedential decision) (same). We see no reason to depart from our holding in Hughes here. As the defendants point out, both objects of the conspiracy charged in Hughes fell under the offense prong of section 371 (i.e., conspiring to commit an offense against the United States), whereas in this ease the charged conspiracy implicates both prongs of the statute (i.e., conspiring to defraud the United States as well as to commit an offense against it). But that distinction does not address Braverman’s essential *462 point that it is the illicit agreement that constitutes the crime of conspiracy rather than the substantive crime or crimes contemplated by that agreement. We acknowledge that there is some division of authority on this point, as summarized by the Third Circuit’s decision in United States v. Rigas, 605 F.3d 194, 210-12 (3d Cir.2010) (en banc). However, we believe the better reasoned view is the one adopted by the Rigas majority, which viewed a charge akin to the one in this case as setting forth one conspiracy with multiple goals rather than two distinct crimes. Id. (Rigas addressed the issue in the context of a double jeopardy claim rather than one of duplicity, but that distinction is immaterial in terms of whether the charge alleges one or two crimes.) The Rigas majority opinion is consistent with our own reasoning in Hughes. Finally, the principal vice of duplicity, as we noted in Hughes, is that it presents the possibility that jury members, although agreeing that there was a conspiracy, might not be unanimous as to what the object of the conspiracy was. 310 F.3d at 561; see also Cephus, 684 F.3d at 706; Starks, 472 F.3d at 471. But the district court instructed the jury in this case that it must unanimously agree on at least one of the alleged objectives of the conspiracy. R. 925 at 7375. That takes care of the jury unanimity concern, as Hughes and Starks acknowledge. Hughes, 310 F.3d at 561; Starks, 472 F.3d at 471. There are other concerns potentially implicated by duplicity, including notice to the defendants. Cephus, 684 F.3d at 706. But no such concerns are raised here. D. Jury Instructions The defendants object to certain jury instructions given at the request of the government and to the court’s refusal to give certain instructions that the defendants themselves proposed. They also argue more generally that the instructions as given favored the government, unduly prejudiced the defense, and exemplify the court’s purported bias against the defendants, which we take up in the next section of this opinion. To the extent a particular jury instruction presents a legal question — for example, whether it accurately states the law — our review is de novo. E.g., United States v. Tanner, 628 F.3d 890, 904 (7th Cir.2010) (citing United States v. DiSantis, 565 F.3d 354, 359 (7th Cir.2009)), cert. denied, — U.S. -, 132 S.Ct. 204, 181 L.Ed.2d 109 (2011). Beyond that, we review the district court’s decision whether or not to give a particular instruction for abuse of discretion. Id. (citing United States v. Wilson, 134 F.3d 855, 868 (7th Cir.1998)). We will reverse a conviction only if the instructions, as a whole, so misled the jury on the relevant principles as to have prejudiced the defendant. E.g., United States v. Quintero, 618 F.3d 746, 753 (7th Cir.2010). For the reasons set forth below, we conclude that the jury instructions as a whole accurately summarized the law and did not interfere with the defendants’ ability to pursue their Cheek defense, and that the district court did not abuse its discretion either in giving a challenged instruction proposed by the government or in refusing an instruction proposed by the defense. 1. Instruction 27A: Income Assigned to Sham Trusts Instruction 27A gave the jury an overview of how income is assigned for tax purposes as between legal entities such as trusts and corporations and the individuals behind these entities and, in particular, the circumstances under which a trust will be disregarded for federal tax purposes. Among other points, the instruction advised the jury that: *463 • “[t]ax consequences flow from the substance rather than the form of a transaction, and control over property, rather than documentary title, marks the real owner for federal tax purposes”; • income is typically attributed to the person who exercises dominion and control over that income and its sources; • ordinarily, the Tax Code will tax a legal entity like a trust separately from its owner; but • when a trust lacks economic substance or functions as the alter ego of the individual taxpayer for the purpose of evading his tax liability, federal tax law will assign the tax burden to the individual rather than the trust. R. 925 Tr. 7379-80. The defendants argue that this instruction was both unnecessary, in that the court had barred the defense from arguing that the Aegis trust system was legal, and prejudicial, in that (as the defendants read the instruction) it effectively precluded them from showing that they had a good faith belief in the legality of the Aegis trust system. “Having prevented the Defendants from presenting their belief in the legality of the system, the court’s instruction now invited the jury to convict if it found [the system] unlawful.” Defendants’ Joint Br. 62. Cf. United States v. McKnight, 671 F.3d 664, 665 (7th Cir.) (Posner, J., dissenting from denial of rehearing en banc) (“[Gratuitous] instructions are apt to confuse jurors, and when as in this case they are proposed by a party rather than given on the initiative of the trial judge, they may be intended to confuse, and in the present case to undermine the efficacy of an instruction desired by the opposing party and given by the judge.”), cert. denied, — U.S. -, 132 S.Ct. 2756, 183 L.Ed.2d 626 (2012); United States v. Hill, 252 F.3d 919, 923 (7th Cir.2001) (“Unless it is necessary to give an instruction, it is necessary not to give it, so that the important instructions stand out and are remembered.”). We find no abuse of discretion in the district court’s decision to give this instruction. The defendants implicitly concede that it was an accurate statement of the law. In order to assess the validity of the defendants’ Cheek defense, and to determine whether the defendants had indeed willfully engaged in a scheme to defraud the government of its tax revenues, the jury had to understand the basic legal principles that the IRS had relied on in deeming the Aegis trusts a sham. Only then could the jury evaluate the plausibility of the defendants’ contention that they had a good faith belief in the legitimacy of the trusts notwithstanding these principles, as well as the plausibility of the government’s contrary contention that the defendants must, in fact, have realized that the Aegis system was illegitimate. The principles of tax and trust law are unfamiliar to most jurors; and the district court could reasonably have concluded that it was both reasonable and necessary to apprise the jury of the basic principles included in instruction 27A. We reject the notion that this instruction somehow impeded, let alone precluded, a Cheek defense. The instruction said nothing which would prevent the defendants from claiming that they did not realize the Aegis trusts were an illegal means of tax avoidance; in fact, the instruction said nothing at all about the legality of the Aegis trust system. The defendants were free to, and did, argue that the Aegis trusts were structured so as to comply with the law and to make it plausible for them to believe in good faith that the trusts were a legitimate means of tax avoidance. There was, at the same time, a wealth of evidence supporting the jury’s *464 conclusion that the defendants were, in fact, aware that the Aegis trust system was illegitimate. It was that evidence that doomed the defendants’ Cheek defense, not this instruction. 2. Rejected Defense Instruction Regarding IRS Notice 97-24. Although it did not cite the Aegis trust by name, IRS Notice 97-24, issued in April 1997, expressed the opinion of the IRS that trusts akin to the Aegis trusts were an unlawful means of tax avoidance. As we noted in our summary of the facts, there was evidence that the defendants were very much aware of this IRS notice, and the government, of course, cited the notice as one piece of evidence that the defendants knew the Aegis system was illegal. The defendants proposed an instruction that would have advised the jury on the relative legal weight of IRS regulations, revenue rulings, letter rulings, and public notices, the last of which “have no force of law.” R. 528 at 2; R. 940 Tr. 6770-72. The district court declined to give the instruction. Without such an instruction, the defendants argue, the jury was left with the impression that IRS Notice 97-24 was an authoritative statement of the law, and that mistaken impression undermined the defendants’ contention that they genuinely believed that the Aegis trusts were a permissible means of tax avoidance. Because reasonable minds might differ as to the propriety of this instruction, we find no abuse of discretion in the district court’s refusal to give it. The government does not quarrel with the legal accuracy of the proposed instruction, and one might argue that given the government’s reliance on Notice 97-24 as proof that the defendants knew that the Aegis system was unlawful, it would be appropriate to inform the jury that the Notice was not an authoritative statement of the law. On the other hand, we are pointed to no evidence that the government ever suggested that it was authoritative; and an IRS agent accurately testified before the jury that the Notice “expresses the IRS’s opinion of the law.” R. 971 Tr. 4580-81. Even if we were persuaded that it was an abuse of discretion for the court not to give this instruction, any error in refusing to give it was harmless, given the overwhelming evidence showing that the defendants appreciated the illegality of their conduct. 3. Pinkerton Instruction The district court properly instructed the jury, consistent with Seventh Circuit Pattern Criminal Jury Instruction 5.09, that if it found a defendant guilty of the conspiracy charged in Count One of the indictment, it could hold that defendant accountable for any criminal act foreseeably committed by a co-conspirator in furtherance of the conspiracy, including in particular the substantive criminal acts alleged in Counts 2 through 34 of the superseding indictment. R. 925 Tr. 7381; see generally Pinkerton v. United States, 328 U.S. 640, 647-48, 66 S.Ct. 1180, 1184, 90 L.Ed. 1489 (1946). The defendants suggest that this instruction “removed the intent to defraud and Cheek issues from the jury’s consideration once it determined that the Count [One] conspiracy had been proven and that each defendant had been a member of the conspiracy,” and “effectively eviscerated the government’s burden of proving that defendants lacked a good faith belief that the Aegis system was lawful and that they had the intent to defraud .... ” Defendants’ Joint Br. 65. This particular contention was not made below, see R. 936 Tr. 6008-09, so our review is solely for plain error, Fed.R.Crim.P. 30(d), 52(b); e.g., United States v. Johnson, 655 *465 F.3d 594, 605 (7th Cir.2011), and we find no such error in the giving of this instruction. The instruction was an accurate statement of the law, and by no means did it “eviscerate” the government’s burden with respect to the Cheek defense. As the government points out, the instructions with respect to Count One required a finding of intent to defraud as to the first prong of section 371 and willfulness as to the second prong. R. 925 at 7375-77. Thus, neither the intent to defraud nor the Cheek defense was removed from the jury’s consideration: before convicting a defendant on the conspiracy count, the jury would necessarily have to find that a defendant harbored an intent to defraud and/or lacked a good faith belief in the Aegis trust system’s legality, and either finding is irreconcilable with the defendants’ contention that they understood the Aegis system of trusts to be a legitimate means of tax minimization. 4. Conscious Avoidance Instruction At the government’s request, and over the strong objections of the defendants, the court gave the jury an instruction on the conscious avoidance of knowledge (also referred to colloquially as the “ostrich” instruction), which advised the jury that it could infer a defendant’s culpable knowledge from a combination of suspicion and indifference to the truth. See Seventh Circuit Pattern Criminal Jury Instruction No. 4.06 ¶ 2. The conscious avoidance instruction serves to alert the jury that “a person may not escape criminal liability by pleading ignorance if he knows or strongly suspects that he is involved in criminal dealings but deliberately avoids learning more exact information about the nature or extent of those dealings.” United States v. Green, 648 F.3d 569, 582 (7th Cir.2011). However, because this instruction poses a risk that a jury might improperly convict a defendant on the basis that he should have known that he was participating in wrongdoing, rather than on the basis of his actual knowledge, United States v. Tanner, supra, 628 F.3d at 904-OS, the instruction “is to be given ‘cautiously’ and only for ‘narrow’ uses,” United States v. Malewicka, 664 F.3d 1099, 1108 (7th Cir.2011) (quoting United States v. Ciesiolka, 614 F.3d 347, 352-53 (7th Cir.2010)). Specifically, the instruction should only be given in cases “where (1) a defendant claims to lack guilty knowledge, i.e., knowledge of her conduct’s illegality, and (2) the government presents evidence from which a jury could conclude that the defendant deliberately avoided the truth.” Green, 648 F.3d at 582 (quoting United States v. Garcia, 580 F.3d 528, 537 (7th Cir.2009)). As an example of the willful blindness that it believed warranted the instruction in this case, the government cited to the district court attorney Parker’s testimony as to why he had remained involved with Aegis despite his own doubts about the Aegis system. R. 1020 Tr. 5966-67. Parker had acknowledged on redirect examination by the government that during the period of his involvement with Aegis from 1997 through 2000, he had harbored suspicions that the Aegis system was not legitimate and yet had pushed his doubts aside for fear of what he might learn if he looked more closely at the state of the law. R. 914 at 2272. He reiterated this point on re-cross examination by the defense. When asked whether the promotional materials distributed at Aegis seminars (at which Parker had spoken for two years) did not contain a wealth of citations to legal authorities indicating that the trusts were, in fact, legal, Parker answered, “I put my head in the sand. I put my fingers in my ears.” Id. at 2282. The government said that Parker’s testimony was just *466 as true of the defendants who were on trial. R. 1020 at 5967. For its part, the district court, in agreeing to give the instruction, cited Vallone’s testimony regarding what he did and did not do in ascertaining the legality of the Aegis system as suggestive of deliberate indifference. R. 1020 Tr. 5968. The defendants contend that the evidence did not warrant such an instruction, because (a) however willfully blind Parker may have been to the legal flaws in the Aegis system, he was not on trial and it was thus improper to attribute his own conscious avoidance to the six defendants who were on trial; and (b) Vallone’s testimony, rather than supporting an inference of deliberate indifference, actually reveals the “zealous care” that he took to keep himself apprised of the state of the law and to confirm that the Aegis trust system complied with the law. Defendants’ Joint Br. 67-68. The district court did not err in giving this instruction. As we have noted, a conscious avoidance instruction is appropriate when the defendant claims not to have known that what he was doing was illegal and there is, at the same time, evidence supporting an inference that the defendant closed his eyes to the illegality of his conduct. Green, supra, 648 F.3d at 582. It was a fair inference, to say the least, that the defendants in this case had deliberately blinded themselves to the variety of warnings they had received as to the ¿¿legality of the Aegis system. Parker’s testimony was relevant on this point, despite his status as a witness for the government, in that he was intimately involved in the promotion of the Aegis system and yet conceded, in retrospect, that he had essentially turned his head away from the multiple clues (and his own suspicion) that the system was illegal. And notwithstanding Vallone’s self-serving testimony that he was diligent in following and responding to the legal developments relevant to the Aegis trusts, the jury nonetheless could infer that he, like Parker, had really been burying his head in the sand. Take the following incident described by Parker. Parker testified that in the summer of 1999, following the Tax Court’s decision in Muhich, there was a meeting at Aegis headquarters, in Vallone’s office. In addition to Vallone and Parker, Dunn and Hopper were present, and Bartoli participated by telephone. In the course of that meeting, Bartoli reported that he was attempting to get an opinion from an Atlanta law firm as to the legality of the Aegis system. According to Parker, Vallone was critical of that idea, both because it was likely to be costly and because “there’s no guarantee as to what the result of that opinion would be, whether it would be a favorable opinion or a nonfavorable opinion or a neutral opinion.” R. 913 Tr. 1954. Parker chimed in that the IRS had a more economical process through which one could seek an opinion ruling. Id. Vallone, according to Parker, rejected that idea as “ridiculous” id., “because we know what the answer will be and, therefore, why bother?” id. Thereafter, Parker was asked to leave the room. Dunn later told him that the group had discussed the Audit Arsenal as a means to fend off looming IRS audits of Aegis clients. Id. Tr. 1955— 56. One can readily infer from Parker’s description of this meeting that the Aegis principals were deliberately avoiding any independent advice as to the legality of the Aegis trusts, realizing that the advice was likely to be that the trusts were an ineffective means of tax avoidance. The defendants were given many warning signs to that effect over the life of the charged conspiracy, from the ARDC complaint *467 against Bartoli to the Tax Court’s decision in Muhich to Judge Plunkett’s sanctions decision, and yet they continued promoting the Aegis system, opting to pursue obstructive tactics like the Audit Arsenal rather than seeking out an independent legal opinion as to the validity of that system. We note that the Third Circuit’s decision in United States v. Stadtmauer, 620 F.3d 238 (3d Cir.2010), sustained the giving of a conscious avoidance instruction based on the defendant’s willful blindness to the legality of various deductions fraudulently claimed on the tax returns that had been filed on behalf of the limited partnerships that the defendant helped manage. (The defendant was charged, inter alia, with aiding and abetting these false or fraudulent tax returns, in violation of 26 U.S.C. § 7206(2).) The court rejected the argument that such an instruction, to the extent it applies to the defendant’s knowledge of the law, is irreconcilable with the good-faith defense endorsed by Cheek. The justification for the Cheek defense, the court explained, is that given the complexity of the tax system, one may in good faith err despite genuine efforts to ascertain and comply with the law. However, “[b]y definition, one who intentionally avoids learning of his tax obligations is not a taxpayer who ‘earnestly wish[es] to follow the law,’ or fails to do so as a result of an ‘innocent error[] made despite the exercise of reasonable care.’ ” 620 F.3d at 256 (quoting Cheek, 498 U.S. at 205, 111 S.Ct. at 612) (emphasis in Stadtmauer). “Rather, a person who deliberately evades learning his legal duties has a subjectively culpable state of mind that goes beyond mere negligence, a good faith misunderstanding, or even recklessness.” Id. As support for giving a willful blindness instruction, the court cited, among other authorities, our own decision in United States v. Hauert, 40 F.3d 197, 203 & n. 7 (7th Cir.1994), which affirmed the propriety of such an instruction in a tax-protester case. 620 F.3d at 256 n. 21. The circumstances supporting the instruction here were at least as compelling, if not more so, than in those cases. 5. Caution and Great Care Instruction The defendants object to a standard instruction admonishing the jury to consider the testimony of David Jenkins, a witness who was granted immunity from prosecution by the government, “with caution and great care.” R. 925 Tr. 7369; Seventh Cir. Pattern Criminal Jury Instruction No. 3.13. Jenkins, of course, testified on behalf of the government. But because the defendants found certain aspects of Jenkins’ testimony to be helpful to their cause, and because the district judge himself voiced skepticism as to certain aspects of Jenkins’ testimony (more on this below), the defendants believe that this instruction all but invited the jury to discredit Jenkins’ testimony, including the portions that were favorable to the defense. We see no error in giving the instruction, however. Jenkins was the government’s witness, and as such the admonishment to consider his testimony with caution and great care applied to those portions of his testimony that helped the government as well as those that were helpful to the defense. Nothing in the instruction suggested to the jury that it should weigh his testimony in any particular way, but rather that it evaluate his testimony carefully. The instruction was unexceptional and could not have unduly prejudiced the defense. 6. The Cheek Instruction and the Conspiracy Instructions The defendants make a wholly undeveloped, two sentence argument which appears to suggest that the district court’s *468 instructions as to the conspiracy charge undercut the pattern instruction on their Cheek defense. The argument is so cursorily made as to be waived. E.g., United States v. Thornton, 642 F.3d 599, 606 (7th Cir.2011). We do take the opportunity to reiterate that the conspiracy instructions did require the jury to find that the defendants harbored an intent to defraud and/or willfulness, and so in no way precluded or undercut the defense contention under Cheek that they genuinely, if mistakenly, believed that the Aegis trust system was lawful. E. Judicial Bias A defendant has a fundamental right to a fair trial in a fair tribunal, Bracy v. Gramley, 520 U.S. 899, 904-05, 117 S.Ct. 1793, 1797, 138 L.Ed.2d 97 (1997) (quoting Withrow v. Larkin, 421 U.S. 35, 46, 95 S.Ct. 1456, 1464, 43 L.Ed.2d 712 (1975)), and that fairness requires absence of actual bias or prejudice on the part of the judge, In re Murchison, 349 U.S. 133, 136, 75 S.Ct. 623, 625, 99 L.Ed. 942 (1955). However, impartiality does not imply passivity: “[fludges ... are not wallflowers or potted plants.” Tagatz v. Marquette Univ., 861 F.2d 1040, 1045 (7th Cir.1988). A judge may question and even challenge an attorney, witness, or evidence without being said to have abandoned his constitutionally mandated impartiality. See, e.g., United States v. McCray, 437 F.3d 639, 643 (7th Cir.2006) (“A district judge is free to interject during direct or cross-examination to clarify an issue, to require an attorney to lay a foundation, or to encourage an examining attorney to get to the point.”) (quoting United States v. Washington, 417 F.3d 780, 784 (7th Cir.2005)); Dugan v. R.J. Coman R.R. Co., 344 F.3d 662, 669-70 (7th Cir.2003) (exclusion of evidence that was not objected to but which judge found unreliable); United States v. Mohammad, 53 F.3d 1426, 1434 (7th Cir.1995) (criticizing trial counsel), overruled on other grounds by United States v. Sawyer, 521 F.3d 792 (7th Cir.2008); United States v. Jackson, 983 F.2d 757, 762 (7th Cir.1993) (same). But, a “judge who is so hostile to a lawyer as to doom the client to defeat deprives the client of the right to an impartial tribunal.” Walberg v. Israel, 766 F.2d 1071, 1077 (7th Cir.1985). “Even when the biased judge neither is the trier of fact nor is shown to have conveyed his bias to the jury that is the trier of fact, there can be a violation of due process which requires a reversal of the conviction.” Id. at 1076. The defendants suggest that the trial judge, in a variety of situations and in a variety of ways, exhibited a bias against the defense that deprived them of a fair trial. For the most part, their claim is not that the court by its conduct communicated a disbelief of or skepticism toward the defense to the jury, e.g., United States v. Barnhart, 599 F.3d 737, 742 (7th Cir.2010), but rather that the judge was actually biased against the defense, see 28 U.S.C. § 455(b)(1). Actual bias requires evidence that the judge was burdened by a conflict of interest or had some personal stake in the proceeding sufficient to cause a reasonable person to believe that the judge was incapable of ruling fairly, and thus to demand that we set aside the usual presumption that the judge has properly discharged his duties. See Liteky v. United States, 510 U.S. 540, 555, 114 S.Ct. 1147, 1157, 127 L.Ed.2d 474 (1994); United States v. Diekemper, 604 F.3d 345, 352 (7th Cir.2010) Collins v. Illinois, 554 F.3d 693, 697 (7th Cir.2009); Harrison v. McBride, 428 F.3d 652, 668 (7th Cir.2005). Actual bias, when shown, is the sort of structural defect that defies harmless-error inquiry and compels reversal regardless of how strong the government’s case against the defendant was or whether the *469 defendant is able to demonstrate’that the bias manifested itself in rulings that actually prejudiced him. Arizona v. Fulminante, 499 U.S. 279, 309, 111 S.Ct. 1246, 1265, 113 L.Ed.2d 302 (1991); Bracy v. Schomig, 286 F.3d 406, 414 (7th Cir.2002) (en banc); Cartalino v. Washington, 122 F.3d 8, 9-10 (7th Cir.1997). However, mere “expressions of impatience, dissatisfaction, annoyance, and even anger that are within the bounds of what imperfect men and women, even after having been confirmed as federal judges, sometimes display,” do not by themselves suffice to show actual bias. Liteky, 510 U.S. at 555-56, 114 S.Ct. at 1157; see also United States v. Twomey, 806 F.2d 1136, 1140 (1st Cir.1986) (citing Offutt v. United States, 348 U.S. 11, 12, 75 S.Ct. 11, 12, 99 L.Ed. 11 (1954)). We proceed to consider each of the actions that the defendants cite as illustrative of the district judge’s bias against them. For the reasons we articulate below, we discern no proof of actual bias on the part of the judge. Furthermore, the defendants have not shown that anything the court did in the course of the trial conveyed any prejudice against the defense to the jury or otherwise deprived the defendants of a fair trial. Appointment of substitute counsel when Vallone’s counsel fell ill. On a morning relatively early in the trial, Vallone’s counsel, Richard McLeese, informed the court by telephone that he was ill with flu-like symptoms and could not participate in the trial that day. Vallone informed the court that Parker, the witness testifying on behalf of the government at that time, was an important witness and that he wanted his attorney present for his testimony rather than relying on another defendant’s counsel or a temporary replacement from the federal defender program, two possibilities that the court had suggested. The court recessed the trial for a day, but when court reconvened the next day, McLeese, who was still under the weather, was again absent. The court reported that he had left the “lamest message one can imagine receiving in terms of illness.” R. 1014 Tr. 1865. Vallone again indicated to the court that he did not wish to proceed in the absence of his attorney. Unwilling to delay the trial any longer, the court, over the vigorous objections of all parties, appointed an attorney from the federal defender’s office — who himself objected, noting that he had no familiarity with the case — to stand in for McLeese as Vallone’s counsel. The court indicated that it would reserve Vallone’s cross-examination of Parker until McLeese returned. The jury was then summoned into the courtroom, and the trial resumed with the continuation of the government’s direct examination of Parker. After Parker had given testimony spanning approximately forty pages of the trial transcript, the jury was excused when two senior members of the U.S. Attorney’s office appeared in the courtroom. The deputy chief of the criminal division expressed the government’s “serious concern” about the court’s decision to proceed in the absence of competent, prepared counsel or a clear waiver from Vallone. Id. Tr. 1908. The court, although still concerned with the pace and length of the trial and the uncertainty as to when McLeese would be well enough to resume work, nonetheless agreed to recess the trial. When the trial resumed the following week with all counsel present, the court offered to have the government re-question Parker on the matters to which he had testified in McLeese’s absence. But McLeese declined the offer. “I have reviewed the transcript of the proceedings that I missed, and I don’t see any need to repeat that testimony.”. R. 913 Tr. 1921. The court then specifically, inquired and confirmed that both Vallone *470 and his attorney wished to waive the option of striking and re-presenting the testimony that Parker had given in McLeese’s absence. Id. Tr. 1921-24. We discern no evidence of bias in the course of action that the court pursued and no prejudice to the defense. The court was understandably and legitimately concerned about the prospect of an open-ended delay in a lengthy trial with a jury already empaneled. Nonetheless, Parker was a key government witness whose testimony substantially incriminated Vallone. Vallone was entitled to representation by an attorney who was knowledgeable about the case and prepared to observe and respond appropriately to Parker’s testimony. All parties agree, as they did below, that the court erred in deciding to proceed in the absence of appropriate representation for Vallone. For present purposes, we may take it as a given that the court’s decision to go forward was mistaken. Still, we see no way in which the decision reflected a bias against Val-lone in particular or the defendants generally as opposed to a legitimate concern about delaying the trial and inconveniencing the jury. Moreover, the extent of the testimony that Parker gave in McLeese’s absence was relatively minimal. McLeese had the opportunity to review the transcript of Parker’s testimony before the trial resumed, and both he and Vallone waived the opportunity to have Parker repeat that portion of his testimony. Val-lone makes no argument that he was, in the end, concretely prejudiced by what occurred in his counsel’s absence; and, indeed, other than as an example of the court’s purported bias, Vallone has not raised this as a stand-alone error that demands a new trial. Within the overall context of a lengthy trial, this was a discrete and ultimately harmless error. Harsh interrogation when Val-lone moved to dismiss indictment on speedy trial grounds. The defendants next cite as evidence of the district court’s bias its reaction to the motion to dismiss the indictment that Vallone filed shortly before the trial, invoking the Speedy Trial Act. They contend that it is evident from the transcript of the hearing on that motion that the court felt it had been “sandbagged” by Vallone’s counsel and took personal offense at the suggestion that it had deprived Vallone (or any other defendant) of the right to a speedy trial by granting the defendants’ own requests for continuances. Defendants’ Joint Br. 72. The defendants contend that the court castigated McLeese, questioned whether the motion had been filed in good faith, and interrupted McLeese repeatedly, evincing an animosity to the defense that went well beyond the impatience that one might otherwise expect in reaction to an eleventh-hour motion of this sort. Having reviewed the transcript of the hearing, we disagree with the contention that the court’s reaction to the motion bespeaks an anti-defense bias. The transcript arguably does suggest that the court was annoyed with the contention that Val-lone had been deprived of his right to a speedy trial, and the court did press Val-lone’s counsel to acknowledge that he had joined in the other defendants’ requests for continuances. But we believe that any annoyance on the part of the court was understandable. Vallone’s motion was brought on the eve of trial after years of pre-trial litigation and multiple requests for delay sought by the defendants themselves, agreed to by Vallone’s counsel, and granted in some instances over the objection of the government. We ourselves have observed that a record of delays sought by the defendant will cast doubt on the validity of his subsequent contention that he has been deprived of his right to a *471 speedy trial. United States v. Adams, supra, 625 F.3d at 379 (citing United States v. Larson, 417 F.3d 741, 746 (7th Cir.2005); United States v. Baskin-Bey, 45 F.3d 200, 204 (7th Cir.1995)). To whatever degree the court may have interrupted McLeese during the hearing and persisted in extracting his acknowledgment that the complained-of delays had been precipitated by the defendants, the court nonetheless did hear both McLeese and the government’s counsel out before denying the motion to dismiss. The motion, for the reasons we have already explained, was not meritorious. And, as we have also noted, expressions of impatience and annoyance — which are to be expected with eleventh-hour motions complaining of delays that the defendants themselves sought — are not sufficient by themselves to establish actual bias on the part of the judge. Liteky, 510 U.S. at 555-56, 114 S.Ct. at 1157. Skeptical reaction to Jenkins. The defendants assert that “the court’s animosity towards defendants was fully on display” during the testimony of David Jenkins. Defendants’ Joint Br. 73. Recall that Jenkins was the individual who helped set up offshore entities in Belize for Aegis clients. As we have said, Jenkins testified under a grant of immunity. And although he was the government’s witness, some of what he said, principally during cross-examination by defense counsel, was favorable to the defense. For example, Jenkins testified that the backdating of documents was not prohibited under Belizean law (R. 929 Tr. 1381; R. 967 Tr. 1517), that the monetary transfers associated with demands on promissory notes were not illegal (R. 929 Tr. 1385), and that Jenkins understood Yallone to be attempting to establish a system that complied with U.S. as well as Belizean law (R. 929 Tr. 1402). There were times during his testimony when the court interrupted Jenkins to ask him if he understood the question that had been posed and to repeat his answer. E.g., R. 929 Tr. 1381; R. 967 Tr. 1501, 1519-20. The defendants suggest that these interruptions communicated the judge’s skepticism and disbelief of Jenkins’ testimony to the jury. Again, we conclude that the record does not bear the defendants’ assertion out. Although the record does confirm that the judge periodically interrupted Jenkins’ testimony, the interruptions on the whole do not support the inference that the judge was biased against the defense or conveyed a disbelief of Jenkins’ testimony to the jury. “District judges have broad discretion in conducting trials and may question witnesses during direct or cross-examination.” Barnhart, supra, 599 F.3d at 743. We note first that the judge’s interruptions began well before Jenkins gave testimony that the defendants perceive as helpful to them. See, e.g., R. 929 Tr. 1310-11, 1367-69, 1390; R. 967 Tr. 1439, 1486. Indeed, our review of the record suggests that the judge was an active questioner of witnesses, often interjecting to ensure that the witness understood an ambiguous question, to clarify an answer, or to have the witness expand on a point that the court was curious about. This was just as true in the case of Jenkins’ testimony as it was with other witnesses. And we note that a number of the interruptions of Jenkins appear to have been occasioned by the court’s legitimate concern that Jenkins may have misunderstood a broad or poorly worded question. E.g., R. 292 Tr. 1385; R. 967 Tr. 1501, 1514, 1519-20. At the same time, there were numerous instances in which Jenkins gave a seemingly defense friendly answer with no interruption or remark by the court. E.g., R. 929 Tr. 1382, 1388, 1401, 1402, 1403; R. 967 Tr. 1469-71, 1473, 1499, 1577. *472 In short, there is nothing in the record that suggests the judge was disbelieving of Jenkins’ testimony, let alone that he conveyed such skepticism to the jury. Of course, our review is confined to a written record that does not reveal the judge’s tone of voice or facial expression. And we must acknowledge the possibility that the judge may have interrupted Jenkins in some instances because it was surprised by the testimony that Jenkins gave. Some of his answers were surprising to us — that backdating documents is not prohibited by Belizean law, for example. The material point, however, is that the record does not reveal a one-sided or prosecutorial bent to the questions posed by the judge. The interruptions were within the bounds of judicial discretion and do not suggest that the court conveyed to the jury an inclination to disbelieve Jenkins’ testimony. The defendants also complain that at the conclusion of Jenkins’ testimony, the judge, with the jury still present, asked Jenkins, “Could you step over here, please?” R. 967 Tr. 1521. Presumably, the court intended to confer with Jenkins in a sidebar conference. Then, remarking that “there’s another way to do this,” the court instead excused the jury from the courtroom. With the jury gone, the judge then suggested to Jenkins that he might wish to speak with his American counsel before returning to Belize. Although the judge did not make explicit' why he thought Jenkins should promptly confer with his attorney, we gather that the judge had some concern that portions of Jenkins’ testimony may have placed him in jeopardy. After Jenkins was excused, the defendants objected to the fact that the court, while the jury was still present, had summoned Jenkins to the side. Defense counsel asserted that both the wording and the “pointed” tone of the court’s request had conveyed its disbelief of Jenkins’ testimony to the jury and an intent to admonish Jenkins.. The court rejected the notion that the words it had used signaled something negative to the jury and, after having the court reporter’s audio recording played back, likewise rejected that there was any such implication in its tone. Nothing in the court’s request that Jenkins “step over here, please” bespeaks bias on the part of the court or demonstrates prejudice to the defendants. It is pure speculation to suggest, even against the backdrop of the judge’s interruptions of Jenkins, that the jury must have inferred the judge’s disbelief of and unhappiness with Jenkins’ testimony. The defendants read entirely too much into this brief request of Jenkins. Reaction to Cross-Examination of Parker and Special Agent Smyros, and Direct Examination of Vallone. The defendants next argue that the judge’s unwillingness to allow Vallone’s counsel to pursue certain relevant lines of inquiry during the cross-examination of two government witnesses (Parker and Special Agent Andrew Smyros), and its apparent impatience with the length of time counsel spent on the direct examination of Vallone, displayed bias. As to Parker and Smyros, the court may have misunderstood the point that Vallone’s counsel was attempting to explore; and as to Vallone, the court appears to have been concerned about one line of inquiry that his counsel was pursuing rather than the overall length of Val-lone’s direct examination. But in none of these three instances do we discern evidence of bias against Vallone, his counsel, or the defense generally. The issue vis-a-vis Parker arose with respect to his testimony concerning the Audit Arsenal letters he sent to the IRS on behalf of Aegis clients who had received notice that they would be audited by the IRS. Parker prepared these letters based *473 on a template that he had been given by Vallone. The letters, among other things, asserted to the IRS that the Aegis clients had various constitutional rights as taxpayers and also posed a series of questions to the IRS. R. 913, Tr. 1941-45. At bottom, the letters were part of an effort to thwart IRS inquiry into the Aegis trusts. On cross-examination, Vallone’s counsel, McLeese, sought to elicit from Parker a confirmation that taxpayers do have certain rights with respect to an IRS audit, including a Fifth Amendment right not to incriminate themselves. See, e.g., United States v. Argomaniz, 925 F.2d 1349, 1352-53 (11th Cir.1991) (citing Kastigar v. United States, 406 U.S. 441, 445, 92 S.Ct. 1653, 1656, 32 L.Ed.2d 212 (1972)). However, the court, in the apparent belief that McLeese was running afoul of its pretrial ruling barring any effort to show that the federal tax laws were unconstitutional, interrupted McLeese sua sponte and at one point instructed the jury that the constitutionality of the tax laws was not at issue. When McLeese persisted in attempting to elicit an answer from Parker on the right against self-incrimination, the court summoned McLeese to a sidebar, and then, as it had with Jenkins, decided instead to excuse the jury from the courtroom, after which it reprimanded McLeese for persisting in the inquiry notwithstanding the court’s warnings. R. 947, Tr. 2044-52. We are inclined to agree with the government that this was an instance of the court misapprehending the' point that McLeese was trying to make with the witness. Eliciting Parker’s acknowledgment that taxpayers do have a Fifth Amendment right against self-incrimination would not have called into question the constitutionality of the Internal Revenue Code or the legitimacy of the IRS audit notices. At the same time, it would have been a legitimate way for the defense to point out that the letters sent out by Parker were not wholly frivolous in their content, and in turn to argue to the jury that the letters were not, contrary to the government’s view, simply a means of evading and obstructing the IRS audits. Perhaps the court was misled on this point, when, at an initial sidebar, McLeese remarked, “What this has to do with is the constitutionality of the tax laws, not of filing a tax return, but rather of asserting your constitutional rights in response to an audit request.” R. 947 Tr. 2045. We understand McLeese to have been trying to distinguish the pretrial ruling which declared the constitutionality of the tax laws off limits, but the ambiguous wording of this remark may have simply confirmed, in the court’s mind, that the constitutionality of the tax laws was precisely what McLeese intended to explore with the witness. In any case, Vallone makes no argument that he was prejudiced by the ruling. He argues only that the court’s repeated interruptions and admonitions show bias at work. We view it instead as an instance of miscommunication and misunderstanding. Much the same is true as to what occurred during Special Agent Smyros’s testimony. Smyros was one of the agents who participated in the March 7, 2003 search of Vallone’s home. On cross-examination, McLeese sought to establish in some detail the context, chronology, and thoroughness of the search. R. 931 Tr. 3010-22. The government objected to the inquiry on the ground of relevance. The court, by contrast, was concerned that McLeese was attempting to suggest that the search was improper in some way. Id. Tr. 3015. McLeese assured the court that he agreed the search was lawful and was not attempting to suggest otherwise. The court then sustained the government’s relevance objection. McLeese continued to pose questions of Smyros aimed at eliciting the purpose and thoroughness of the *474 search. But the court, believing that McLeese’s questions implicated the legality of the search, repeatedly interrupted McLeese, saying it had already ruled on this line of inquiry, and told him to move on. Again, we believe that the court likely misunderstood what McLeese hoped to show through this barred line of questioning. We gather that what McLeese hoped to establish is that despite what he expected Smyros to say was a thorough search of Vallone’s home, the agents did not discover any email or other document in which Val-lone in some way acknowledged (in MeLeese’s words), “I know what we’re doing doesn’t comply with the requirements of the federal tax laws, but I think we can get away with it anyway.” R. 931 Tr. 3022. Arguably this was an appropriate line of inquiry given Vallone’s Cheek defense and the government’s burden to prove his willfulness, and certainly it would have in no way called into question the legality of the search. But we see no sign that the court in limiting this line of inquiry was motivated by bias rather than a genuine misunderstanding of what McLeese hoped to establish. And McLeese ultimately was able to elicit Smyros’s acknowledgment that he did not recall seeing any smoking gun admission along the lines that McLeese posited, so there was no prejudice in the limits imposed on him by the court. Finally, the following brief exchange occurred during Vallone’s first day on the witness stand. When McLeese suggested that he had reached a point in his examination of Vallone that would be convenient for the lunch break, the court asked him how much longer he expected to be with his direct examination. When McLeese responded that he expected his examination to continue into the following day, the court called for a sidebar. McLeese, apparently anticipating that he was about to be scolded, immediately pointed out that the government’s first witness had been on the stand for three days. The court admonished McLeese for making such a statement in front of the jury. At the sidebar, the court seemed to be primarily concerned with the amount of time McLeese was spending on a particular point rather than with the overall length of Vallone’s testimony. See R. 920 Tr. 5137-38. Although by now it should be clear that McLeese and the court did not have an easy relationship, we see no hint of any bias or unfairness in this exchange. Val-lone went on to testify for a total of five days, so there can be no argument that the court imposed any undue limitation on his testimony. The court, as we have said, appears to have been primarily concerned with something other than the length of Vallone’s testimony. We view the court’s decision to summon McLeese to a sidebar, and the exchange that followed, as immaterial. Court in Role of Prosecutor. The defendants contend that the record is “replete” with instances in which the court assumed a partisan role on behalf of the government. Defendants’ Joint Br. 77. They cite three groups of examples in support of their contention: (1) the court’s interruptions during Jenkins’ testimony, which we described earlier; (2) the court’s purported pattern of prompting the government to make objections to questions posed by the defense or making its own objections to such questions, and ultimately cutting off defense questioning; and (3) the court’s purported “bolstering” of the credibility of Mary Robinson during her testimony regarding the ARDC proceeding involving Bartoli. Having reviewed the examples that the defendants have cited, we find no meaning *475 ful evidence of the court assuming a prosecutorial role. We have thoroughly discussed Jenkins’ testimony and the reasons why the court’s interruptions of Jenkins do not show bias; no more need be said on that subject. As to the court’s purported proclivity to prompt objections by the government and to sustain its own objections to defense questions, the defendants cite only a handful of examples, which in the context of an eleven-week trial is insufficient to demonstrate anything approaching a pattern raising an inference of bias. Our own impression from the trial record is that the court consistently paid close attention to the testimony and showed no reticence to interrupt the government’s witnesses either. When the court did interpose its own objections, it typically had a neutral and legitimate reason to do so. Finally, having reviewed Robinson’s testimony, we have found no evidence that the court was in any way attempting to bolster her credibility. Robinson’s role was to identify and read from certain documents related to the ARDC proceeding; as such, her credibility was largely beside the point. Insofar as the court sustained objections to certain questions posed by the defense, we believe it had wholly legitimate grounds for doing so. Evidentiary Rulings. The defendant’s next contention is that the court “made numerous evidentiary rulings which allowed the government to present nearly any evidence it desired.” Defendants’ Joint Br. 78. In examining the examples cited by the defendants, however, we see no sign that the court admitted evidence improperly or in a one-sided manner. (1) The first example is again one we have discussed: the admission of evidence related to Bartoli’s ARDC proceeding, including the Hearing Board’s summary of Marutzky’s testimony that the Heritage/Aegis trusts were ineffective as a means of tax avoidance. The defendants’ argument in this instance is principally one of asymmetry: they note that the court allowed the ARDC evidence as proof of notice to Bartoli (as well as his codefendants) that the Aegis system was illegitimate, yet improperly restricted the attempts of Bartoli’s counsel to establish that Bartoli’s participation in the ARDC proceeding, and thus his familiarity with what occurred, was minimal. The defendants posit that the probative worth of the ARDC evidence as proof of notice to Bartoli (let alone his co-defendants) was weak, in that (a) Bartoli was not finally disbarred until May 2002, late in the life of the conspiracy and years after Bartoli had left his role as counsel to Aegis, and (b) the inference that Bartoli and others were aware of what occurred in the ARDC proceeding hinged on the mere discovery of ARDC materials in Aegis’s Illinois office in 2000, again well after Bartoli had retired to South Carolina. Nonetheless, in allowing the government to present the ARDC evidence, the court told Bartoli’s counsel that “[i]f your position is that Mr. Bartoli never received notice [of the ARDC proceeding] formally, informally, de facto, or otherwise, whatever your claim may be, then you can pursue that on cross-examination.” R. 916 Tr. 2663-64. But when counsel attempted to ask Robinson on cross-examination whether she knew whether Bartoli’s attorney in the ARDC proceeding had ever communicated to Bartoli the opinion Marutzky had given in that proceeding, the court sustained the government’s objection to the question. R. 916 Tr. 2727. And when counsel asked Robinson to confirm that Bartoli was not present in person for the hearing before the ARDC’s Hearing Board, and Robinson did so, the court interrupted and remarked that the relevant notice was “notice of what had occurred and the ultimate decision.” Id. Tr. 2728. Finally, the de *476 fendants note that in addition to reading excerpts from the ARDC proceeding, Robinson was also permitted to read portions of the sanctions opinion that Judge Plunkett entered in the lawsuit Bartoli and others filed against the ARDC. They argue that the relevant portion of Judge Plunkett’s opinion, which addressed the legality of the Aegis system, was dicta, because that point was not at issue in the proceeding before him. They add that when Bartoli’s counsel attempted to clarify certain points about what was alleged in the lawsuit before Judge Plunkett by referencing the complaint filed in that action, the court castigated counsel for doing so, suggesting that he was attempting to resurrect allegations that Judge Plunkett had deemed frivolous. Id. Tr. 2737-42. We have already explained why we believe that the ARDC proceeding was fairly strong evidence of notice that was relevant to the defendants’ Cheek defense and willfulness. The defendants’ contention to the contrary ignores both the sequence of events in the ARDC proceeding and the extent to which the proceeding involved not just Bartoli, but several of his co-defendants. Although the final order of disbarment did not issue until May 2002, the ARDC’s original complaint was filed in November 1996 and was succeeded by an amended complaint in September 1998. We have discussed the reasons why Aegis and its principals would have an interest in the proceeding, notwithstanding the fact that Bartoli was the sole respondent. In fact, as we have noted, Bartoli, Vallone, and Hopper were all deposed in the course of the proceeding; and Robinson testified that she recalled taking a statement from Dunn. Bartoli, of course, regardless of his physical absence from the evidentiary hearing before the Hearing Board, was represented by counsel throughout the proceeding. The Hearing Board’s Report and Recommendation was issued in February 2000, and a copy of that decision along with other Aegis materials, including a copy of Marutzky’s testimony, was found in the Aegis offices. The alleged conspiracy was in full swing when the ARDC filed its complaint against Bartoli, and it persisted even after the Hearing Board’s decision issued in early 2000. And, of course, Bartoli remained involved with Aegis long after his nominal retirement to South Carolina. For all of these reasons, the evidence concerning the ARDC proceeding was strong, not weak, evidence of notice. Robinson’s testimony about the lawsuit that four of the defendants filed before Judge Plunkett was also relevant as notice. Judge Plunkett’s decision to dismiss the suit as frivolous, noting among other things that the Aegis system was not “a legal means to avoid paying taxes,” R. 916 Tr. 2695, whether dicta or not, was yet another warning to the defendants that what they were doing was illegal. As for the court’s multiple interruptions of Bartoli’s cross-examination of Robinson, we see nothing that constituted an abuse of discretion or was so unusual or unjustified as to suggest bias. Robinson, obviously, could not speak to what Bartoli’s counsel did or did not tell Bartoli about what occurred in the ARDC proceeding. She could testify to whether Bartoli was physically present for the evidentiary hearing, and she did confirm that he was not. That the court interjected to clarify that it had admitted the ARDC evidence as proof of notice of what ultimately occurred in the proceeding, rather than notice of every detail of the proceeding, arguably was a legitimate effort to keep counsel as well as the jury focused on the purpose for which the evidence was offered. Finally, with respect to the lawsuit against the ARDC, the court’s legitimate concern was that Bartoli’s counsel might be trying to relitigate the validity of that *477 lawsuit. If there was another purpose to the inquiry, counsel never made that clear. (2) Counts 11 through 34 of the indictment charged Bartoli, Vallone, Hopper, and Dunn with willfully aiding and assisting, procuring, counseling, and advising the preparation and presentation of the false and fraudulent income tax returns filed by multiple Aegis clients, in violation of 26 U.S.C. § 7206(2). The tax returns of Bruce and Tammy Groen and John and Colleen McNinney, were among the false and fraudulent returns underlying these charges. None of these four taxpayers testified at the trial; Bruce Groen, in fact, was deceased by that time. Instead, Internal Revenue Agent Michael Welch was permitted to testify about various aspects of their returns, including the reported income, claimed deductions, and income tax paid, as well as the substantial adjustment later made to those returns as a result of the audits that the IRS conducted. In addition, Welch testified that the returns appeared to have been signed by taxpayers and their preparer, CPA Laura Baxter. (Baxter was indicted separately for her role in supporting the Aegis scheme as a tax preparer.) The defendants contend that Welch’s testimony concerning these tax returns was contrary to Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004), which essentially disapproved the admission, for their truth, of out-of-court testimonial statements that are not subject to cross-examination. Welch’s testimony was meant to show that the tax returns in question fraudulently understated the taxpayers’ income and that they had been signed by both the taxpayers (elsewhere identified as Aegis clients) and their tax preparer (elsewhere identified as an Aegis-approved preparer). As such, his testimony was one piece of the government’s case for the notion that Bartoli, Vallone, Hopper, and Dunn had aided and abetted the preparation of these tax returns in violation of section 7206(2). But, as an IRS agent, Welch obviously had no knowledge of any interactions that these taxpayers might have had with the defendants, and thus could not be cross-examined on any such interactions. In view of that fact, the defendants contend that allowing Welch to testify about the returns deprived them of their Sixth Amendment right of confrontation. To summarize the defendants’ argument is to see how misguided it is. Welch did not recount any out-of-court statements that the taxpayers in question may have made about any contact they had with any of the defendants. Welch instead testified as both a summary witness, identifying the tax returns and describing their contents, and as an expert, explaining the extent to which the returns had understated the taxpayers’ actual income. See United States v. Pree, 408 F.3d 855, 869 (7th Cir.2005) (permissible for IRS agent to testify as an “expert summary witness,” giving testimony that both summarizes what the evidence shows and analyzing the tax consequences of that evidence based on his own expertise). Insofar as Welch’s testimony summarized what the tax returns themselves declared, it did not implicate the Confrontation Clause. As Crawford recognizes, the Confrontation Clause only applies to testimonial statements. 541 U.S. at 68, 124 S.Ct. at 1374. To describe what a taxpayer has claimed on a tax return is not to recount a testimonial statement. See United States v. Doughty, 460 F.2d 1360, 1363 n. 2 (7th Cir.1972) (testimony as to contents of tax return is not hearsay, because it is not offered for its truth but rather to show what was declared); United States v. Garth, 540 F.3d 766, 778 (8th Cir.2008) (testimony regarding tax returns filed by *478 non-testifying individuals not a Confrontation Clause violation), abrogated on other grounds by United States v. Villareal-Amarillas, 562 F.3d 892, 895-98 (8th Cir.2009); United States v. Jimenez, 513 F.3d 62, 81 (3d Cir.2008) (admission of tax returns as filed does not implicate Confrontation Clause when returns not admitted for truth); United States v. Solomon, 825 F.2d 1292, 1299-1300 (9th Cir.1987) (testimony regarding tax returns did not pose a Confrontation Clause problem, as contents of returns were admitted not for their truth but to show what deductions were claimed; no need to cross-examine taxpayer, as deductions were either claimed or not); United States v. Austin, 774 F.2d 99, 101-02 (5th Cir.1985) (false tax returns were not hearsay because they were not admitted for the truth of what they asserted). Internal Revenue Agent James Pogue gave testimony regarding the investigation of an Aegis client, T. David Ring, and certain documents related to Ring that were recovered from defendant Cover’s office. Pogue was involved in the civil audit that led to the Muhieh decision as well as the audits of other taxpayers who were clients of Heritage and Aegis, including Ring. Ring ultimately became a client of Aegis, but he was a client of Heritage when he filed the 1993 income tax return that Pogue was investigating. Pogue was permitted, over objection, to read from a letter that Ring had written to Jennifer Sodaro, an attorney for Aegis. That letter related to the IRS investigation and a motion to quash a summons (which Ring mislabeled a “motion to squash”) issued in connection with the IRS’s investigation of his 1993 return. R. 949 Tr. 2813-15. The letter also mentioned that “Mike” would be getting back to Ring with a plan to eliminate his tax liability. The “Mike” to whom Ring was referring could have been either Michael Vallone or Michael Dowd. Id. Tr. 2833-35. Because Pogue could not clarify which “Mike” was being referenced, see id. Tr. 2837, the defendants contend that Pogue’s testimony posed a Crawford problem. We disagree. The letter from Ring to Sodaro was among the documents recovered from Cover’s office. Pogue’s testimony about what the letter said was not offered for its truth but rather to establish context for later testimony concerning backdated trust documents that Aegis personnel prepared for Ring. Id. Tr. 2817. Moreover, the defendants have made no showing that they were prejudiced by the letter’s ambiguous reference to “Mike.” On cross-examination of Pogue, the defense made clear that he had no idea who “Mike” was. Id. Tr. 2837. IRS Special Agent Bernard Coleman led a team of ten agents who searched the premises of a business in Charleston, Illinois in March 2000. 8 While cross-examining Coleman, Dowd’s counsel began to ask the agent about the steps he had taken to procure the warrant which authorized the search. (For example: “Before you obtained a search warrant, you went before a federal magistrate, right?” R. 914 Tr. 2340.) The court had previously ruled on the legality of the search and evidently became concerned that these questions were meant to suggest some impropriety in the search. The court interrupted the questioning to remind counsel that the search had taken place pursuant to a lawful warrant, and advised him that he could *479 not question the agent about anything that had occurred before the search warrant was issued. “You cannot bring to the attention of the jury anything that preceded the issuance of the order by the court.” R. 914 Tr. 2342. The court explained, Once the court entered an order authorizing the search and seizure, that was a lawful order of the court and cannot be challenged indirectly by some inquiry of the witness on the stand. That was an order of the court. Now, if you have other questions of this witness beyond the issue of the warrant, go ahead. Id. Tr. 2341. Counsel told the court he was not questioning the legality of the search warrant nor its execution, but instead wanted to explore some of the information contained in the affidavit submitted in support of the application for the warrant. The only question I would proffer to the witness is that there was an affidavit, and the affidavit lists the names of certain individuals who the Internal Revenue Service is investigating. All I want to do is explore that affidavit before the signing of the search warrant, an affidavit that this agent prepared and signed under oath. Id. Tr. 2343. The court denied counsel’s request to question Coleman about the affidavit, reasoning that the affidavit was subsumed within the order of the court authorizing the search and was thus off-limits. Counsel clarified that he just wanted to inquire about the agent’s knowledge. The court allowed counsel to ask Coleman if he knew of Dowd at the time he sought the warrant; Coleman replied that he was not sure. Counsel then attempted to show Coleman the affidavit — presumably to confirm that Dowd’s name was not mentioned — but the court would not permit him to do so. The court indicated it would allow additional questions as to what Coleman knew at that time, and counsel was able to establish that Coleman knew of some twenty individuals whom he believed were involved with Aegis. But the court would not permit counsel to establish that Coleman’s affidavit named these twenty individuals and that Dowd was not among them. The court also refused counsel’s repeated requests for a sidebar so that he could articulate what he was attempting to elicit from Coleman. Ultimately, Dowd’s counsel gave up. “Your Honor, I can’t proceed, respectfully, based on the Court’s rulings. I would like to develop a point, but I cannot.” Id. Tr. 2348. “Then that’s it,” the court replied. Id. There is little to make of this exchange. It seems clear that Dowd’s counsel wanted to extract an acknowledgment from Coleman that Dowd was not one of the twenty alleged participants in the Aegis conspiracy who were named in the affidavit that Coleman prepared and presented to the federal magistrate who issued the search warrant. This was a minor point that ultimately had little, if anything, to do with Dowd’s guilt or innocence on the charges. If there is more that Dowd’s attorney wished to establish with Coleman, the defendants’ brief does not identify what that was. Reasonable minds might differ as to whether the court ought to have allowed the question that Dowd’s counsel wanted to pose (which we agree did not appear to in any way challenge the validity of the warrant and the ensuing search) and as to whether the court ought to have allowed counsel to clarify whatever point he wanted to make at sidebar. But the point that counsel was exploring was of such minimal relevance that it is difficult to understand why this is an illustration of bias on the part of the court. Finally, the defendants contend that bias is evident from the fact that the district court allowed the government to *480 cross-examine Vallone about the contents of certain documents admitted into evidence for purposes of showing that the defendants had notice of the illegality of the Aegis trust system, but which Vallone denied having seen. Vallone was asked, for example, about two documents related to the ARDC proceeding against his co-defendant Bartoli that had been discovered in Aegis’s Illinois office. These included one of the two complaints that the ARDC had filed against Bartoli, as well as the eventual Report and Recommendation issued by the ARDC’s Hearing Board. Val-lone acknowledged that he was aware of the ARDC proceeding. In fact, as we have pointed out, Vallone had been deposed in the course of that proceeding. But when questioned about the complaint and the Hearing Board’s recommended decision, he said that he did not recall having ever read the complaint and that he had not read the Board’s Report and Recommendation. E.g., R. 954 Tr. 5454, 5456, 5458. Over the objection of defense counsel, the government was allowed to press Vallone on these documents, asking him several follow-up questions as to whether he was aware of certain statements made in the complaint and the hearing board’s recommended decision concerning the legality of the Aegis system. Id. Tr. 5454-55, 5457-58, 5458-59. The defendants contend that this was improper, and that the district court in overruling their objections unfairly changed the limited purpose for which it had admitted these documents into evidence. Again, we discern no impropriety that bespeaks bias or prejudice on the part of the district court. As we read the record, the district court allowed the government to question Vallone on specific passages from these documents because Vallone was admittedly aware of the ARDC proceedings and yet denied awareness of what specifically the ARDC had alleged and what the ARDC’s Hearing Board later found. The court reasoned that questioning Vallone about the contents of these documents was an appropriate means of testing Vallone’s credibility. Id. Tr. 5460-61. That rationale did not alter the purpose for which the court had admitted these documents into evidence. The court in fact reiterated that the documents had been admitted for purposes of notice. Id. Tr. 5461-62. We do not believe that the district court abused its discretion in allowing the government to ask Vallone whether or not he was aware of some of the specific charges and findings reflected in these documents. Copies of the documents were, after all, found in Aegis’s headquarters, and it is reasonable to surmise that they were present because the Aegis principals had an interest in the ARDC proceeding. As we have discussed, the ARDC’s charges, which were premised on the sham nature of the trusts marketed by Heritage and Aegis, struck at the heart of the Aegis scheme. The defendants, including Vallone, had every reason to pay attention to the ARDC proceeding. Given Vallone’s awareness of the proceeding— indeed, his participation in that proceeding as a witness — one would think that he would have some knowledge of what the ARDC charged and what its Hearing Board later concluded, even if he did not read those documents. (Vallone conceded that he was aware of the contents of other documents that the government relied on for notice purposes, including IRS Notice 97-24.) The fact that Vallone was one of the plaintiffs in the suit against the ARDC makes this inference all the more plausible. We add, as a last observation, that this questioning was not nearly as belabored as the defense suggests it was. Cumulative Effect of Alleged Errors. Finally, the defendants make a catch-all *481 assertion that the cumulative effect of all of the purported errors they have cited— which they describe as an “avalanche of errors,” see United States v. Santos, 201 F.3d 953, 965 (7th Cir.2000) — deprived them of a fair trial, even if those errors do not demonstrate bias. As set forth above, we have disagreed -with the premise that many of these were errors, and in any event we have concluded that none of them, individually, deprived the defendants of a fair trial. We reach the same conclusion with the respect to all of these instances taken together. III. VALLONE Vallone makes his own individual challenge to the instruction on conscious avoidance of knowledge that the court gave the jury over his objection (among others). Our earlier discussion of the defendants’ joint challenge to this same instruction suffices to dispose of Vallone’s challenge. We simply reiterate two points. First, a defendant’s willful blindness to the law can merit a conscious avoidance instruction just as his willful blindness to the facts can. United States v. Stadtmauer, supra, 620 F.3d at 256-57. Second, there is ample evidence supporting an inference that Vallone in particular willfully blinded himself to the state of the law as to the validity of the Aegis system, and this evidence confirms the propriety of the instruction as to him. We have already discussed much of this evidence. To cite just a few salient examples: (1) After the Tax Court handed down its decision in Muhich, and Bartoli raised the possibility of soliciting a legal opinion from a law firm as to the legality of the Aegis system, Vallone opposed the proposal because he was not confident that the opinion would be positive. (2) When Parker suggested soliciting an opinion from the IRS, Vallone criticized that idea as “ridiculous,” “because we know what the answer will be.” R. 913 Tr. 1954. (3) At another meeting at the Aegis office headquarters in the fall of 1999, at which Bartoli, Vallone, Hopper, Parker, Dunn, and possibly Cover were present, Vallone and Hopper became embroiled in an argument over what actions Aegis clients should be advised to take in response to the audit notices they were receiving from the IRS. Hopper viewed the wave of notices as a sign that the government was about to bring an end to Aegis. “[Tit’s over,” Hopper told the others. R. 913 Tr. 1957. “[W]e’re all going to jail.” Id. Hopper argued that Aegis clients should be encouraged to do what they thought best, including finding legal representation. Vallone agreed that clients needed counsel, but argued that clients should be advised to consult only with attorneys approved by Aegis. Hopper, on the other hand, thought that clients should be free to act in their own interests. Their dispute grew more heated, culminating in a pronouncement by Vallone that “God will be the ultimate judge,” or words to that effect. Id. Tr. 1959. Vallone’s disagreement with Hopper signals his unwillingness to allow independent attorneys to look at the Aegis system as well as his ongoing refusal to acknowledge the government’s view that the Aegis system was illegitimate. (4) Vallone spearheaded the creation and promotion of the Aegis Arsenal, which as we have said was essentially a means of obstructing any IRS inquiry into the Aegis trusts. (Earlier we cited a letter sent to the IRS by Parker on behalf of an Aegis client as an example of the Arsenal.) (5) Vallone, as we have mentioned, did not file income tax returns for a number of years. In response to the IRS’s inquiry into why he had not, Vallone wrote a letter to the IRS in which he made a variety of baseless claims, including the *482 assertions that he enjoyed certain rights unique to a “sovereign citizen” born in the United States; that he was neither a citizen nor resident of the United States as those terms are used in the Fourteenth Amendment or 26 C.F.R. § 1.1 — 1(a)—(c), the IRS regulation identifying those persons who are subject to income tax by the United States; and that the Declaration of Independence and the Bill of Rights conferred to him an inalienable right to his property, including his labor, which when exchanged for income was not a gain that could lawfully be taxed. R. 908 Tr. 5583. Vallone made these assertions, which are emblematic of tax protestors and which repeatedly and unequivocally had already been deemed frivolous by this court and others, e.g. United States v. Hilgeford, 7 F.3d 1340, 1342 (7th Cir.1993) (citing United States v. Sloan, 939 F.2d 499, 501 (7th Cir.1991)), without conducting any research of his own into the validity of his claims. R. 908 Tr. 5595-5600. This was in marked contrast to the careful research he claimed to have done on other matters related to Aegis. A jury could view the frivolous content of Yallone’s letter as a sign that he was intentionally turning his mind away from any warning or effort that would have disclosed the Aegis trusts as a sham. It was appropriate for the court to give the conscious avoidance instruction. COVER Cover challenges only his 160-month sentence. He makes no argument that the district court improperly applied Sentencing Guidelines in calculating the advisory Guidelines sentencing range, which was 210 to 262 months. His sole objection is to the substantive reasonableness of the sentence that the court imposed. Noting the court’s obligation to consider the sentencing factors identified in 18 U.S.C. § 3553(a), Cover makes two principal points. His first centers on the three-point increase in his offense level based on the district court’s finding that he played a managerial or supervisory role in the offense by overseeing Dowd (whose role he characterizes as little more than a paper pusher and floor sweeper) and a number of tax preparers. See U.S.S.G. § 3Bl.l(b). 9 Cover does not question the propriety of this enhancement on appeal. What he does contend is that any instruction or advice he gave to Dowd and the tax preparers was minimal, and that in real terms he was less culpable than all of the other defendants but Dowd. Cover points out that he received much less financial benefit from the fraud ($347,000) than other defendants, was not a founder or principal in the Aegis scheme, and, at age seventy-two, posed little or no prospective danger to the public notwithstanding whatever nominal supervision he had given to others in furtherance of the scheme. His second point is broader. Cover suggests that the district court in determining the sentence was driven solely by the immensity of the fraud perpetrated by the defendants to the exclusion of other mitigating factors, including his age, his college degree, his long-term marriage, his lengthy employment history, his involvement with his church, and his contrition. Assessing Cover’s sentence through the deferential abuse-of-discretion lens, see Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 597, 169 L.Ed.2d 445 (2007); United States v. Bradley, 675 F.3d 1021, 1024 (7th Cir.2012), we cannot say that Cover’s sentence was unreasonable. The sentence was fifty months below the low-end of the Guidelines range (210 to 262 months), which represents a nearly twen *483 ty-fíve percent reduction. It is also within — indeed, near the bottom of — what the range would have been (155-188 months) had the court not applied the three-point leadership enhancement that Cover suggests was not “a perfect fit” for his actual role in the offense. Cover Br. 8. It is thus a presumptively reasonable sentence even under the more charitable assessment of his culpability that Cover advocates. See, e.g., United States v. Lucas, 670 F.3d 784, 789 (7th Cir.2012) (sentence within Guidelines range is presumed reasonable on appeal), petition for cert, filed, 81 U.S.L.W. 3033 (U.S. June 25, 2012) (No. 11-1536); United States v. Klug, 670 F.3d 797, 800 (7th Cir.2012) (below-Guidelines sentence is also presumed reasonable). Having reviewed the transcript of Cover’s sentencing, we reject the notion that the court focused on the scope of the fraud to the exclusion of other pertinent circumstances. The court, with good reason, gave considerable weight to the “monumental proportion” of the fraud, It. 1036 at 37, which Cover does not suggest he failed to appreciate. But the court considered other pertinent factors as well, including in particular’ Cover’s age, which the court expressly cited in choosing a below-Guidelines sentence. Id. at 42. The court also cited his remorse, the unlikely prospect that he might recidivate, his difficult childhood (following his father’s death, he was raised in a home for boys), his wife’s health problems, and the favorable comments on his character contained in letters to the court. Id. at 37-45. Cover’s below-Guidelines sentence, although still lengthy (as the district court itself acknowledged, id. at 44), appropriately reflects his lesser degree of culpability. DOWD A. Sufficiency of Evidence Dowd was found guilty of conspiracy, one count of mail fraud, and four counts of filing a false tax return. All three charges presume that Dowd knew the Aegis trusts were not a lawful means of tax avoidance. Under Cheek, his good faith belief in the legality of the trusts, even if it was mistaken, would thus preclude a finding that he conspired to defraud the United States and/or to commit a tax offense against the United States (Count One), that he used the U.S. mail in furtherance of a scheme to defraud (Count Three), or that he willfully made or subscribed to a false tax return (Counts Fifty-Two through Fifty-Five). See United States v. Hills, supra, 618 F.3d at 637 (conspiracy to defraud United States by impeding functions of IRS requires proof, inter alia, of agreement to accomplish illegal objective against United States and intent to defraud United States); United States v. Howard, 619 F.3d 723, 727 (7th Cir.2010) (mail fraud requires proof, inter alia, of intent to defraud, which entails “a wilful act by the defendant with the specific intent to deceive or cheat ... ”) (quoting United States v. Britton, 289 F.3d 976, 981 (7th Cir.2002)); United States v. Kokenis, 662 F.3d 919, 930 (7th Cir.2011) (“Willfulness is an essential element of the tax evasion offenses charged under 26 U.S.C. § 7206(1).”) (citing Hills, 618 F.3d at 634, 638-39). Dowd contends that the government’s proof was insufficient to overcome his Cheek defense, and that the district court therefore erred in denying his motions for a judgment of acquittal pursuant to Fed. R.Crim.P. 29. Dowd points out that he was just twenty-three years old when he joined Aegis, armed with a degree in business finance but no significant knowledge or experience with respect to trusts, estate planning, or taxes. He had never before encountered a business trust, but was told by both his father and Cover that it was an *484 effective tool. Dowd contends that he relied on his superiors at Aegis (in addition to his father) regarding the relevant trust and taxation principles, and they consistently dispelled his doubts as to the legitimacy of the Aegis trusts. Dowd represents that he was not privy to meetings among the Aegis principals regarding the structuring of Aegis and its product; he did not draft letters to clients; he did not speak or lecture at seminars; and he did not do legal research. With respect to the tax return charges, Dowd acknowledges that his returns did understate his income. But he adds that he also filed tax returns for his asset management trusts that included any income omitted from personal tax returns. Moreover, he hired certified public accountant Donald Todd to prepare his returns each year he was at Aegis, and there is no evidence he told Todd to omit items or falsely calculate his income. (Todd, by the way, like Laura Baxter, was himself indicted in connection with his work on behalf of Aegis clients.) Nor, according to Dowd, is there evidence that he tried to conceal any assets or cover up sources of income. We review the denial of Dowd’s Rule 29 motions de novo. E.g., United States v. Hassebrock, 663 F.3d 906, 918 (7th Cir.2011), cert. denied, — U.S. -, 132 S.Ct. 2377, 182 L.Ed.2d 1018 (2012). But we will find the evidence insufficient only if the record is devoid of evidence from which a reasonable jury could find Dowd guilty beyond a reasonable doubt. Cavazos v. Smith, — U.S. -, 132 S.Ct. 2, 4, 181 L.Ed.2d 311 (2011) (per curiam). This is an “onerous burden” for Dowd. Hills, 618 F.3d at 637. In assessing the sufficiency of the evidence, we consider the trial record in the light most favorable to the government, granting it the benefit of all reasonable inferences. E.g., id. The government presented ample evidence from which a jury could conclude that Dowd lacked a good faith belief in the legality of the Aegis trust system. First, Dowd admitted that he saw various documents that called into question the legitimacy of the Aegis trusts. Among these were IRS Notice 97-24, R. 922 Tr. 6416-17, 6460-61, the Tax Court’s decision in Muhich, id. Tr. 6473-80, 6490-99; a memorandum from the Aegis legal department summarizing what characteristics the IRS looks at in assessing the legitimacy of a trust (e.g., the deduction of personal expenses), id. Tr. 6467-69; and an article in the Wall Street Journal, id. Tr. 6409-10. He acknowledged that he read and understood these items. R. 922 Tr. 6461-67, 6473-81, 6490-99. 10 Dowd, in fact, kept a cabinet drawer full of similar materials, including a file labeled “Trusts — Attacks on.” R. 950, Tr. 3880-98; R. 922 Tr. 6459, 6467-68; Gov’t Ex. Aegis Office 68 Group Room 5. 11 He admitted that these materials raised questions in his mind about Aegis; and although he said that he relied on the assurances that Vallone and Cover gave him that the Aegis system was materially different from trusts that had been found to be ineffective, he realized that neither Vallone nor Cover was an attorney or accountant, and he never sought independent advice. He also acknowledged that some of what Vallone told him was “mumbo jumbo” that he did not understand. R. 922 Tr. 6458. Dowd also knew *485 that large numbers of Aegis clients were facing inquiries by the IRS; he compiled a list of some ninety clients who were under inquiry as of March 15, 1999. R. 918 Tr. 4322-23; Gov’t Ex. Aegis Office Room 5 Computer 17. Moreover, Dowd was present on a 1999 Aegis cruise when trust “guru” Joe Izen warned participants that “people are gonna get put in jail” for not reporting personal purchases paid for with foreign credit cards drawing on funds they had placed in offshore trusts. R. 917 Tr. 3514; Gov’t Ex. DVD Tr. 5 (Gov’t App. 150). Izen, in fact, had a brief exchange with Dowd during his presentation, which provides ample support for the inference that Dowd heard Izen’s warning. R. 917 Tr. 3508-12; Gov’t Ex. Cruise DVD Tr. 4. 12 Yet, Dowd himself used a Swiss Americard linked to an offshore trust to do precisely that. R. 922 Tr. 6536-37; R. 971 Tr. 4534-42. Finally, he advised Aegis/Sigma client Joseph Kelly that he could deduct the cost of vacation travel so long as Kelly contemplated and actually made a charitable donation to a local charity during the trip. R. 967 Tr. 1576; R. 961 Tr. 1715-16. This was advice which, although consistent with what other Aegis clients were told, was dubious on its face. Collectively, this sort of evidence is more than what this court found sufficient to overcome the Cheek defense asserted in Hills, 618 F.3d at 637-39. The evidence was also more than sufficient to establish Dowd’s guilt on the false tax return charges. First, the amply-supported inference that Dowd understood the Aegis system to be a sham in turn supports an inference that he knew, as a consequence of his own use of that system, that he was under-reporting his income on his individual income tax returns. (There was ample testimony, by the way, that Dowd did under-report his income on his own tax returns. R. 971 Tr. 4522-42; R. 939 Tr. 6558-63.) Second, Dowd — like other defendants and Aegis clients generally — was not just underreporting his income but doing so to a patently ridiculous degree. To cite one example, in 1999, Dowd had income of $60,000, but he reported only $5,250 of that total on his federal income tax return, an amount so low that he (nominally) qualified for— and claimed — an earned income tax credit. R. 939 Tr. 6559-60. Recall that claiming that same tax credit is the very type of thing that Hopper joked about at Aegis seminars. It is an entirely reasonable inference that even a young, deferential, and purportedly naive individual would realize that something was wrong with reporting less than ten percent of his income to the government and claiming a tax credit meant for the working poor. B. Severance Before the trial commenced, Dowd made an oral motion to sever his own case from those of his co-defendants after the district court announced it would allow evidence regarding the Bartoli ARDC proceeding as proof of notice to the defendants. Dowd’s counsel characterized the ARDC evidence as a “bombshell” that would have a preju *486 dicial spillover effect on Dowd, who was not a party to and was otherwise unaware of the ARDC proceeding. R. 1046 at 28. The district court denied the motion, reasoning that the danger of undue prejudice due to the asserted spillover effect was insufficiently grave to warrant a separate trial. Id. at 29-30. Dowd contends that the denial of his request was error, particularly in light of the court’s rationale that notice to one member of the conspiracy served as notice to all. He adds that it was “impossible for the jury to suppose that Mr. Dowd actually believed in the legality of the Aegis system where they were flooded with evidence of other’s [sic] knowledge of its illegality.” Dowd Br. 32. We note that the district court invited Dowd’s counsel to draft an appropriate limiting instruction to address the possibility of spillover prejudice from the ARDC evidence. However, no such instruction was ever tendered: Dowd contends that no such instruction could have remedied the problem. Demonstrating prejudicial error in the district court’s refusal to sever Dowd’s trial would be an uphill battle. We would review that decision under the deferential abuse-of-discretion standard. E.g., United States v. Del Valle, 674 F.3d 696, 704 (7th Cir.2012), petition for cert. filed (U.S. Aug. 16, 2012) (No. 12-219). There is a preference for the joint trial of defendants who are charged together. United States v. Souffront, 338 F.3d 809, 828 (7th Cir.2003) (citing Zafiro v. United States, 506 U.S. 534, 537, 113 S.Ct. 933, 937, 122 L.Ed.2d 317 (1993)). When the defendants have been properly joined in a single indictment pursuant to Federal Rule of Criminal Procedure 8(b), as is conceded here, a court should grant a severance only when “there is a serious risk that a joint trial would compromise a specific trial right of one of the defendants, or prevent the jury from making a reliable judgment about guilt or innocence.” Id. (quoting Zafiro, 506 U.S. at 539, 113 S.Ct. at 938). In challenging the denial of his request for a severance, the defendant must show that the refusal to sever resulted in “actual prejudice” that deprived him of a fair trial. Id. (citing United States v. Rollins, 301 F.3d 511, 518 (7th Cir.2002)). Relevant to the question of prejudice would be (a) the district court’s instruction to the jury that it was to consider each defendant individually (R. 925 Tr. 7389; Seventh Circuit Pattern Criminal Jury Instruction No. 4.05); (b) as we have discussed, the district court never communicated its theory that notice of illegality to one conspirator, or notice to the conspiracy generally, constitutes notice to all members of the conspiracy; (c) the government argued notice as an individual matter, and each defendant was free to argue that he did not have notice that the Aegis system was illegitimate; and (d) despite the court’s express invitation, Dowd never tendered a cautionary instruction as to the ARDC evidence that he contends was so prejudicial. However, Dowd’s failure to renew his motion to sever at the close of evidence precludes us from reaching the merits of his argument on appeal. As the government points out, “[a] motion for severance is typically waived if it is not renewed at the close of evidence, primarily because it is then that any prejudice which may have resulted from the joint trial is ascertainable.” United States v. Williams, 553 F.3d 1073, 1079 (7th Cir.2009) (quoting United States v. Phillips, 239 F.3d 829, 838 (7th Cir.2001)); see also United States v. Ross, 510 F.3d 702, 711 (7th Cir.2007) (coll, cases). Dowd, in his opening brief, offered no explanation for his failure to renew the motion. In his reply brief, he belatedly argues that renewal of the motion would have been futile in light of the *487 court’s notice-to-one rationale. Whatever the court’s thinking may have been as to notice, Dowd has made no showing that the court was so close-minded on the subject of severance that it would have been futile for him to renew his motion at the close of evidence. Renewing the motion at that time would have given the court an opportunity to consider any specific ways in which Dowd believed the joint trial had resulted in actual prejudice to his defense. His failure to renew the motion cannot be excused. C. Minor Role Adjustment The district court overruled Dowd’s objection to the probation officer’s pre-sentence report (“PSR”), which did not grant him a two-level reduction in his offense level for being a minor participant in the offense. See U.S.S.G. § 3B1.2(b). The court reasoned: In terms of culpability or a hierarchy, [Dowd] certainly did not play a role equal to that of Mr. Vallone, or yet to be sentenced Mr. Dunn, or yet to be sentenced Mr. Bartoli. But he was very actively engaged in doing what he could to accomplish the conspiratorial objectives and on a day-to-day basis, so he did not play a minor role..... R. 1039 at 62-63. Dowd contends that the court clearly erred in denying him this reduction. See, e.g., United States v. Smith, 674 F.3d 722, 728 (7th Cir.2012) (district court’s findings as to defendants’ role in the offense are reviewed for clear error), petition for cert. filed (U.S. Sept. 14, 2012) (No. 12-325). Dowd argues that as an administrative assistant, he occupied an entry level position in Aegis, for which he was paid roughly $25,000 per year. As we have discussed, he represents that he was not sophisticated in the laws governing trusts, taxation, or offshore banking and that he did not comprehend the scope and nature of the Aegis scheme; instead, he trusted his father, Vallone, Bartoli and others who assured him that Aegis was legitimate. The PSR acknowledged that Dowd did not create the Aegis scheme, did not manage other participants, and did not receive the largest share of profits from the scheme. Dowd contends that he did not profit from the scheme at all. Finally, he points out that he was named in just ten of 114 overt acts listed in the indictment. Although we agree that Dowd played a lesser role in the offense than other defendants, we are not left with the definite and firm conviction that the court erred in declining to treat him as a minor participant in the offense. See Smith, 674 F.3d at 728. The commentary to Guidelines section 3B1.2 defines a minor participant as one who is substantially less culpable than the average participant in the offense and who is less culpable than most other participants, but whose role cannot be described as minimal. § 3B1.2, comment. (n.5). In assessing a defendant’s relative culpability, a court must consider all of the individuals who participated in the offense, not just those who have been convicted. See id. (n.l); U.S.S.G. § 3B1.1, comment, (n.l). Dowd participated in the Aegis scheme for a period of five years. He may have started out as an administrative assistant, but his role in the offense ultimately went far beyond that. The district court found that Dowd “was very actively engaged” “on a day-to-day basis” during that time (R. 1039 at 62-63), and the evidence certainly supports that finding. He had check-signing authority so that he could pay Aegis’s bills. He was the primary person who dealt with Jenkins in Belize to arrange for the requisite documentation as to offshore companies and trusts for Aegis clients and to ensure that clients made demands on their promissory *488 notes in the offshore system in order to make those notes appear legitimate. Over time, he came to provide certain trust management services to clients. He occasionally gave clients advice about operating their trusts — for example, on what deductions they could take. E.g., R. 967 Tr. 1575-76; R. 961 Tr. 1715-16. He signed a commission agreement, promoted Aegis trusts to several clients, and actually sold trust packages to three clients (although he denied playing any meaningful role in recruiting these clients). In 2000, he was promoted to “operations manager” of Aegis and Heritage, and although that may have been more of an administrative role than a managerial one, it supports the notion that he was not a minor participant in the Aegis scheme. He was subsequently named to the Aegis Advisory Board, which consulted with Vallone on the operation of the Fortress Trust. Without question, Dowd was less culpable than Vallone and Bartoli, as he argues, but one must remember that they received organizer/leader enhancements to their offense levels; and they were not average participants in the offense. Dowd contends that all of the facts we have cited, including his titles, overstate his actual role in the offense, but suffice it to say that it was not clearly erroneous for the court to conclude that he was not substantially less culpable than the average participant. (The average participant, arguably, was the Aegis client — and several Aegis clients went to jail.) D. Reasonableness of Sentence The district court ordered Dowd incarcerated for a period of 120 months, which he contends was an unreasonably harsh sentence given his degree of culpability relative to the other defendants. Again, Dowd emphasizes that he was neither the instigator nor a leader of the Aegis scheme but rather someone who happened into it by taking a job with Heritage at the suggestion of his father and with no intent to become a felon. He likens himself to the “accidental criminal” lured into the scheme, as discussed in United States v. Nachamie, 121 F.Supp.2d 285, 296 (S.D.N.Y.2000),j. aff'd, 5 Fed.Appx. 95 (2d Cir.2001). Dowd also contends that the district court failed to give meaningful consideration to the sentencing factors identified in 18 U.S.C. § 3553(a). In particular, Dowd contends that the court ignored the fact that holding him responsible for a loss amount of $50 million vastly overstated his culpability and resulted in a Guidelines sentencing range that was “grossly disproportional” to his relatively minor role in the offense. Dowd Br. 40. In that respect, Dowd (like other defendants) was put at a disadvantage by a 2008 change in the Guidelines, which resulted in more punitive offense levels for losses of this magnitude. At the same time, he believes the court did not give serious consideration to mitigating factors that included his strong family ties, lack of criminal history, employment as an airline pilot, and the prospect that he would lose his pilot’s license as a result of his conviction. Dowd believes that the unreasonableness of the 120-month sentence imposed on him is evident from the fact that it is the same length as the penalty imposed on Bartoli, who was among the most culpable participants, and only forty months less than that imposed on Cover, who was also much more culpable. The sentence imposed on Dowd, being one month below the low end of the advisory Guidelines range, is one that we presume to be reasonable, e.g., United States v. Russell, 662 F.3d 831, 853 (7th Cir.2011), cert. denied, — U.S. -, 132 S.Ct. 1816, 182 L.Ed.2d 634 (2012), and Dowd has not succeeded in rebutting that presumption. Dowd’s situation is sympa *489 thetic in that his employment with Heritage and Aegis was his first job after college, he was initially led astray as to the legitimacy of the business trust by his father, of all people, and he did not realize at the outset that he was joining a criminal organization. Yet, he remained with Heritage and Aegis for five years, took on an increasing level of responsibility, and was actively involved in the promotion and management of Aegis trusts, despite multiple forms of notice that the Aegis trust was a sham. As an employee at Aegis’s home office in Illinois, Dowd knew that Aegis had hundreds of clients and thus was in a position to appreciate the scope of the Aegis scheme. He knew as of 1999 (two years before his departure) that roughly ninety of those clients were under investigation by the IRS. Moreover, as the government points out, Dowd benefitted from certain breaks in the district court’s Guidelines calculations: because the court held Dowd responsible for a loss amount of $50 million rather than $60 million based on the five years of his involvement, R. 1039 at 67, Dowd faced a sentencing range of 121 to 151 months rather than 151 to 188 months; and the court declined to apply an enhancement for obstruction of justice despite its acknowledgment that the government had a “very strong argument” that Dowd had committed perjury while testifying in his own defense, id. at 57. The court also took into consideration Dowd’s “rationalization” as opposed to willingness to accept responsibility for his conduct. R. 1039 at 57. The comparable length of the sentences imposed on Bartoli and Cover were based on their respective ages and health. We may assume that another judge might have imposed a lesser sentence on Dowd. But for all of the reasons we have cited, we cannot conclude that Judge Norgle abused his discretion in concluding that a sentence one month below the bottom of the range advised by the Sentencing Guidelines was unreasonable. See United States v. Tahzib, 513 F.3d 692, 695 (7th Cir.2008) (below-Guidelines sentence will almost never be unreasonable). E. Ex Post Facto Clause As we have indicated, a relatively recent change in the Guidelines resulted in an increase to Dowd’s offense level and the resulting Guidelines sentencing range. The November 2000 version of the Guidelines in effect at the time Dowd’s offense conduct ended specified a base offense level of 25 for a $50 million dollar loss amount (see U.S.S.G. § 2T4.1(T) (Nov. 2000)), whereas the November 2008 version of the Guidelines that the district court applied at sentencing specified an offense level of 28 for that loss amount (see U.S.S.G. § 2T4.1(L) (Nov. 2008)) — a difference of three levels. Had the district court applied the earlier version, the advisory sentencing range would have been 87 to 108 months rather than 121 to 151 months. Dowd contends that relying on the later version amounts to a violation of his rights under the ex post facto clause of the Constitution. See U.S. Const. Art. I, sec. 9, cl. 3 We have already rejected the ex post facto argument that Dowd is making. See United States v. Demaree, 459 F.3d 791, 793-95 (7th Cir.2006). Dowd invites us to reconsider Demaree, but we have repeatedly declined similar invitations. E.g., United States v. Wasson, supra, 679 F.3d at 951. HOPPER A. Sufficiency of the Evidence The jury convicted Hopper on all counts in which he was charged. He moved pursuant to Rule 29 for a judgment of acquittal both at the close of the government’s *490 case and after the jury returned its verdict. The district court denied his motions, reasoning that “[a]t trial, the government presented overwhelming evidence that the tax shelters marketed by Aegis were unlawful shams designed ‘to make life harder for the revenooers’ by transferring clients’ income to both domestic and offshore trusts, so that clients could pretend they had no income.” R. 650 at 11-12 (quoting United States v. Patridge, supra, 507 F.3d at 1092). Hopper concedes that the trial exposed the Aegis trust system as a sham, but he contends that the court’s ruling failed to recognize that the government never proved that he lacked a good faith belief in the legality of the Aegis trust system. As we noted with respect to Dowd, our review of the sufficiency of the evidence is de novo, United States v. Has sebrock, supra, 663 F.3d at 918, but we will reverse only if, in considering the evidence in the light most favorable to the government, no reasonable jury could have found Hopper guilty beyond a reasonable doubt, United States v. Hills, supra, 618 F.3d at 637. Hopper’s position is that he had a much stronger Cheek defense than his fellow defendants, and that the government failed to overcome it. He asserts that his good faith in the legitimacy of the Aegis system is demonstrated by the fact that when he eventually came to realize that the system was a sham, he took steps to separate himself from the conspiracy. Until the Tax Court issued its June 1999 decision in Muhich, Hopper argues, he genuinely believed that the Aegis system was legitimate. Once that decision was issued, he began to have doubts. He spoke with others at Aegis in an effort to determine what, in fact, was lawful. And when Vallone proposed the Audit Arsenal as a means of thwarting IRS inquiry, Hopper opposed him. (Recall Parker’s testimony regarding the fall 1999 showdown between Vallone and Hopper.) When his efforts to pursue a more constructive response to the IRS inquiries facing Aegis clients proved unavailing, he resigned his position as the Managing Director of Aegis in a letter to Vallone dated January 17, 2000. 13 He therefore ended his involvement sooner than others, like Parker, who were more educated and sophisticated than he was (Hopper had only a high school diploma) and thus should have been among the first to realize that the Aegis trust system was a sham. That he extricated himself from Aegis relatively soon after the Muhich decision confirms — in Hopper’s view — his good faith belief in the lawfulness of the trust system until that time and precluded a reasonable finding by the jury that he exhibited the willfulness necessary to convict him on the charges of conspiracy, mail fraud, or aiding and assisting in the preparation of false or fraudulent tax returns. Although Hopper’s Cheek defense was, in some superficial respects, more appealing than those of other defendants, the record is by no means devoid of evidence from which the jury could reasonably find that Hopper lacked a subjective good faith belief in the legality of the Aegis system even prior to the Tax Court’s decision in Muhich and his subsequent decision to resign from Aegis. On the contrary. From the very beginning, the Aegis trust system was obviously and ineontrovertibly at odds with the fundamental proposition that the tax liability on income and assets rests with the individual who controls those assets. The ways in which the Aegis *491 trusts were structured and used (for example, the routine resignation of the nominally-independent Aegis trustee and replacement with the client shortly after each trust was formed, typically pursuant to paperwork that was executed when the trust was created) would make plain even to a non-lawyer and non-accountant that the transfer of income and assets to the trusts was in form only, and that the Aegis client never in fact surrendered any control of those assets and income. Hopper’s own words at a videotaped Aegis seminar — the recording of which was offered for sale and, in fact, was purchased by Agent Priess — suggest that he understood full well that the purpose of the Aegis trusts was simply to hide a client’s money from the IRS: It’s, it’s taking it from one pocket and putting it in the other and you know and then, and then standing before your wife and saying, “See, I got no money, see.” That’s, that’s what it amounts to. Uhh, to the IRS. Okay. Gov’t Ex. Priess Tr. 2 (Gov’t Supp. App. 246), Gov’t Ex. Priess Video DVD. Hopper also told seminar attendees in 1995 that he was taking tax deductions for obviously personal expenses such as clothes, exercise equipment, and cable television. Gov’t Ex. Coleman Tr. 2-5 (Gov’t Supp. App. 93-96). He even boasted that his reported income was so low that he qualified for an Earned Income Tax Credit from the IRS and financial aid for his daughters to attend college. Gov’t Ex. Coleman Tr. 6-7 (Gov’t Supp. App. 97-98). As outrageous as these statements were, they were not simply exaggerations but rather outright falsehoods, in the sense that Hopper did not file any federal income tax returns at all from 1995 through 2002. Instead, he was periodically writing to the IRS contending that he owed no taxes, even as he was earning hundreds of thousands of dollars from Aegis. (He earned a total of $701,000 from 1997 through 2000.) A jury might reasonably infer from these facts that Hopper had not been led astray by his more sophisticated co-defendants as to the legitimacy of the Aegis system but understood all along that the system was merely a shell game, and one that he eagerly embraced and used to his own profit. There is also evidence undermining Hopper’s contention that he was a true believer in the legitimacy of the Aegis system until the Muhich decision set him straight. Muhich, as the government points out, was not the first warning of illegality that the defendants received. IRS Notice 97-24, issued more than two years prior to the Tax Court’s decision, specifically addressed abusive trusts very much like the Aegis trusts and touched upon such highly relevant points as the deductibility of personal expenses: Personal expenses are generally nondeductible .... The courts have consistently held that non-deductible personal expenses cannot be transformed into deductible expenses by the use of trusts. IRS Notice 97-24 at 3 (citing, inter alia, Schulz v. C.I.R., supra, 686 F.2d 490). And the ARDC complaint issued against Bartoli in November 1996 asserted that Bartoli was defrauding Heritage and Aegis clients by representing to them that the CBO and trust systems Aegis was peddling would minimize, if not eliminate, their tax liability, when, in reality, “applicable trust, tax and common law do not recognize the CBO, as employed by Aegis[] and [Bartoli], as a viable entity formed for the purpose of eliminating or reducing taxes.” R. 961 Tr. 2652; Gov’t Ex. ARDC 1. As we noted earlier, the jury could infer that Hopper, along with other defendants, was aware of the ARDC proceeding given that he was one of the witnesses deposed in the course of that proceeding. Indeed, it was Hopper who *492 prepared a summary of the testimony that William Marutzky gave during that proceeding in March 1999, opining that the Aegis system would not legally provide the tax benefits to the defendants that Aegis had advertised. R. 918 Tr. 4323-24; Gov’t Ex. Aegis Office Hallway Computer 1. Moreover, whatever distance Hopper eventually may have put between himself and the other defendants in 2000 with respect to such aspects of the Aegis scheme as the Fortress Trust and the Audit Arsenal, there is also evidence that he was by no means averse to participating in efforts to throw roadblocks in the path of the government as it sought to expose and unwind the defendants’ crimes. He was, after all, one of the plaintiffs in the lawsuit against IRS auditor Pogue and the ARDC in 1997 that Judge Plunkett later dismissed as frivolous in November 1999, sanctioning the plaintiffs for their “fictional claims.” Bartoli v. ARDC, supra, 1999 WL 1045210, at *3. Finally, although Hopper now contends that it was Muhich that caused him to see the light and to withdraw from Aegis, his behavior subsequent to that June 1999 decision was not wholly consistent with that of a convert. In November 1999, five months after the Muhich decision, Hopper signed a corporate resolution confirming that he along with Vallone and Bartoli shared equal management authority over Aegis. R. 950 Tr. 3838-41; R. 910 Tr. 6226; Gov’t Ex. Aegis Office 80. And although Hopper eventually did resign as the Managing Director of Aegis in January 2000, he continued to provide consulting services and support until May 2000 and did not formally break off his ties with Vallone until June 2000 (more on that below). He continued to receive money from Aegis until June 2000 and from Aegis Management Company (which provided management services to trust clients) until December 2000. See Gov’t Ex. Hopper Income Summary. We may assume for the sake of argument that a jury could have been persuaded by Hopper’s Cheek defense. He was neither an attorney nor an accountant, and he ultimately did end his involvement in the Aegis scheme somewhat sooner than other defendants. In the fall of 1999, he also voiced reservations to his co-conspirators about the Audit Arsenal and argued that Aegis clients ought to be encouraged to seek out legal representation of their own. But as we have discussed, the jury reasonably could infer from Hopper’s own words and deeds that he understood the essentially fraudulent nature of the Aegis system from the start, that he continued his involvement in the defendants’ scheme — and continued to profit from it— long after he and the other defendants received notice that the Aegis system was not a valid means of tax minimization, and that he joined the other defendants in seeking to block exposure of the scheme. From all of this, the jury could reasonably find that Hopper did not have a good faith belief in the legality of the Aegis system and instead willfully conspired and schemed to defraud the government. 14 A few additional words are in order as to Hopper’s convictions on the counts of the indictment charging him *493 (among others) with knowingly aiding and assisting the preparation of false tax returns, in violation of section 7206(2). 15 As we discuss below with respect to defendant Dunn, infra at 505-06, the fact that Hopper did not prepare returns for others does not preclude his liability on these charges. Our decision in United States v. Hooks recognizes that liability under section 7206(2) “ ‘extends to all participants in a scheme which results in the filing of a false return, whether or not those parties actually prepare it.’” 848 F.2d 785, 791 (7th Cir.1988), (quoting United States v. Siegel, 472 F.Supp. 440, 444 (N.D.Ill.1979), judgment affd sub nom. United States v. Winograd, 656 F.2d 279 (7th Cir.1981)). Hopper without doubt understood that Aegis clients would be filing tax returns based on their use of the Aegis trusts; and as we have discussed, his appreciation that the trusts were not a lawful means of tax avoidance meant that he also understood that those returns would be fraudulently understating the clients’ income. Thus, the jury had a more than sufficient basis on which to find Hopper guilty under section 7206(2). To the extent that Hopper suggests the government did not adequately prove the identity of the taxpayers whose returns framed the basis for these charges, our own review of the record convinces us otherwise. E.g., R. 963 Tr. 4807-08, 4795-97; Gov’t Ex. Taxpayers A through O. B. Loss Amount Hopper contends that the district court clearly erred in holding him responsible for a loss amount in excess of $50 million, because that total included losses associated with the 2000 tax year (i.e., tax returns filed in 2001 for 2000) despite his (purported) withdrawal from the conspiracy and scheme to defraud in early 2000. 16 Hopper notes that after the Muhich decision, he prepared a detailed letter to Bartoli and Vallone suggesting ways in which the Aegis system might be changed in order to comply with the law. R. 762 at 99-108; Gov’t Ex. Aegis Office 13. He also opposed Vallone’s decision to pursue the Audit Arsenal in the fall of 1999, as Parker testified. R. 913 Tr. 1954-58; R. 947 Tr. 2082-89. And he ultimately resigned as a Managing Director of Aegis in January 2000, at which point he no longer had supervisory authority at Aegis. By May 2000, he was out of the Aegis picture altogether. In Hopper’s view, this marked his withdrawal not only from Aegis but from the charged conspiracy and scheme to defraud, and it terminated his liability for losses that were incurred later. The district court rejected that notion, reasoning that Hopper’s resignation did not constitute a legally effective withdrawal from the conspiracy and scheme. R. 1085 at 13-15. The court’s finding as to Hopper’s withdrawal is a factual finding that we review for clear error, see United States v. Vaughn, 433 F.3d 917, 922-23 (7th Cir.2006), as is its determination of the loss amount for which Hopper is responsible, e.g. United States v. Borrasi, 639 F.3d 774, 783 (7th Cir.2011). *494 The court committed no clear error in concluding that Hopper’s departure from Aegis in 2000 did not constitute a legally effective withdrawal from the conspiracy. In addition to his resignation as Managing Director in January 2000, R. 761-1 at 3, Hopper relies on a letter that he wrote to Vallone in June 2000 severing his ties to Vallone, id. at 7. Bartoli and Parker were copied on that letter. Hopper reasons that this constituted an announcement sufficient to notify his coconspirators of his withdrawal. See United States v. Wilson, supra, 134 F.3d at 863 (“The affirmative step required to constitute withdrawal must be either a full confession by the defendant to the authorities, or communication by the defendant of the fact of his withdrawal in a manner designed to reach his co-conspirators.”) (emphasis ours). We may assume that the letter constituted adequate notice to the other defendants that Hopper would no longer be an active member of the conspiracy; but in order to effectuate a legally meaningful withdrawal from the conspiracy, the defendant’s announcement must also “disavow! 1 the conspiracy and its criminal objectives.” United States v. Morales, 655 F.3d 608, 640-41 (7th Cir.2011) (noting defendant never “renounced the goals of the conspiracy”) (citing United States v. Emerson, 501 F.3d 804, 812 (7th Cir.2007)), ce rt. denied, - U.S. -, 132 S.Ct. 1121, 181 L.Ed.2d 1000 (2012). Nothing in Hopper’s letter disavowed or renounced the Aegis system. It expressed Hopper’s disapproval of certain actions Vallone had taken, including what Hopper perceived as Vallone’s behind-the-scenes efforts to undermine the audit representation that Parker & Associates was attempting to provide to Aegis clients. Hopper was of the view that Vallone’s attempts to avoid IRS audits “in all probability will be looked upon by the IRS as obstruction or interfering with the administration of the Internal Revenue Laws.” R. 761-1 at 8. But it voiced no disapproval of the Aegis system or of the validity of the tax returns Aegis clients had been and would be filing based on the use of Aegis trusts. Even as to Vallone’s efforts with respect to the audits, Hopper remarked, “I truly hope that you are successful in your efforts. And I really mean that.” R. 761-1 at 8. This is not the language of renunciation. Because the facts support the district court’s finding that Hopper did not withdraw from the conspiracy early in 2000, it was appropriate to charge Hopper with the additional tax losses that occurred in the 2000 tax year. See U.S.S.G. § lB1.3(a)(l)(A), (B) and (a)(3) (defendant’s relevant conduct includes all harm resulting from his own acts and all reasonably foreseeable acts of others in furtherance of jointly undertaken criminal activity). As there is no dispute that these additional losses caused the total loss amount to exceed $50 million, there was no error in the loss-amount calculation or in the offense-level calculations that turned on the loss amount. C. Use of Guidelines in Effect at Time of Sentencing In calculating Hopper’s offense level, the district court used the 2008 Guidelines in effect at the time of his sentencing rather than the November 2000 version in effect in the waning days of the offense. As was true in Dowd’s case, this worked to Hopper’s disadvantage, in that the newer version of the Guidelines specified a significantly higher offense level for losses in excess of $50 million. Under the November 2000 Guidelines, Hopper’s adjusted offense level would have been five levels lower than it was under the 2008 Guidelines (compare U.S.S.G. § 2T4.1(T) (2000) (specifying a base offense level of 25) with U.S.S.G. § 2T4.RM) (2008) (sped *495 fying base offense level of 30)), which would have resulted in an advisory sentencing range of 135 to 168 months rather than the range of 235 to 293 months that the court referenced. Hopper contends that the court’s use of the newer, and more punitive, version of the Guidelines constitutes a violation of the ex post facto clause of the Constitution. As Hopper acknowledges, our decision in United States v. Demaree, supra, 459 F.3d at 794-95, forecloses his ex post facto argument. Like Dowd, Hopper invites us to reconsider Demaree, but, as we have noted, we have already rejected multiple invitations to do so. E.g., United States v. Wasson, supra, 679 F.3d at 951. D. Sentencing Manipulation Finally, Hopper argues that the government boosted the loss amount, and thus his Guidelines sentencing range, by not acting sooner than it did to stop what the defendants were doing. Hopper notes that Special Agent Priess commenced his undercover investigation of the Aegis CBO scheme in 1996, attended a series of Aegis seminars in that year and the ensuing three years, and (still in his undercover capacity) held conversations with a number of the defendants, tax preparers working with Aegis, and individual taxpayers during that time. No later than 1998, Hopper reasons, the government had all of the information that it needed to conclude that the Aegis system was a criminal tax-avoidance system. Yet, not until March 2000, when it executed the search warrant on Aegis’s headquarters did it begin to signal to the defendants their criminal exposure, and at no time prior to the indictment in 2004 did it seek to enjoin the defendants’ activities. In effect, Hopper suggests, the government engaged in sentencing manipulation by allowing the tax losses resulting from the scheme to continue mounting, exposing him to a much longer sentence as a consequence of the delay. A variation of Hopper’s argument could be made in any number of cases, particularly those involving undercover investigations of large-scale criminal activity with many participants. Typically, the government’s goal is to build a strong evidentiary case that is likely to result in the conviction not just of low-level players but also the leaders and instigators of the scheme; and that takes time. We know of no legal principle that requires the government to intervene to stop ongoing non-violent criminal activity as soon as it arguably has a sufficient case to prosecute the defendants. But the dispositive point is that this circuit does not recognize sentencing manipulation. E.g., United States v. Mandel, 647 F.3d 710, 720 n. 3 (7th Cir.2011); United States v. Long, 639 F.3d 293, 300-01 (7th Cir.2011). Moreover, to the extent Hopper is simply arguing that the government’s delay in intervening to stop the scheme constitutes a factor that should have been considered in mitigation under section 3553(a), we repeat the observation that we made in United States v. Knox, 573 F.3d 441, 452 (7th Cir.2009): “Although the agent’s tactics had the effect of increasing [the defendant’s] guidelines sentencing range, it also served the legitimate purpose of investigating the full extent of [the defendant’s] criminal activity----” (citing United States v. Wagner, 467 F.3d 1085, 1090 (7th Cir.2006) (“It is within the discretion of law enforcement to decide whether delaying the arrest of the suspect will help ensnare co-conspirators, give law enforcement greater understanding of the nature of the criminal enterprise, or allow the suspect enough ‘rope to hang himself.’ ”)). E. Organizer Enhancement The district court increased Hopper’s offense level by four points pursuant to *496 section 3Bl.l(a) of the Guidelines, deeming him an organizer or leader of a criminal activity that involved five or more participants. The court reasoned that Hopper had been the managing director of Aegis, supervised the company’s employees, and ran the day-to-day operations of the business. R. 1085 at 15-16. Hopper concedes that “he was one of the founders of Aegis, shared in monetary distributions];,] and at least until 1998-99 was involved in day-today supervision of the staff.” Hopper Br. 37. On that basis, he agrees that a three-level managerial enhancement would be appropriate. See U.S.S.G. § 3Bl.l(b). But he believes that the more substantial organizer/leader enhancement overstates his actual role in the offense. His role “was much more subsidiary” than those of Vallone and Cover, he posits, Hopper Br. 37: he did not write the Aegis Directors’ Manual, he was not involved with the backdating of trusts or other documents, he was not responsible for the development of either the CBO charitable trust or the foreign trust system, he did not have the working relationship with David Jenkins in Belize that Vallone and Cover did and had only minimal involvement in the foreign trust operation, he had relatively little contact with most Aegis customers, and his role in supervising the staff was much more akin to that of a mid-level manager. Hopper adds that his lesser station in the Aegis power structure is demonstrated by the fact that he was unable to prevail in his opposition to the creation of the Audit Arsenal and the strategy of obstructing IRS audits that Vallone championed. Our review of the district court’s decision to impose the organizer/leader enhancement rather than the managerial enhancement is for clear error, e.g., United States v. Smith, supra, 674 F.3d at 728, and the court did not clearly err in choosing to apply the former. Factors bearing on the appropriate label to give the defendant’s role in the offense “include the exercise of decision making authority, the nature of participation in the commission of the offense, the recruitment of accomplices, the claimed right to a larger share of the fruits of the crime, the degree of participation in the planning or organizing of the offense, the nature and scope of the illegal activity, and the degree of control and authority exercised over others.” § 3B1.1, comment, (n.4). “No one of these factors is considered a prerequisite to the enhancement, and, at the same time, the factors are not necessarily entitled to equal weight.” United States v. Wasz, 450 F.3d 720, 729 (7th Cir.2006) (citing United States v. Matthews, 222 F.3d 305, 307 (7th Cir.2000)). “And although the nature and purposes of the enhancement certainly require the defendant to have played a leading role in the offense, he need not literally have been the boss of his cohorts in order to qualify for the enhancement, for a leader can influence others through indirect as well as direct means[.]” Id. at 729-30. Hopper was a founder and, until 2000, the managing director of Aegis. He held ownership interests in both Aegis and Aegis Management Company. Along with Bartoli and Vallone, he claimed a substantial share of the profits of Aegis, earning over $1.6 million from Aegis and related companies from 1994 through 2000. Gov’t Ex. Hopper Income Summary (Gov’t Supp. App. 200). Hopper and Vallone certainly had their disagreements, and according to Hopper it was ultimately his inability to stop Vallone from attempting to obstruct IRS audits that caused him to leave the company in 2000. But as we have pointed out, as late as November 1999, a resolution adopted by the Aegis Board of Directors (and signed by Hopper) recognized that Hopper shared management authority over the company equally with Vallone and *497 Bartoli. At least until 2000, then, Hopper was at the uppermost echelon of Aegis’s leadership, oversaw the company’s operations, enjoyed a greater share in the income generated by Aegis than everyone but Vallone and Bartoli, and possessed management authority on a level with theirs. All of these facts support the district court’s decision to deem him an organizer or leader of the Aegis scheme rather than a manager. F. Weight Given to Guidelines in Determining Sentence In the wake of Booker, a district court in choosing a reasonable sentence must not presume, as we may, that a sentence within the range advised by the Guidelines is reasonable. See Gall v. United States, supra, 552 U.S. at 50, 128 S.Ct. at 596-97; Rita v. United States, 551 U.S. 338, 351, 127 S.Ct. 2456, 2465, 168 L.Ed.2d 203 (2007). Instead, after ascertaining the Guidelines sentencing range, the court must consult the statutory sentencing factors set forth in section 3553(a) and determine independently what sentence is reasonable. Gall, 552 U.S. at 49-50, 128 S.Ct. at 596; e.g., United States v. Young, 590 F.3d 467, 473-74 (7th Cir.2009); see also United States v. Robertson, 662 F.3d 871, 880 (7th Cir.2011) (“A sentencing court need not comprehensively discuss each of the factors listed in 18 U.S.C. § 3553(a), but it must give the reasons for its sentencing decision and address all of a defendant’s principal arguments that ‘are not so weak as to not merit discussion.’ ”) (quoting United States v. Cunningham, 429 F.3d 673, 679 (7th Cir.2005)). Among other things, section 3553(a) commands that the sentence must be sufficient but not greater than necessary to serve the sentencing aims set out in the statute. E.g., United States v. Pennington, 667 F.3d 953, 957 (7th Cir.2012). Hopper contends that the district court violated this so-called “parsimony” admonition here by giving too much weight to the advisory Guidelines range, which in this case was driven to a significant extent by the loss amount of more than $50 million. The court acknowledged the set of mitigating factors that supported a lower sentence, including the abuse that Hopper had suffered as a child, his military service in Vietnam, the injuries he incurred during that service and the post-traumatic stress disorder he continues to experience as a result of that service, the physical ailments (including degenerative arthritis) from which he suffers, his age (sixty-three at the time of sentencing), his strong relationship with his wife and children, his sincere remorse, and certain efforts he made to rectify his criminal wrongdoing. R. 1085 at 45-48, 50-51, 52. And the court ultimately did impose a sentence thirty-five months below the bottom of the Guidelines range. But, according to Hopper, the court believed itself constrained by the loss amount from deviating too far from the Guidelines range absent a compelling justification for doing so. The court thus committed a legal error, in Hopper’s view, by treating the Guidelines, and in particular the loss amount, as limiting the extent to which it could impose a sentence below the Guidelines sentencing range, even if the mitigating factors otherwise weighed in favor of a substantially below-Guidelines sentence. See, e.g., United States v. Grigg, 442 F.3d 560, 565-66 (7th Cir.2006). We reject this argument. Our review of the sentencing transcript convinces us that the district court merely viewed the loss amount as a significant factor — in the court’s words, “one of the heaviest factors” — that weighed against a lower sentence, not one that tied the court’s hands. R. 1085 at 44. The court expressly acknowledged that it could not presume a *498 sentence within the Guidelines range to be appropriate, see id. at 44-45, acknowledged its duty to consider the section 3553(a) factors, id. at 45, and proceeded to give careful attention to those factors, see id. at 45-53. As Hopper acknowledges, the court recognized and took into consideration the many factors that weighed in Hopper’s favor, id. at 45^48, 50-51, 52, and in fact chose to impose a sentence that was nearly three years below the minimum sentence of 235 months recommended by the Guidelines. The court simply did not believe that an even lower sentence was warranted given the scope of the loss resulting from Hopper’s offense. The court did not misunderstand its own authority nor did it commit any other form of error. G. Reasonableness of the Sentence Finally, Hopper challenges the reasonableness of the sentence that the district court imposed on him. The court ordered Hopper to serve a sentence of 200 months. Although the sentence was 35 months below the low end of the range advised by the Guidelines, Hopper nonetheless contends it was excessive and therefore unreasonable. Hopper emphasizes the mitigating factors that the district court itself acknowledged in arriving at the sentence and which we have already mentioned. For a man in his sixties, Hopper argues, a 200-month sentence is a life sentence. In arriving at that sentence, Hopper again argues, the district court was fixated on the loss amount to the exclusion of the many mitigating factors which demonstrate that a much lower sentence would be reasonable. As a below-Guidelines sentence, Hopper’s sentence is presumptively reasonable, e.g., United States v. Russell, supra, 662 F.3d at 853, and Hopper has not succeeded in rebutting that presumption. We acknowledge that the sentence will require Hopper to spend most, if not all, of his remaining years in prison. See id. at 852-53. However, his offense was one that took place over a substantial period of time, enticed over six hundred taxpayers into a fraudulent scheme of tax evasion, and resulted in tens of millions of dollars of lost revenue to the government. We have no reason to question the sincerity of the remorse that Hopper expressed at sentencing, but Hopper’s offense evidenced much more than a fleeting lapse in judgment: Beginning in 1994, Hopper knowingly and willfully engaged in a scheme to defy the tax laws and defraud the government; and he had continued to perpetrate the scheme even as he was repeatedly put on notice that what he and his co-defendants were doing was illegal. Hopper, being at the head of the scheme along with Bartoli and Vallone, was well situated to appreciate the magnitude of the fraud he and his codefendants were perpetrating. Tax evasion has a long and storied history in this country, and Hopper joins a long list of practitioners that includes AI Capone, Spiro Agnew, and Leona Helmsley. But the scheme that Hopper and his partners perpetrated was particularly insidious. Perhaps a different judge might have deemed a more modest sentence sufficient to serve the aims of sentencing set forth in section 3553(a)(2). But examining Hopper’s sentence pursuant to the deferential, abuse-of-discretion standard, see Gall, 552 U.S. at 51, 128 S.Ct. at 597, we cannot say that it was unreasonable. DUNN A. Treatment of the Guidelines Dunn’s opening contention is that the district court committed legal error in treating the Guidelines as mandatory. As we have discussed, after Booker, the Guidelines are advisory rather than mandatory. The district court’s ultimate obli *499 gation is to impose a sentence that is reasonable in light of the factors set forth in section 3553(a), e.g., United States v. Young, supra, 590 F.3d at 473-74; and although the court is obliged to properly apply the Guidelines, Gall v. United States, supra, 552 U.S. at 49, 128 S.Ct. at 596, and to consider the resulting Guidelines sentencing range in arriving at a reasonable sentence, Freeman v. United States, — U.S. -, 131 S.Ct. 2685, 2692, 180 L.Ed.2d 519 (2011) (“the judge will use the Guidelines range as the starting point in the analysis”), it must do so without placing a “thumb on the scale favoring a guideline sentence,” United States v. Sachsenmaier, 491 F.3d 680, 685 (7th Cir.2007). Dunn contends that a thumb in favor of the Guidelines is evidenced in this case by the district court’s remark that the base offense level resulting from a $60 million loss “doesn’t give much latitude in terms of the ultimate sentence in the case.” R. 1086 at 29. The district court made that remark not long before it began to go through the various section 3553(a) sentencing factors, and Dunn suggests that the context of the remark suggests that the district court had already determined that it was effectively required to impose a sentence consistent with what the Guidelines advised. But we do not believe that the district court was operating under any misconception that it was bound by the Guidelines. Although the court’s use of the term “leeway” is somewhat similar to the language of obligation that we have said is inconsistent with a court’s duty after Booker to treat the Guidelines as a reference point but not as a mandate, e.g., United States v. Pennington, supra, 667 F.3d at 958 (court stated it must “follow” the Guidelines), in context it is clear that the court in no sense was treating the Guidelines as either binding or presumptively correct as to the recommended sentence. Much as it had with Hopper, the court noted that the key factor in determining Dunn’s base offense level under the Guidelines was the size of the tax loss, and it was in view of the size of that loss that the court saw little justification for imposing a sentence below the Guidelines range. R. 1086 at 27-28, 29, 35. The balance of the court’s sentencing remarks make clear that the court was wholly aware that it had both the authority to impose a non-Guidelines sentence as well as the duty to determine a reasonable sentence independent of what the Guidelines recommended. Id. at 30-31. The court considered the full range of the factors that Dunn’s counsel had cited in support of a below-Guidelines sentence — including his challenging youth, his ethic of hard work and self-improvement, his friendship and generosity to others, and his reputation as a good and honest man. Id. at 32-33. Still, the court believed that “the nature and the circumstances of the offense,” id. at 32, including the “extremely conservative figure” of the $60 million loss, id. at 28, outweighed these mitigating factors, id. at 33. The court emphasized that “[t]his was not a simple, one-time impulsive act,” id., and pointed out that Dunn had shown no remorse, id. at 34. Ultimately, the court found, in light of the statutory sentencing factors, that the Guidelines range was “a fair range,” id. at 34, and imposed a sentence at the bottom of that range. B. Amount of Loss As noted, the district court held Dunn responsible for a loss amount of $60 million — i.e., the full amount of the loss resulting from the Aegis scheme. Dunn challenges the loss amount on two grounds. First, he questions the accuracy of the method that the government used to calculate the total loss, which loss the district court cited as an “overriding consider *500 ation” in determining his sentence. At trial, Agent Welch acknowledged that he could not accurately calculate the actual tax loss for every Aegis client, R. 963 Tr. 4851, 17 and that “[r]easonable people could differ” on the best way to calculate that loss, R. 973 Tr. 5038. Welch had opted to estimate the loss by multiplying each taxpayer’s income by twenty-eight percent, the lowest of the federal income tax rates. R. 963 Tr. 4851-52. As Dunn points out, this is not a method that has been generally accepted in the accounting profession or by the IRS, but one that Welch nonetheless decided to follow in this case. R. 973 Tr. 4978-80. Dunn also adds that in the case of one Aegis client, the IRS ultimately accepted a settlement that was a fraction of the tax loss that Welch himself had estimated. R. 973 Tr. 5035-36. In Dunn’s view, all of this calls into question the reliability of the method by which the total tax loss in this case was arrived at. Second, the total loss included tax losses incurred after Dunn left Aegis in the spring of 2000. Dunn contends that his departure constituted a withdrawal from the conspiracy and that he should not be held liable for subsequent tax losses. Had those later losses been excluded from the calculation, the total tax loss, according to Dunn, would have come to less than $50 million and resulted in a lower Guidelines offense level and thus a lower (advisory) sentencing range. As Dunn acknowledges, neither of these contentions was made in the district court, where Dunn did not challenge the loss amount, so our review of the loss calculation is for plain error alone. E.g., United States v. Jumah, 599 F.3d 799, 811 (7th Cir.2010). There was no such error here. The Guidelines themselves recommend use of the twenty-eight percent rate in estimating the loss amount in tax fraud cases. U.S.S.G. § 2Tl.l(c)(l)(A). Assuming that the income of each Aegis client would have been taxed at a rate of twenty-eight percent is, if anything, a conservative approach, as it is entirely possible that the income of some clients would have exceeded the twenty-eight percent tax bracket and would therefore have been subject to a higher marginal rate. Indeed, given the evidence that Aegis targeted high income individuals, this may be more of a likelihood than a mere possibility. See R. 963 Tr. 4852-55. Thus, even recognizing, as Welch himself did, that reasonable people might differ as to the best way of determining a tax loss in this case, it does not follow that there was an obvious flaw in the approach that Welch followed. See United States v. Julian, 427 F.3d 471, 482 (7th Cir.2005) (plain error is one that is obvious in retrospect); United States v. Mandel, supra, 647 F.3d at 722-23 (divergent holdings among courts demonstrate that any error district court may have committed was not plain). Nor does the fact that the IRS in one case settled an audit for a figure far less than the amount that Welch had estimated as the loss call into question the reliability of his calculations. As the government points out, the IRS might choose to accept a settlement far below the estimated tax due for any number of reasons. The record as to this one case is insufficient to cast doubt on the loss amount figure that the district court employed. Second, although Dunn terminated his employment with Aegis, he did not legally withdraw from the conspiracy. As we have already discussed with respect to Hopper, a legally effective withdrawal re *501 quires more than merely ceasing one’s active involvement; one must also renounce the aims of the conspiracy. E.g., United States v. Morales, supra, 655 F.3d at 640-41. This Dunn never did. Indeed, although Dunn indicated to others (including Parker) in the spring and summer of 2000 that he would no longer be taking on new Aegis clients, he also indicated that he would continue to service existing clients. R. 947 Tr. 1995; R. 909 Tr. 5872-73, 5876. Consequently, Dunn is responsible for all harm that was the result of his acts up to that point, see U.S.S.G. § 1B1.3(a)(1)(A) & (a)(3); and, at a minimum, the filing of fraudulent tax returns for 2000 was certainly both foreseeable to Dunn and in furtherance of the criminal activity he had previously undertaken with his co-eonspirators, see lB1.3(a)(l)(B). As we have pointed out before, the filing of tax returns that minimized or eliminated a taxpayer’s taxable income was the entire point of the Aegis system that Dunn and others marketed. It would thus have been entirely foreseeable to Dunn, as someone who sold Aegis trusts and provided follow-up trust management services to purchasers, that the clients of Aegis would be filing fraudulent tax returns which were based on the use of Aegis trusts. As with Hopper, even if the losses associated with the 2001 and 2002 tax years are excluded, the total loss still exceeded $50 million, which was the threshold for the base offense level of 30 that the district court referenced in this case. See U.S.S.G. § 2T4.1(M). C. Role in the Offense Pursuant to Guidelines section 3Bl.l(b), the district court enhanced Dunn’s offense level by three points for being a manager or supervisor. R. 1086 at 4-5, 29. Dunn contends on appeal that the court clearly erred in applying this enhancement, because he in fact played no managerial or supervisory role in the Aegis scheme. Dunn contends that he did not oversee any other participant in the scheme, did not manage any Aegis assets or activities, did not possess any decision-making authority as to the scheme’s goals or means of attaining those goals, and did not help to plan or organize the offense. He was merely “a salesman following orders,” Dunn Br. 16, playing a relatively minor role in a fairly extensive organization. Our review is again one for clear error. United States v. Smith, supra, 674 F.3d at 728. The court did not clearly err in treating Dunn as a manager or supervisor. The court appears to have based the enhancement in part on a finding that Dunn recruited attorney Parker into the scheme. R. 1086 at 4-5; see § 3B1.1, comment. (n.4) (citing the recruitment of accomplices as a relevant factor in determining whether leadership enhancement appropriate); e.g., United States v. Cerna, 676 F.3d 605, 608 (7th Cir.2012). Dunn contends that it is implausible to say that he recruited Parker, given Parker’s acknowledgment at the trial that it was his brother-in-law, Dennis Repka, a retired judge, and not Dunn, who introduced him to the Aegis system of trusts in June 1996. R. 913 Tr. 1939. But Dunn omits the material fact that Parker did not actually become involved in the conspiracy and scheme until Dunn asked him in March 2007 if he would be interested in creating CBO trusts for Aegis and offered to pay him $1,000 for each Aegis closing that he handled. R. 961 Tr. 1832, 1836-37. Parker accepted the offer. Parker also testified that he completed the paperwork for approximately fifteen closings for Dunn following the instructions that Dunn gave him as to how the documents should be dated. R. 961 Tr. 1839; R. 1014 Tr. 1879-80. The district court therefore had a sound evidentiary basis for finding that Dunn had in fact *502 successfully recruited Parker into the scheme. Moreover, as the government points out, Dunn reaped some $1.5 million in income from the scheme, which was a relatively large share of the income generated by the conspiracy — on par with Hopper’s share, for example. Gov’t Ex. Dunn Income Summary (Gov’t Supp. App. 151); see § 3B1.1, comment, (n.4) (citing claimed right to larger share of proceeds as a hallmark of leadership role). And, in contrast to other low-level players, Dunn did attend and participate in some policy meetings with Vallone, Bartoli, and Hopper. R. 913 Tr. 1951-59. These included the meetings (described by Parker) that took place among the Aegis principals in the summer and fall of 1999 to discuss how Aegis should proceed in light of the Muhich decision. R. 913 Tr. 1951-59. This evidence defeats any contention that it was clear error to recognize that Dunn played a more culpable role in the conspiracy by deeming him a manager or supervisor for sentencing purposes. D. Reasonableness of the Sentence The district court ordered Dunn to serve a prison term of 210 months, a sentence at the bottom of the range recommended by the Guidelines. Dunn contends that the sentence is substantively unreasonable, because the district court either failed to consider or did not give appropriate weight to a number of the factors identified as relevant by section 3553(a), including Dunn’s background and characteristics, the sentences imposed on his co-defendants, and the nature and severity of his offense. First, given his age at the time of sentencing (forty-nine), Dunn argues that a sentence of seventeen years is effectively a life sentence. By contrast, he notes, the District of Columbia Circuit upheld a sentence of 108 months for an individual it characterized as possibly “the largest tax evader in the history of the country.” United States v. Anderson, 545 F.3d 1072, 1073-74 (D.C.Cir.2008) (loss amount exceeding $100 million). Even that sentence represented a substantial upward variance from the high end of the range recommended by the version of the Guidelines that the defendant argued was applicable. Still, it is little more than half of the penalty imposed on Dunn. Second, Dunn points out that the defendants in this case faced basically the same set of charges and all had the same lack of prior criminal history, yet there are significant disparities in the sentences they received. For example, Dunn’s sentence was ten months longer than that of Hopper, who was convicted of twenty-six counts to Dunn’s fifteen and was one of the Aegis principals. Dunn was also ordered to serve fifty more months than Cover; and his sentence is almost twice as long as that of Bartoli, who conceived of the scheme. Third, Dunn points out that the district court held Dunn culpable for the full breadth of the scheme and ignored his purported withdrawal in 2000. Dunn’s sentence is at the bottom of the Guidelines range, which was properly calculated, so we presume that it is reasonable, e.g., United States v. Fouse, 578 F.3d 643, 654-55 (7th Cir.2009); and Dunn has not persuaded us that it is otherwise when examined against the sentencing factors identified in section 3553(a), see United States v. Mykytiuk, 415 F.3d 606, 608 (7th Cir.2005). As to the sentences of his co-defendants: Bartoli and Cover were each given significant reductions in their sentences either because of their advanced age: Bartoli was eighty years old when he was sentenced and Cover was seventy-two. Even so, their sentences are much more likely to be life sentences than Dunn’s is: with credit for good time, Dunn will be in his mid- *503 sixties when he completes his sentence— younger than either Bartoli or Cover were when they began serving their terms. Hopper, although his sentence is still slightly longer than Dunn’s, was also given a significant reduction based on his military service and what the court found to be his genuine remorse, as well as his age (sixty-three). The disparities that Dunn cites are thus the result of the district court’s legitimate and reasonable attempt to recognize both the greater culpability of Dunn’s co-defendants along with mitigating factors that are not present in Dunn’s ease. Dunn’s observation that his sentence is nearly twice the term imposed on the defendant in Anderson, the D.C. Circuit case is explained by a number of distinctions, including most prominently the fact that the 2000 version of the Guidelines under which Anderson was sentenced were significantly more lenient as to large-scale tax frauds. That is why a number of Dunn’s co-defendants have made ex post facto arguments with respect to the district court’s use of the 2008 Guidelines in sentencing them. The lesser sentence imposed (and sustained) in Anderson thus does not call into question the reasonableness of Dunn’s sentence. Nor does the fact that the court in sentencing Dunn held him to account for all of the consequences of the conspiracy, including the total loss amount, give us pause. Dunn contends that his liability should have ended with his purported withdrawal in June 2000. But as we discussed above, Dunn never legally withdrew. He stopped selling Aegis trusts in June 2000 at the request of his employer, the financial services firm SunAmerica, but he continued to service existing clients. At the same time, he never took steps to renounce the aims of the conspiracy. 18 The fact that fraudulent tax returns based on Aegis trusts would continue to be filed after his involvement wound down was both foreseeable to Dunn and, to a meaningful degree, the natural consequence of his earlier acts in marketing Aegis trusts and providing trust management services to Aegis clients. Dunn promoted and sold Aegis trusts, but that was not the extent of his involvement in the Aegis scheme. He also gave instructions to tax preparers as to how tax returns should be prepared in light of the Aegis trusts. He was one of the plaintiffs in the frivolous lawsuit filed against the ARDC. He participated, as we have noted, in Aegis policy meetings. As the district court noted, Dunn, in contrast to Bartoli, Vallone, and Hopper, already had successful employment with SunAmerica when he became involved with Aegis and so, arguably, should not have been as susceptible to a lucrative fraud. Like other defendants, Dunn used the Aegis system to dramatically under-report his taxable income: he reported income of only $16,000 in 1997 and $9,000 in 1998, for example, when his actual income in those years was roughly $400,000 and $600,000, respectively. R. 1086 at 28; Gov’t Ex. Dunn Income Summary (Gov’t Supp. App. 151). There were mitigating factors which the district court noted and considered, including Dunn’s financially difficult childhood, putting himself through school, caring for his mother until her death (Judge Norgle characterized Dunn as “an extremely good son,” R. 1086 at 32), and his readiness to help others. Yet, as the court noted, Dunn’s involvement in this extensive crime was anything but a one-time, impulsive act. *504 We cannot characterize the sentence imposed on Dunn as unreasonable. E. Fifth and Sixth Amendments and Notice-to-One Dunn repeats and expands upon an argument that the defendants made jointly: that the district court improperly treated notice of the trusts’ illegality received by one defendant as notice to the conspiracy and thus notice to all of the conspiracy’s members. Dunn contends that the court’s erroneous ruling relieved the government of the burden to show that Dunn himself realized that the Aegis trusts were a sham and yet participated in the conspiracy and marketed the trusts to clients with that knowledge, and with the intent to defraud the government and/or violate the tax laws. In effect, Dunn posits, the court eliminated an element of the government’s burden of proof and simultaneously eliminated the presumption of innocence as to that element, forcing Dunn to offer proof (e.g., by cross-examining government’s witnesses) that he did not knowingly become a party to an unlawful agreement. His conviction on the conspiracy charge, Dunn maintains, was obtained in violation of his Fifth Amendment right to due process and his Sixth Amendment right to a jury finding as to his guilt or innocence. Our prior discussion of the defendants’ joint argument on this point disposes of Dunn’s individual claim. So far as we can determine, the district court voiced its notice-to-the-conspiracy rationale solely to counsel at sidebar in the context of admitting certain evidence: neither Dunn nor the defendants collectively have been able to point to any instance in which this rationale was communicated to the jury. Consequently, the jury was never erroneously informed, whether by way of a formal instruction or otherwise, that it could presume Dunn’s knowledge of the illegality of the Aegis scheme based on evidence that Bartoli or Vallone knew that the Aegis trusts were a sham, for example. And although Dunn suggests that the court’s ruling relieved the government of the burden to show that Dunn became a party to the conspiracy with knowledge that the Aegis system was unlawful, there is no evidence that the government itself ever argued to the jury that simply because another defendant had notice of the illegality that Dunn necessarily did as well. Instead, as it did with each of the six defendants, the government made a case that Dunn himself knew, based on the facts surrounding the trusts and on the notice that he individually received, that the trusts were a sham and that he was acting with an intent to defraud the government and to violate the federal income tax laws. R. 923 Tr. 6808-24; R. 911 Tr. 6827-71. Whatever possible misconceptions the district court may have held and communicated to counsel, the jury was properly instructed on the law (e.g., to give separate consideration both to each count and to each defendant, R. 925 Tr. 7389) and on the government’s burden of proof, and Dunn was not deprived of his Fifth or Sixth Amendment rights. 19 F. Denial of Severance Dunn contends that the district court abused its discretion in denying him a separate trial. Like Dowd, Dunn sought to sever his own trial from that of his co-defendants. R. 391. Dunn’s theory was that his defense was antagonistic to his co-defendants in the sense that he was an outsider vis-a-vis Aegis (in that he was an outside salesperson rather than an employee or officer of Aegis), did not truly believe *505 in the Aegis trust system, and lacked the history that his co-defendants Bartoli, Val-lone, and Hopper had of refusing to file any tax returns. He also suggested that in a separate trial, he could call Bartoli as a witness to testify that he had relied in good faith on Bartoli’s representations as to the legitimacy of the Aegis system. The court denied the motion in advance of the trial and again when Dunn renewed it during the direct examination of the government’s final witness. But Dunn did not renew the motion at the close of evidence. Dunn now contends that the court’s refusal to grant him a separate trial, coupled with the court’s erroneous notice-to-the-conspiracy rationale, deprived him of an individual assessment of his knowledge of the illegality of the Aegis scheme (and thus of his guilt or innocence) and a fundamentally fair trial. However, as we noted earlier with respect to Dowd, the failure of Dunn’s counsel to renew the motion to sever at the close of evidence resulted in a waiver of this issue that renders the district court’s ruling unreviewable. United States v. Phillips, supra, 239 F.3d at 837-40. Dunn has made no attempt to show that it would have been futile for him to renew his motion and his arguments in support thereof at the close of evidence. In any case, for the reasons we have already discussed, the district court’s notice-to-one/notice-to-theconspiraey rationale, which is the principal if not sole basis on which Dunn argues that the joint trial worked to his substantial prejudice, did not in fact deprive Dunn or any other defendant of a fair trial. G. Sufficiency of the Evidence: Fraudulent Tax Returns Finally, Dunn contends that the evidence was insufficient to establish his guilt on the charges that he aided, counseled, or otherwise encouraged the preparation of false or fraudulent income tax returns in violation of section 7206(2). Much like Hopper’s challenge on this point, Dunn’s appeal presumes that the government was required to show that he had some kind of personal involvement in the preparation of the fraudulent tax returns in order for him to be held liable under section 7206(2). Dunn concedes that there was a videotape of him remarking at an Aegis seminar that he had to give direction to tax preparers, but he contends that this has been taken out of context. He emphasizes the lack of any evidence as to what he might have said to any tax preparer, for example. No such tax preparer ever testified; and, for that matter, no Aegis client whose false returns Dunn was found guilty of aiding or assisting ever testified that Dunn was involved in the preparation of those returns. In short, the jury could only speculate as to what role he may have played in the preparation of any tax return other than his own, and in Dunn’s view the evidence thus was insufficient to support his convictions under section 7206(2). 20 That Dunn did not prepare any of the charged tax returns himself does not preclude his convictions under section 7206(2). United States v. Hooks, supra, *506 848 F.2d at 791. The plain language of the statute states that a person need only knowingly assist or advise the preparation or presentation of a false tax return in order to be liable. United States v. Clark, 577 F.3d 273, 285 (5th Cir.2009). It is worth repeating Hooks ’ observation that “ ‘the scope of the statute extends to all participants of a scheme which results in the filing of a false return, whether or not those parties actually prepare it.’ ” 848 F.2d at 791 (quoting United States v. Siegel, supra, 472 F.Supp. at 444); see also United States v. Fletcher, 322 F.3d 508, 514-15 (8th Cir.2003) (coll, cases). This includes individuals who help to promote a tax avoidance scheme, as the Eighth Circuit concluded in Fletcher. The defendant in that case had given a series of seminars to promote the services of a tax consultation and preparation company, James Otis & Company (“JO & C”), which advised its clients in the use of trusts and other vehicles as a means of allowing individual taxpayers to write off ordinary personal expenditures as business expenses— a fraudulent scheme not so different from the one that the defendants promoted in this case. Although the defendant had not actually prepared tax returns, the court nonetheless sustained his convictions under section 7206(2) based on the false tax returns that had been filed on behalf of two individuals, James and Ginger McNair, that he had successfully recruited as clients of the tax consulting company at one of his seminars. “It was as a result of attending Mr. Fletcher’s seminar in 1994 that the McNairs retained JO & C to implement Mr. Fletcher’s tax strategy of converting ordinary personal expenses into business expenditures,” the court pointed out. Id. at 515. From this fact, along with Fletcher’s efforts on one occasion to allay the clients’ subsequent concerns as to the legitimacy of the scheme, the court found it reasonable for the jury to conclude that he had willfully aided in, assisted, procured, counseled, or advised the preparation of the false or fraudulent tax returns filed by those clients. Id. The filing of false tax returns was, as the government argues, the “essence” of the tax-avoidance scheme that Dunn and the other defendants perpetrated. The Aegis trusts were marketed to clients as a means through which they could substantially reduce, if not eliminate, their individual income tax liability. The filing of federal income tax returns purporting to accomplish that end was thus the natural, inevitable, and entirely foreseeable result of what Dunn and his co-conspirators were doing. Dunn, as a promoter of the Aegis system, regularly spoke with prospective clients about the sorts of deductions they would be able to take on their tax returns by making use of the Aegis trusts and the significantly reduced taxes they would pay as a result. To cite one example, Dunn client David Vermeulen testified that in the fall of 1995, Dunn had told him that he would “pay a lot less in taxes” by using the Aegis system and could use the tax savings to buy a motorcycle, boat, or other “toy[ ].” R. 915 Tr. 2472. Dunn also boasted to Agent Priess, who posed as prospective client Mike Jordan, that another client had saved $300,000 in taxes in just one year by using the offshore version of the Aegis system. R. 965 Tr. 289-90. In other (covertly recorded) conversations, Dunn and Priess discussed the types of deductions that Priess might take on his tax returns, how much income Priess should report as salary on his individual returns, how he might make use of a charitable trust, and other issues related to the tax returns that Priess would be filing once he began using the Aegis system. R. 943 Tr. 221-23; R. 965 Tr. 338-39. The sorts of conversations that Dunn had with Priess were typical of the interactions that *507 Dunn and his coconspirators had with existing and prospective Aegis clients. E.g., R. 959 Tr. 931-32; R. 946 Tr. 1102, 1105; R. 967 Tr. 1560, 1574-76. Dunn also addressed similar topics at the Aegis promotion seminars in which he participated. An excerpt from one videotaped seminar was played for the jury at trial. After speaking at length about how an Aegis client’s tax return would look after taking various deductions, exemptions, and so forth, Dunn concluded: “So how much tax do we pay once we’re set up in this fashion!?] How much tax do you wanna pay? (Audience laughter.)” R. 914 Tr. 2315-16; Gov’t Ex. Coleman Tr. 17 (Gov’t Supp. App. 101). Evidence along these lines is more than sufficient to support a finding that Dunn, in marketing and managing Aegis trusts, not only envisioned but promoted the fraudulent tax returns that Aegis clients ultimately filed based on those trusts. The fact that Dunn had the descriptor “Tax Engineering Services” printed on his Aegis Management Company letterhead, R. 965 Tr. 285; Gov’t Ex. Priess 6, is just one more indication that he knew full well that what he was providing to Aegis clients was a means of reducing their tax liability. In addition to the foregoing evidence, there was additional evidence that the defendants — including Dunn- — had at least some involvement in the preparation of tax returns for Aegis clients. Recall that Aegis required its clients to use a tax preparer pre-cleared by Aegis for at least one year following their purchase of an Aegis package. R. 965 Tr. 283; R. 944 Tr. 423; R. 918 Tr. 4312; R. 921 Tr. 5428-29. One could infer from that requirement that the defendants were interested in making sure that tax returns would be prepared by preparers who were, shall we say, sympathetic to the Aegis philosophy. Beyond that, there was evidence that Dunn, among other defendants, regularly gave advice to tax preparers and accountants as to how a client’s income and expenses should be treated on tax returns. Dunn himself remarked at a May 1997 seminar that “because many accounting people are unfamiliar with the process, we are getting to a point where we almost have to become CPAs in addition to attorneys to be able to teach them how to do the accounting work.” R. 914 Tr. 2315; Gov’t Ex. Coleman Tr. 16 (Gov’t Supp. App. 100). Dunn urges us not to put too much weight on that particular remark. But even if we discard the inference that Dunn himself was one of the individuals advising others as to the way in which tax returns should be prepared, Dunn’s remark at the seminar, much like his recorded remarks to Priess about the deductions Priess would be able to take, demonstrates Dunn’s awareness that his own actions in promoting and managing Aegis trusts would lead directly to the preparation and filing of tax returns that reflected what he was saying and doing in furtherance of the charged conspiracy. Just as in Fletcher, the jury could reasonably find, based on the steps that Dunn took to promote, sell, and manage Aegis trusts, that Dunn willfully aided in, assisted, procured, counseled, or advised the preparation of the false or fraudulent tax returns filed by the clients he recruited and served. H. Venue in the Northern District of Illinois Dunn contends that as to six of the false tax return counts in which he was charged, venue was not proper in the Northern District of Illinois. Generally speaking, a defendant is to be tried in the district where the alleged offense was committed. U.S. Const, art. III, § 2, cl. 3; Fed. R.Crim.P. 18. But an offense that involves multiple steps or continues over a period of time may occur in multiple districts. *508 Venue as to that type of offense is proper “in any district in which such offense was begun, continued, or completed.” 18 U.S.C. § 3237(a). The preparation of a false tax return can be a multi-district offense, as the return may be prepared in one district, subscribed to in another district, and filed in a third district; venue would thus be appropriate in any of these districts. United States v. Mammon, 832 F.2d 1465, 1475 (7th Cir.1987). Dunn acknowledges this point, but contends that the government did not present evidence sufficient to establish where the relevant acts underlying a particular tax return took place. Viewing the record in the light most favorable to the government, e.g., United States v. Ochoa, 229 F.3d 631, 636 (7th Cir.2000), we are satisfied that a preponderance of the evidence, see id., confirms the propriety of venue in the Northern District of Illinois as to each of the counts in question. Counts 24 through 26 of the indictment were based on the 1997-1999 tax returns filed for Bruce and Tammy Groen, who were clients of Dunn. Although, as Dunn reminds us, the Groens themselves did not testify, the evidence admitted at trial showed that all three returns were prepared and signed by CPA Laura Baxter, as evidenced not only by the returns themselves but also the recovery of many documents related to those returns from Baxter’s office files, and Baxter’s office was located in Frankfort, Illinois — a municipality within the Northern District of Illinois. The evidence thus readily supported the inference that all three returns were prepared and subscribed to by their preparer in the Northern District of Illinois. Counts 33 and 34 were based on the 1997 and 1998 tax returns filed for Dunn clients John and Colleen McNinney. Like the Groens’ returns, these returns were prepared and signed by Baxter, as evidenced by the returns themselves as well as documentation recovered from Baxter’s office in the Northern District of Illinois. Finally, Counts 46 and 47 were based on Dunn’s own returns for 1997 and 1998. Those returns were prepared and signed by CPA Robert Clausing, as evidenced by his signature on the returns as well as extensive documentation recovered from his office. Clausing’s office was in Lansing, Illinois — again, within the Northern District. The evidence was thus more than sufficient to establish that each of these counts was based on acts which took place within the Northern District of Illinois. Venue was therefore proper in that district. BARTOLI A. Competency to Stand Trial Bartoli contends that the district court erred in refusing to appoint a defense expert to assess his competency to stand trial and to conduct a proper competency hearing before commencing with the trial. Although Bartoli was examined by an expert agreed to by both Bartoli and the government, and that expert concluded that Bartoli was competent, Bartoli suggests that the court breached an earlier promise to appoint a defense expert and, in any case, should have conducted an evidentiary hearing before declaring him competent to stand trial. Bartoli’s counsel first sought a competency assessment pursuant to 18 U.S.C. § 4241(a) in December 2007. Counsel had became concerned that Bartoli, then seventy-eight years old, was exhibiting poor memory and irrational beliefs about the Tax Code. He then learned that Bartoli had been preliminarily diagnosed with vascular dementia or early-stage Alzheimer’s Disease. R. 321. The court granted the request for an evaluation, but, in the exercise of its authority under 18 U.S.C. *509 § 4247(b), ordered that Bartoli be committed to the custody of the Bureau of Prisons (“BOP”) for purposes of an inpatient evaluation by a BOP physician. R. 324; see United States v. Shawar, 865 F.2d 856, 860 n. 4 (7th Cir.1989). At the government’s suggestion, the court also recommended that Bartoli be committed to the U.S. Medical Center for Federal Prisoners in Springfield, Missouri, for evaluation by Dr. Robert L. Denney, a forensic psychologist and neuropsychologist. R. 324 at 2 ¶ 7. The court advised Bartoli’s counsel that if the government’s physician deemed Bartoli competent, the court would appoint another expert of defendant’s choosing to conduct a second examination. R. 1042 at 14. Bartoli, who was unwilling to be committed to a BOP facility for purposes of the evaluation, moved for reconsideration, R. 329, arguing that the government had not shown, and the court had not found, that it was necessary for Bartoli to be committed to BOP custody for purposes of the evaluation. The court denied the request for reconsideration in relevant part. R. 336; R. 1044. Bartoli then appealed the district court’s order to this court. R. 344. However, that appeal was dismissed on the joint motion of the parties, R. 358, after they reached an agreement for Bartoli to be evaluated on an outpatient basis by Diana B. Goldstein, Ph.D., Director of Neuropsychology with the Isaac Ray Forensic Group in Chicago. On remand, the district court acceded to the parties’ choice of Dr. Goldstein. R. 362; R. 363; R. 1010. Dr. Goldstein evaluated Bartoli and on February 14, 2008, issued a detailed, fifteen-page report setting forth her determination that Bartoli was competent to stand trial. R. 1090-1. Among her findings: Bartoli’s cognitive functioning was not significantly impaired; medical tests revealed the beginnings of small vessel disease that ultimately could disrupt optimal brain function; Bartoli demonstrated a full understanding of both the nature of the charges against him and the court proceeding, and was able to fully participate in that proceeding and collaborate with his counsel; and although Bartoli exhibited some fatigue and diminished ability to concentrate at the end of the day, this should not interfere with his ability to work with his attorney on his defense. Id. at 11-13. On learning that Goldstein’s report would deem Bartoli fit for trial, Bartoli’s counsel filed a motion requesting the appointment of two physicians so that a second assessment could be performed. R. 412. The motion also requested a continuance of the trial date (February 19, 2008), to accommodate both the additional assessment and, in the event that assessment reached a different conclusion than the first, a competency hearing before the court. The court denied the request. R. 416. At the hearing on the motion, the court observed preliminarily that Goldstein had been selected “by agreement of counsel and as an alternative or as a compromise to having Mr. Bartoli go to the Bureau of Prisons.” R. 1051 at 69. The court then proceeded to independently consider whether a second evaluation was warranted and should be ordered in the exercise of its discretion. See United States v. Andrews, 469 F.3d 1113, 1121 (7th Cir.2006). The court remarked that Goldstein’s report was comprehensive, “one of best I have seen in a long time.” R. 1051 at 74; see also id. at 69, 72, 73. It noted that Goldstein’s assessment was based on a substantial series of tests, and that much of the material she had considered in evaluating Bartoli’s competency had been provided by Bartoli’s counsel. Bartoli’s counsel himself conceded that Goldstein’s examination of his client “was comprehensive and thorough.” Id. at 77. Under these circumstances, the court saw no need for a second evaluation: *510 So I think that’s the key here. If the Court were not confronted with such a comprehensive in-depth report, which involved testing by an eminently qualified forensic group, I would be inclined to say a second expert should be brought into the case. And so the expert, Dr. Goldstein, has taken into account all of the submissions of Dr. Bartoli, and she certainly has gone well beyond all of that in her analysis and the testing procedures. So the motion for a second testing is denied. R. 1051 at 77. Subsequently, at the start of the trial, the court expressly found Bartoli competent to stand trial, taking into consideration Dr. Goldstein’s report as well as everything that had been presented by Bartoli’s counsel. R. 988 Tr. 7. The decision whether or not to order a competency examination is one that we review for abuse of discretion, see Andrews, 469 F.3d at 1121, and the court in this instance did not abuse its discretion by refusing the appointment of additional physicians for purposes of a second assessment. The premise for Bartoli’s contention that the court was obliged to order a second evaluation is not that there was some deficiency in Dr. Goldstein’s evaluation, which Bartoli’s lawyer agreed was thorough and comprehensive, but rather that the court had originally committed to the appointment of a second expert and examination in the event that the first expert found Bartoli competent. But the court made that commitment in the context of ordering that Bartoli first be examined by an expert of the government’s choosing at a BOP facility. The context changed significantly when, for purposes of resolving Bartoli’s appeal of the court’s order, the parties agreed that Bartoli would be examined by an expert — Dr. Goldstein — acceptable to both of them. Thus, the district court’s understanding— one that we share — was that Dr. Goldstein was not the government’s expert, but an independent expert submitted to by agreement. Because Dr. Goldstein was appointed by agreement of the parties, fairness no longer dictated that a second expert be permitted as a matter of course in the event that Bartoli was dissatisfied with the results of the first examination. Once Dr. Goldstein concluded that Bartoli was competent, the pertinent question vis-á-vis the need for a second expert was whether there was some reason to question the soundness of Dr. Goldstein’s examination and conclusion. No such deficiency was cited to the district court and none has been cited to us. In this context, the district court reasonably concluded that a second evaluation was not necessary. Bartoli also faults the court for not conducting an evidentiary hearing before finding him competent, but again we find no abuse of discretion in the court’s decision to determine his competency without a hearing. A hearing is required when there is reasonable cause to believe that the defendant may be suffering from a mental disease or defect that renders him unable to understand the nature or consequences of the proceedings against him or to properly assist in his defense. § 4241(a); see United States v. Grimes, 173 F.3d 634, 635-36 (7th Cir.1999) (coll, cases); United States v. Graves, 98 F.3d 258, 261-62 (7th Cir.1996) (evidentiary hearing becomes mandatory if, on preliminary inquiry, reasonable cause to believe defendant may be incompetent persists). Certainly, based on the preliminary diagnosis of Bartoli’s physician coupled with the concerns that Bartoli’s counsel articulated, there was cause to order an examination of Bartoli. But once a thorough evaluation had been undertaken by an independent expert, and *511 that expert had concluded that Bartoli was competent to stand trial, there was no longer reasonable cause to believe that Bartoli was incompetent and thus no need for a hearing. Dr. Goldstein’s report dispelled the initial doubts which had triggered the inquiry into Bartoli’s condition. Finally, we note that in finding Bartoli competent to stand trial, the court itself took into consideration not only Goldstein’s report, but the materials Bartoli’s counsel had submitted. So the court’s finding was based not simply on the psychologist’s report, but all of the circumstances that Bartoli’s counsel deemed relevant to the competency determination. R. 988 Tr. 7. We find no procedural flaw in the court’s finding. B. Statutes of Limitations and Withdrawal Bartoli and the other defendants were indicted in 2004, seven and one-half years after Bartoli retired as Aegis’s in-house counsel in 1996 and moved to Myrtle Beach, South Carolina. Given his retirement, Bartoli contends that the governing statutes of limitations — -the longest of which is six years — preclude all of the charges against him. Of course, the Aegis scheme continued into 2002, many years after Bartoli’s retirement as Aegis’s counsel; and each of the acts underlying the charges of mail, wire, and tax fraud all occurred within the relevant limitations period. But, in essence, Bartoli’s theory is that his relocation marked his withdrawal from the Aegis scheme and thus caused the limitations clock to start running much sooner for him than it did for his co-defendants. Notwithstanding his retirement, Bartoli remained a director and part owner of Aegis, and he continued to receive distributions of profits from its operations until 2002. But he reasons that he was not sufficiently involved in the operations of Aegis after 1996 to render him liable for any acts of the charged conspiracy — including the acts of mail fraud, wire fraud, and aiding in the preparation of false or fraudulent tax returns — which took place after his retirement and relocation. He notes, for example, that he had no hand in preparing any of the tax returns underlying the charges filed under section 7206(2); in his view, the sole connection he had with those returns was that he came up with the concept of using the business trust as a tax avoidance vehicle five or six years before those returns were filed. He adds that, at the time of his retirement, it was still entirely plausible to view the Aegis system as a lawful and legitimate means of tax reduction. Thus, to the extent it was foreseeable to Bartoli in 1996 that Aegis clients would be filing income tax returns in subsequent years based on the Aegis trusts, he insists that it was not foreseeable to him that those returns would be deemed fraudulent. As he sees things, only after his 1996 retirement did the clues as to the illegality of the system begin to emerge. The IRS did not issue Notice 97-24 until April 1997, for example, and the Tax Court did not issue its decision in Muhich (concerning the legitimacy of an Aegis-like trust system that Bartoli had established) until 1999. And given how minimal Bartoli’s involvement with Aegis purportedly was after 1996, he believes he cannot be held liable on charges that were filed more than seven years after he retired from Aegis. (He also notes, parenthetically, that changes were made in the Aegis trust documents and systems subsequent to his retirement.) Plainly, Bartoli’s statute-of-limitations claim hinges on the notion that he legally withdrew from the alleged conspiracy (and any effort to defraud the government of its tax income) in 1996. A defendant’s withdrawal from a conspiracy does not, in itself, absolve him of criminal liabili *512 ty for his (prior) membership in that conspiracy. United States v. Nava-Salazar, 30 F.3d 788, 799 (7th Cir.1994); see also United States v. Hughes, 191 F.3d 1317, 1323 (10th Cir.1999); United States v. Grimmett, 150 F.3d 958, 961 (8th Cir.1998). But it can foreclose such liability when coupled with the statute of limitations. Nava-Salazar, 30 F.3d at 799 (citing United States v. Read, 658 F.2d 1225, 1232-33 (7th Cir.1981)). The pertinent question is whether Bartoli’s retirement constituted a genuine withdrawal from the conspiracy, such that he could not be held liable for acts that occurred after that date. As we have discussed, simply stopping one’s active participation in a conspiracy does not constitute a legally meaningful withdrawal from that conspiracy. E.g., United States v. Julian, supra, 427 F.3d at 483. You do not absolve yourself of guilt by walking away from the ticking bomb. And similarly the law will not let you wash your hands of a dangerous scheme that you have set in motion and that can continue to operate and cause great harm without your continued participation. The courts hold that for withdrawal to limit a conspirator’s liability ... “mere cessation of activity is not enough ... there must also be affirmative action, either the making of a clean breast to the authorities, or communication of the abandonment in a manner calculated to reach co-conspirators. And the burden of withdrawal lies on the defendant.” United States v. Patel, 879 F.2d 292, 294 (7th Cir.1989) (quoting United States v. Borelli, 336 F.2d 376, 388 (2d Cir.1964) (Friendly, J.)); see also United States v. Schiro, 679 F.3d 521, 528-29 (7th Cir.2012), petition for cert, filed (U.S. July 30, 2012) (No. 12-5571); United States v. Paladino, 401 F.3d 471, 479-80 (7th Cir.2005); United States v. Wilson, supra, 134 F.3d at 863. In order to effectuate a genuine withdrawal from a conspiracy, a defendant must “terminate completely his active involvement in the conspiracy, as well as take affirmative steps to defeat or disavow the conspiracy’s purpose.” United States v. Hargrove, 508 F.3d 445, 449 (7th Cir.2007) (emphasis supplied). By his own admission, Bartoli did not completely end his active involvement with Aegis, let alone take affirmative steps to defeat or disavow use of the Aegis trusts. His retirement and relocation to South Carolina may have signaled a reduced role in the day-to-day operations of Aegis (he no longer signed trust documents as he had before, for example), but it did not constitute a withdrawal from the charged conspiracy. See id. at 449 (“That [defendant] retired in March 2000 and moved to Las Vegas does not by itself mean he withdrew from the conspiracy.”) On the contrary, there is significant evidence, some of which Bartoli himself cites, that he remained involved with Aegis, and took steps in furtherance of the charged conspiracy, long after his 1996 retirement as Aegis’s counsel. He still participated in Aegis seminars, which pitched the Aegis trust system to prospective clients, as late as May 1997. R. 954 Tr. 5463-64. Val-lone and Bartoli consulted regularly about various issues related to Aegis, and this continued through 2001 and 2002. R. 910 Tr. 6226-27. Bartoli participated in Aegis management meetings in the summer and fall of 1999, R. 913 Tr. 1952-54; he tried to keep the peace between Vallone and Hopper after their falling out over what they should advise clients in the wake of the Muhich decision, R. 913 Tr. 1958; R. 947 Tr. 2122; and on November 12, 1999, he signed the resolution indicating that he, Vallone, and Hopper shared equal manage *513 ment authority over Aegis, R. 910 Tr. 6226. Bartoli was listed as one of three managing directors of Aegis in a January 2000 letter received by at least two Aegis clients, David Vermeulen and Genevieve Riccordino, regarding IRS audits. R. 915 Tr. 2493; R. 930 Tr. 2882. In a February 11, 2001, email, Bartoli noted that he was “still a director [of Aegis] along with Michael Vallone....” R. 971 Tr. 4354-55. Bartoli, along with Vallone and Hopper, received periodic distributions of profits from Aegis. R. 921 Tr. 5401-02. He also received occasional checks for his consulting services work for Aegis, R. 970 Tr. 3941-43; see also R. 921 Tr. 5399-5401, and he continued to receive these checks as late as August 2002, R. 919 Tr. 4663-83; R. 910 Tr. 6226-27. And the jury could infer that he was the moving force behind the $565 billion class action suit filed by Vallone in May 2001 against the IRS and three of its agents. R. 971 Tr. 4354-55, 4357-61. Bartoli thus did not withdraw from the conspiracy in a way that might support his statute of limitations argument and preclude his liability for the acts of his coconspirators. The government has a point when it likens Bartoli to the man walking away from the ticking bomb that we referred to in Patel. Bartoli, after all, was the one who pitched the idea of the business trusts to his fellow defendants; in a May 15, 2001, email, he reminded Vallone that he (Bartoli) was “the old fart who started it all” and that he “want[ed] Dustin Hoffman to play [his] part in the movie.” R. 971 Tr. 4356-57. In fact, however, Bartoli never walked away from Aegis. He remained involved in the company and in the efforts to defraud the government, and continued to profit, as late as 2002. We remarked earlier with respect to Hopper that it was clear from the start that the trust system that Bartoli devised did not comply with certain fundamental principles of trust and taxation law. Those principles did not change over time. But whatever Bartoli’s professed belief as to the legality of the Aegis trust system may have been at the time of his retirement as counsel to the firm, he continued his involvement well after he and the other defendants had direct and specific notice that the government regarded the system as an unlawful means of tax evasion. The jury was instructed on the concept of withdrawal pursuant to an instruction proposed by defendant Hopper and joined by Bartoli. R. 936 Tr. 6018; R. 925 Tr. 7381-82. There was little evidence to support the withdrawal defense and much evidence supporting the jury’s decision to reject it. The district court did not err in denying Bartoli’s motion for a judgment of acquittal insofar as it was based on the notion that his claimed withdrawal from the conspiracy caused the statutes of limitations to run on the charges against him. We note finally that to the extent Bartoli, like Hopper and Dunn, contends that he had no involvement with, and thus cannot be held liable for, the preparation of the false or fraudulent tax returns filed by Aegis clients, his contention fails for the same reasons. See supra at 492-93, 505-07; United States v. Hooks, supra, 848 F.2d at 791. C. Admission of Evidence Concerning ARDC Proceedings Against Bartoli Finally, Bartoli contends that the district court erred in allowing evidence and argument as to the disbarment proceedings against him. Bartoli notes that these proceedings were offered to establish his notice of the illegality of the Aegis trust system, but the final order of disbarment was not issued until May 2002, more than two years after the March 2000 IRS raid on Aegis offices that signaled the begin *514 ning of the end of the conspiracy; and even the Hearing Board’s recommended decision was not issued until February 2000, a month before that raid. Moreover, the court allowed the government to introduce into evidence long, prejudicial excerpts from the ARDC hearing — including excerpts from the Hearing Board’s summary of Marutzky’s testimony — during Robinson’s testimony and during the cross-examination of Vallone. But Bartoli was not physically present at that hearing due to illness and had already retired and taken inactive status; so he would not have heard the Marutzky testimony or the other evidence presented to the Hearing Board. In short, Bartoli views this evidence as having little or no probative value in terms of his notice as to the dubious legality of the Aegis trust system. He believes the evidence served only to inflame the jury and to suggest that Bartoli was a bad person who must have committed the charged crimes. As with the defendants’ joint challenge, we find no abuse of discretion by the district court in admitting this evidence as to Bartoli. Bartoli himself was the respondent in the ARDC proceedings, and there is no dispute that he was aware of the proceedings. The charges themselves would have alerted Bartoli to the suspect nature of the Aegis trusts. Moreover, although he was not present to hear the evidence presented to the Hearing Board, he was represented by counsel during the proceeding. A jury could reasonably infer that his counsel would have apprised him of the testimony, including that of Marutzky. Alternatively, or additionally, a jury might infer that Bartoli’s ignorance of what occurred during the ARDC proceedings, given his status as the respondent, represented a willful blindness to the illegality of the Aegis system. Moreover, there was evidence that Bartoli, like other defendants, remained active in the conspiracy as late as 2002, so the fact that the opinion of the ARDC’s Hearing Board did not issue until February 16, 2000, does not undermine its relevance as notice evidence. (The government did not, in fact, introduce or rely upon the final disbarment order issued in May 2002.) Bartoli points out that although the government agreed to redact all references to disbarment from its evidence concerning the ARDC proceedings, Dunn’s counsel nonetheless characterized the proceedings as disbarment proceedings twice during his opening statement. R. 942 Tr. 128. However, the court instructed the jury to disregard those references, R. 942 Tr. 136, and given the overwhelming evidence of Bartoli’s guilt, we believe it highly unlikely that those references had any impact on the jury’s assessment of the evidence. IV. For all of the reasons we have discussed, we Affirm the defendants’ convictions and sentences. Footnotes [1] As originally envisioned by Bartoli, a client's wife would first convey all of her interest in the couple's property to her husband, she would then become the temporary "independent” trustee of the business trust, her husband would transfer the property to that trust, and finally he would succeed his wife as the trustee. As the defendants implemented the system, an Aegis attorney replaced the client's spouse as the initial trustee. [2] In a supplement to his motion, Vallone contended without elaboration that his speedy trial claims were based on the Sixth Amendment as well as the Speedy Trial Act. R. 414. However, Vallone’s appeal relies solely on the statute. [3] Hanis notes that among the evidence a defendant may present in support of a defense that he "subjectively, but wrongly" believed his conduct was consistent with the Internal Revenue Code and the cases interpreting it is expert testimony as to the case law on which the defendant purports to have actually relied. 942 F.2d at 1132 n. 6. See United States v. Garber, 607 F.2d 92, 95-99 (5th Cir.1979) (en banc) (in tax evasion case, district court erred, inter alia, by excluding expert testimony proffered by defense on novel question of whether certain payments defendant received in exchange for her rare blood plasma constituted taxable income: "In a case such as this where the element of willfulness is critical to the defense, the defendant is entitled to wide latitude in the introduction of evidence tending to show lack of intent. The defendant testified that she subjectively thought that proceeds from the sale of part of her body were not taxable. By disallowing [the expert’s] testimony that a recognized theory of tax law supports Garber’s feelings, the court deprived the defendant of evidence showing her state of mind to be reasonable.”), cited with approval in United States v. Clardy, 612 F.2d 1139, 1153 (9th Cir.1980) (district court did not err in permitting IRS agent to give expert testimony that particular deduction was not proper: "we believe that this type of testimony is relevant to the issue of willfulness where the theory of the defense is that there is a good faith dispute as to the interpretation of the tax laws”); but see also United States v. Klaphake, 64 F.3d 435, 438-39 (8th Cir.1995) (where defendant’s attorney was permitted to testify he was retained to prepare prototype trust document and as to legitimate purposes and advantages of business trust, and where attorney’s opinion letter to defendant was also admitted into evidence, court properly excluded attorney from testifying on legality of trust arrangement; latter point presented question of law for court, and given the evidence that was admitted, defendant’s defense that he reasonably relied on advice of counsel was not eviscerated); United States v. West, 22 F.3d 586, 597-600 (5th Cir.1994) (in bankruptcy fraud case, where defendant’s bankruptcy experts were permitted to testify that they advised defendant to structure relevant transactions as he did and that the transactions were lawful, district court did not abuse its discretion in refusing to let experts explain the legal basis for their advice); United States v. Bryan, 896 F.2d 68, 72-73 (5th Cir.1990) (although expert testimony might be relevant to willfulness in certain cases, it was properly excluded where tax shelters devised by defendants were clearly shams lacking any valid business purpose); United States v. Curtis, 782 F.2d 593, 599 (6th Cir.1986) (rejecting Garber and sustaining exclusion of defendant’s proffered expert testimony regarding uncertainty in particular area of tax law, reasoning in part that absent connection between uncertain state of law and defendant’s state of mind, expert’s testimony regarding uncertainty in law is irrelevant); United States v. Ingredient Tech. Corp., 698 F.2d 88, 96-97 (2d Cir.1983) (declining to follow Garber and sustaining exclusion of expert testimony as to Department of Treasury regulations that defendant offered to show defendant could not have formed willful intent to evade taxes); United ■States v. Herzog, 632 F.2d 469, 473 (5th Cir.1980) (expert’s view on complexity of tax laws sheds no light on defendant’s intent). [4] In fact, as the government suggests, the defendants had no difficulty introducing these exhibits in their own cases. See, e.g., R. 920 Tr. 5111-34 (American Jurisprudence and American Law Reports articles on business trusts, among other authorities that Vallone purportedly relied upon); R. 953 Tr. 5237-5248 (three positive opinion letters that Val-lone relied upon); id. Tr. 5248-63 (three additional opinion letters admitted as to Val-lone's state of mind), id. Tr. 5295; R. 921 Tr. 5300-03 (multiple versions of Aegis Directors’ Manual, which included citations to authorities that Vallone believed supported legitimacy of Aegis trusts); R. 938 Tr. 6359-60 (Heritage promotional brochure, indicating that Heritage was represented by “one of the finest counsels possible,” given to Dowd by his father); id. Tr. 6369-70 (additional documents Dowd was given). [5] See also R. 927 Tr. 58 ("And so you can make your argument to the jury somehow that it doesn’t apply to you, but there is an agreement here, the Court said there was an agreement by a preponderance of the evidence. There is notice to one and, therefore, other members of the conspiracy.”); R. 914 Tr. 2265-66 ("So it's [admissible] in terms of the effect on Mr. Parker, the notice that he had ... at a time when the conspiracy was in existence, which is to say notice to him is notice to the coconspirators.... ”); R. 955 Tr. 6-7 ("where one member of a conspiracy knows certain things, is confronted with certain things or matters, it means that those who have joined the agreement have also been confronted with those things and others”); R. 969 Tr. 3774 (in discussion of willfulness, and whether defense exhibits should be admitted during government’s case to show good faith: "In terms of Count 1, any act by any one member of the conspiracy may be enough, along with the other elements of the offense, to make out a prima [facie] case.”). [6] Bartoli sold the Alumbaughs the CBO pursuant to his affiliation with the Athens Company ("Athens”), an Ohio firm that marketed CBOs in much the same manner as Aegis. Bartoli served as the legal director for Athens. There was a separate count in the amended complaint based on Bartoli's activities with Aegis generally. The ARDC’s Hearing Board ultimately dismissed that count of the complaint as moot based on its findings with respect to the "nearly identical allegations of misconduct” in the count dealing with Bartoli’s sale of the Athens trust system to the Alumbaughs. Hearing Board's Report & Recommendation at 58-59, available at http:// www.iardc.org. [7] In the briefing, the defendants state that Robinson read from Marutzky's testimony, but what she actually read were excerpts from the Hearing Board’s description of Marutzky’s testimony. [8] The business belonged to Kenton Tylman, who sold videotapes, among other items. The items seized from the business included approximately 140 videotapes related to Aegis; primarily these were recordings of Aegis promotional seminars. Agent Priess had purchased some of these videotapes, and excerpts from these recordings were played at trial. [9] Unless otherwise noted, all citations to the Guidelines in this decision are to the November 2008 version of the Guidelines. [10] He marked up his copy of the Muhich decision, which of course involved a trust prepared and marketed by Bartoli and others Dowd was working with. [11] Among the additional items was a negative opinion as to the Aegis CBO from an independent CPA, forwarded to Aegis by a prospective client (R. 950 Tr. 3899 + ), and multiple news articles regarding abusive trusts. [12] In an effort to defeat that inference, Dowd contended that it was his brother to whom Izen was referring during this exchange. Dowd’s brother Paul evidently was on the same cruise. However, after the cruise, Dowd wrote a letter to Izen in which he mentioned Izen’s presentation and joked, "I overheard both IRS agents in the audience telling each other they didn’t get what they came for (just kidding).” R. 918, Tr. 4311; Gov't Ex. Aegis Office 5 Computer 3. It is at least a fair inference that when Izen singled out "Dowd” during his presentation, he was referring to the defendant Dowd rather than his brother. That point aside, it is also a fair inference from the letter that Dowd was present for Izen's presentation, even if Izen’s reference was to Dowd’s brother. [13] Hopper’s involvement with Aegis did not end immediately. He continued in a “consultant and support capacity” until May 1, 2000. Then, on June 8, 2000, he wrote a letter severing all ties with Val lone. [14] We note that the jury was instructed, in the form proposed by Hopper’s counsel, that following a defendant's withdrawal from a conspiracy, he could not be held liable for the acts of his former co-conspirators. See Hopper Instruction 4; R. 936 Tr. 6018-21; R. 925 Tr. 7381-82. Thus, if the jury was persuaded by Hopper’s contention that he withdrew from the charged conspiracy in the wake of the Tax Court’s decision in Muhich, the jury would have understood that it could not convict Hopper based solely on what other members of the conspiracy knew or did following Hopper’s withdrawal. [15] These include Counts 11 through 13, 15, 16, 18, 19, 24 and 25, and 27 through 34 of the Superseding Indictment. [16] The court assumed that the total loss amount would come to at least $56 million even if losses for tax years after 2000 were excluded from the loss calculation. Hopper's counsel conceded that the only way to get the loss amount below $50 million (and thereby reduce the offense level) was to exclude losses occurring after May 2000, when Hopper's resignation took effect, if not all losses that occurred in 2000. The court rejected the contention that losses for any part of 2000 should be excluded. See R. 1085 Tr. 10-11, 17-22. [17] Welch could not do this because he did not have access to all of the clients' original tax returns, tax preparers' files, and other information (e.g., as to applicable deductions) that would have permitted him to compute the actual tax loss as to each Aegis client. [18] We note that, as in Hopper's case, the loss amount would have exceeded $50 million, and thus the offense level would have been the same, even if losses occurring after the 2000 tax year were excluded. See supra at 493 n.16. [19] Dunn does not separately argue that the evidence was otherwise insufficient to overcome his Cheek defense and to establish his willfulness. [20] Dunn separately suggests that the district court committed legal error by denying his Rule 29 motions for a judgment of acquittal without explanation. The argument is so cursorily made, however, as to have been waived. E.g., United States v. Adams, supra, 625 F.3d at 378. We would point out, however, that the court in its post-trial opinion disposing of the defendants' motions for judgments for acquittal and for a new trial did address Dunn's motions to the extent of noting that both Dunn and Cover had raised many of the same issues that had been argued by defendants Bartoli and Hopper (and which the court had expressly addressed), and that the arguments made in the motions were otherwise inadequately developed with citations to case law or other legal authorities. R. 650 at 12.