United States v. Lionel Reifler, Glenn B. Laken, John M. Black, Jr.

KEARSE, Circuit Judge. Defendants Glenn B. Laken and John M. Black, Jr., charged along with more than a dozen other individuals in a 26-count indictment that was eventually redacted at trial to seven counts, appeal from judgments entered in the United States District Court for the Southern District of New York (A) convicting both Laken and Black, following a jury trial before William H. Pauley III, Judge, on one count of racketeering conspiracy, in violation of 18 U.S.C. § 1962(d) (Count One) (“RICO conspiracy”), one count of wire fraud, in violation of 18 U.S.C. §§ 1343 and 2 (Count Five), one count of wire fraud, in violation of 18 U.S.C. §§ 1343, 1346, and 2 (Count Three), two counts of illegal kickbacks, in violation of 18 U.S.C. §§ 1954 and 2 (Counts Four and Seven), one count of theft of honest services, in violation of 18 U.S.C. §§ 1343, 1346, and 2 (Count Six), and one count of conspiracy to commit the above substantive offenses and to commit union pension fund fraud, securities fraud, and fraud by an investment advisor, in violation of 18 U.S.C. § 371 (Count Two) (the “pension fund fraud/kickbacks conspiracy”); and (B) convicting Laken, following his plea of guilty before Sidney H. Stein, Judge, on one count of conspiracy to commit securities fraud, wiré fraud, and commercial bribery in connection with stock issued by FinancialWeb.com, Incorporated (“FWEB”), in violation of 18 U.S.C. § 371 (the “FWEB conspiracy”). Judge Pauley sentenced Black principally to serve 37 months’ imprisonment, to be followed by a three-year term of supervised release. Laken’s offenses were consolidated for sentencing before Judge Pau-ley, who entered judgment ordering Laken principally to serve a total of 63 months’ imprisonment, to be followed by a two-year term of supervised release, and entered an amended judgment ordering him also to pay $6,620,675.33 in restitution to victims of the FWEB conspiracy. Defendant Lionel Reifler appeals from a judgment, entered in the same court following his plea of guilty before Judge Stein, convicting him on one count of conspiracy — the FWEB conspiracy — to commit securities fraud, wire fraud, and commercial bribery, in violation of 18 U.S.C. § 371, and two counts of credit card fraud, in violation of 15 U.S.C. § 1644(a). Judge Stein entered judgment sentencing Reifler principally to 63 months’ imprisonment, to be followed by a three-year term of supervised release, and entered an amended judgment ordering him also to pay $2 million in restitution to victims of the FWEB conspiracy. On appeal, Laken and Black contend principally (1) that the district court (a) violated their Sixth Amendment rights of confrontation by admitting in evidence the plea allocutions of two of their alleged coconspirators, and (b) deprived them of a fair trial by allowing the government to introduce certain evidence, including evidence that Black and others had ties to organized crime; (2) that the evidence was insufficient to support their convictions on (a) the RICO conspiracy count, (b) one of the wire fraud counts, and (c) both of the illegal kickbacks counts; and (3) that the insufficiency of the evidence to support their convictions on those counts requires, on a theory of retroactive misjoinder, the *71 invalidation of their convictions on all other counts. All three appellants (a) challenge various aspects of the sentencing judges’ calculations under the United States Sentencing Guidelines (“Guidelines”) (2000), and (b) seek remands for resentencing in light of United States v. Booker, 543 U.S. 220, 244, 259, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005) (invalidating mandatory application of the Guidelines), and United States v. Crosby, 397 F.3d 103, 119 (2d Cir.2005) (“Crosby ”) (establishing procedures in connection with Booker error). In addition, Laken and Reifler make several challenges, including a Booker challenge, to the orders of restitution. For the reasons that follow we find no basis for reversal of any of appellants’ convictions; we remand for consideration of resentencing in accordance with Crosby; and we vacate the restitution orders imposed on Laken and Reifler and remand for further proceedings in accordance with 18 U.S.C. §§ 3663A and 3664. I. BACKGROUND The prosecutions at issue on these appeals arose out of a lengthy securities-fraud investigation by the Federal Bureau of Investigation (“FBI”), culminating in the June 2000 arrests of approximately 120 persons, including Laken, Black, and Reifler, and the filing of more than a score of indictments and criminal complaints. Laken and Black were indicted and tried on charges that they, along with others, engaged in a scheme to bribe officials of unions to invest pension fund assets in corrupt investment vehicles. In one format, coconspirators employed in the securities industry planned to receive substantial sums from excessive commissions generated by the churning of securities in a corrupt hedge fund. In another format, they planned simply to retain some 10-20 percent of the amount that each pension fund meant to invest, and they hoped that sufficiently profitable returns on the moneys actually invested would mask that initial diversion. In either case, those coconspirators were to use part of the illegally gained moneys to fund their bribery payments to the union officials. In addition, the indictment alleged that the coconspirators schemed to manipulate the prices of various securities and to pay secret bribes to brokers in furtherance of those schemes. A separate indictment charged Laken and Reifler with, inter alia, conspiring to manipulate the price of FWEB stock. A. The Pension Fund Fraud/Kickbacks Trial Laken and Black were tried in a 15-week trial in 2001-2002, along with defendants William M. Stephens, Gene Phillips, and A. Cal Rossi, all of whom won acquittals on all counts. Defendant Angelo Cal-vello also began the trial, but prior to its conclusion he entered into a plea agreement with the government. At trial, the principal government witness was Jeffrey Pokross. Pokross, until he was arrested in 1996 and agreed to cooperate with the government, had been an associate of the Bonan-no organized crime family (see Trial Transcript (“Trial Tr.”) at 2504-05). Pokross was a principal in DMN Capital Investments, Inc. (“DMN Capital” or “DMN”), a small firm in Manhattan that provided investment banking and stock promotion services to small companies. His partners in that firm included James (“Jimmy”) La-bate, “a high level ... associate” of the Gambino Crime Family (id. at 2504); and the affairs of DMN Capital were overseen by Robert Lino, a “captain or capo in the Bonan[n]o crime family” (id. at 2930). With Pokross’s cooperation many conversations were recorded, as the government *72 obtained court authorization to install microphones in DMN Capital’s offices, and Pokross wore a wire for meetings at other locations. The resulting tapes introduced as government exhibits with the prefixes “GX Conf,” “GX Desk,” or “GX” were recordings of conversations that took place in the DMN conference room, in the DMN desk area, or beyond DMN’s premises, respectively; transcripts given to the jury as aids in listening to the tapes bear the corresponding numbers and prefixes, with the further designation “-T” (and with “... ” denoting a pause and “UI” signifying that some words were unintelligible). The tape recordings and the testimony of Pokross were the principal evidence at trial. Taken in the light most favorable to the government, the trial evidence showed the following. 1. The Targeted Union Pension Funds Laken, Black, Labate, and others schemed principally to engage in fraudulent activity with respect to the pension funds of three unions: Local 400 of the Production Workers Union (“Local 400”); the Detectives’ Endowment Association (“DEA”), which handled an annuity fund for Detectives in the New York City Police Department; and Local 137 of the Operating Engineers Union (“Local 137”). Pok-ross described the beginnings and progress of the scheme with respect to each of these unions, and recordings of pertinent conversations were played for the jury. Except where indicated, all of the events described below took place in 2000. a. Local k00 Prior to 1999, Pokross had worked on a number of stock deals with Frank A. Pér-sico (“Pérsico”), whom Pokross described at trial as “a corrupt stockbroker” who would “readily take bribes,” make “unrealistic predictions” to promote house stocks (i.e., thinly-traded stocks for which his firm was a market maker), arrange undisclosed compensation to brokers, and “run[ ] the crew[s] of other corrupt stockbrokers” (Trial Tr. 2536). Pérsico, a neighbor of Labate, was an associate of the Colombo Crime Family. (See id.) In 1999, Pérsico gained control of Local 400 and contacted Pokross to discuss the possibility of DMN Capital’s finding ways to invest Local 400 pension fund assets that would be profitable for Pérsico personally. Meeting with Labate in late 1999, Pérsico said he had “t[aken] over and was running Production Workers Local 400” and “had $20 million that he wanted to put into a product to earn money on.” (Id. at 2613.) On January 13, 2000, Pérsico, Pok-ross, and Labate discussed various types of investment vehicles, including bonds, preferred stock, and real-estate investment trusts (“REITs”), and hypothetical maturity dates for those investments. Pokross stated, and Pérsico agreed, that “[t]he longer the thing goes, the more fat there is, for us. The shorter it goes, the less fat.” (GX 30A Conf-T at 3.) They also discussed the means by which, and the frequency with which, an investment advis- or could pay them. (See, e.g., id. at 4 (“PERSICO: So, how, how is this guy gonna get... get... raise the money? That’s what I wanna know?”).) Labate suggested simply taking a portion of the money at the outset. (See id. at 5 (“Take first money.. .And you let the fund replenish the money that you took.”).) Pér-sico, however, preferred receiving a sum of money annually, suggesting that their approach to an investment advisor should be “ ‘we want “this”, every year. I don’t care what you get, maybe you gonna get “this”, but we want “this”, Can that be done?’ ” (Id. at 4.) Pérsico said, “[wje’ll tell them we want 200,000,” “[e]very year though!” (Id. at 5.) On January 19, 2000, Pérsico, Pok- *73 ross, and Labate met at Labate’s home and “discussed a plan for the investment” of Local 400 assets “and getting some splits, some commission sharing.” (Trial Tr. 2752-53.) There followed several weeks of non-communication between Pérsico and Pok-ross; and in a February 25, 2000 conversation with Pokross and Labate, Lino asked whether Pérsico had lost interest. Pok-ross said he thought not, pointing out that Pérsico had asked them to “find a friendly” investment advisor who would do what they wanted. (GX 57C Conf-T at 2.) Lino suggested that perhaps the plan was simply being delayed because “[t]his kid’s got heat,” ie., because Pérsico was receiving attention from law enforcement agents (id. at 10). Thereafter, Lino inquired of the underboss of the Colombo Crime Family (see Trial Tr. 3039) — whose “boss” was Persico’s “cousin, Alley Boy Pérsico” (id. at 2536) — and reported to Labate and Pok-ross on March 2 that the Colombo Crime Family was still interested in pursuing the scheme to defraud Local 400 (see GX 61C Desk-T at 3). Pokross testified that the union pension fund scheme was also discussed with Pérsico at a meeting on April 25 (see Trial Tr. 3151-52) and that Pérsico confirmed “[t]hat the scheme was going to continue to move forward” (id. at 3152). b. The DEA In January 2000, Labate had suggested that additional unions be approached with respect to the possibility of their making pension fund investment arrangements similar to that envisioned by Pérsico for Local 400. (See GX 33E Conf-T at 3-5.) In particular, Labate targeted the DEA, whose president and treasurer, Thomas J. Scotto and Stephen (“Steve”) Gardell, respectively, were also neighbors of Labate (see id.; Trial Tr. 2749-50). Labate knew that Gardell lived beyond his means and had a gambling problem. (See, e.g., GX 318-T at 12; Trial Tr. 3670.) Pokross testified that on February 8, 2000, Labate reported that he .had informed Gardell on the previous evening that “[Gardell] would be getting 50,000 per million back as kickback.” (Id. at 2968-69.) c. Local 137 Local 137 of the Operating Engineers Union, sometimes referred to as the Operating Engineers, the Westchester Operating Engineers, or simply the Engineers, was controlled by its business manager, Nicholas Signorelli Sr. Calvello, a member of Local 137 who sometimes received remuneration from DMN Capital for bringing it clients (see GX 88C Desk-T at 2), and who was a good Mend of Nicholas Signorelli Jr., Local 137’s president (a figurehead position, according to Calvello) (see id. at 5), had discussions with Pokross and Labate in March and April about the possible fraudulent investment of Local 137’s pension fund assets (see, e.g., id. at 6-9; Trial Tr. 4163). Calvello said there was “a lot of money in the Fund” (GX 88C Desk-T at 6); Labate told Calvello that if Local 137 would “do 500,000 dollars, you got yourself 20 grand more money” (id. at 17). Labate hypothesized that Local 137 “is a billion dollar Fund” (id. at 6), and he and Pokross explained that the plan would be to seek the placement of $100 million with an investment advisor; the advisor would put $90 million of that into secure investments and put the remaining $10 million into an investment vehicle from which 10 percent, or $1 million, could be skimmed for payments to the individuals (see id. at 6-8; id. at 8 (“10 million gets a million dollars... the right way for a chop”)). Labate told Calvello that DMN would be happy with a “60/40” split of the $1 million, *74 and the Signorellis could “walk away with 200,000 apiece.” (Id.) 2. The Participation of Laken and Black In early 2000, Black had introduced Pokross and Labate to Laken. Black, a corrupt securities broker dealer in Manhattan (see Trial Tr. 2644), was a self-described associate of the Luchese Crime Family (see id. at 2692-93). Black’s friend Laken was an experienced Chicago-based commodities trader who planned to open a hedge fund called Trade Venture Fund. On or about February 7, 2000, Black approached Labate and proposed that DMN Capital find investors for Laken’s hedge fund, in return for which Laken would pay DMN secret commissions. (See GX 44A Conf(2)-T at 2.) Pokross testified that the plan to “bribe [DMN] to find investors for Trade[ ]Venture[ ]Fund” was originated by “Mr. Black and then Mr. Laken.” (Trial Tr. 5199.) Labate responded to this proposal by telling Black that DMN had “access to 2” possible investors for Laken’s fund (GX 44B Conf-T at 3), which were “[ujnions” (id. at 4). Labate cautioned Black, however, that Laken must be instructed not to disclose that Black had secured the union pension fund investments through Labate and his associates: Labate: And it’s gotta stop at you. If anybody ever asks him questions, it goes to him or I got it through you. “Where did you get it from”? Black: Right. (UI) I mean, that could be it. ‘Where did I get it from”? “I got it from”... Labate: [ ]You, you, you started investi- . gating it. You started investigating with unions (UI). You seen an open market because of CIGNA taking over Unions, and you’re seeing all these other companies... Black: Give me the script. Tell me what I gotta do. (Id. at 7.) In conversations with Pokross and La-bate on February 7, 8, and 9, Black described the process by which Laken, using his own clearing firm, would churn a pension fund’s account by making matching purchases and sales of securities (see GX 46C Conf(l)-T at 12), which Black referred to as “round trips” (GX 44A Conf(2)-T at 2) and “in and outs and in and outs” (GX 45B Conf-T at 3), and which Laken called “round turns” (GX 46C Conf(l)-T at 12). On February 7, for example, Black stated that Laken would pay commissions of $150,000 to $200,000 each year for every million dollars invested by DMN-produced investors, with a portion of those commissions going to Black. Black stated: [F]or every, for every million dollars uh, about a buck fifty to 200 a year they’ll give back. Alright? And that’s after they make 40 something percent. It’s just on the clearing side... ‘cause he owns the clearing. The Fund has got... Labate: 10 million would be a $1,500,000 a year coming back. Black: Yeah. That’s what I said. Labate: And that’s guaranteed. Black: He’ll put it in writing. Labate: What would you want out of that. Black: Give me a little smidgeon. You know.... Labate: [ JYeah, ‘cause the guy’s gonna want 60%. Black: I mean, we’ll... however, however we gotta take care of it. You know? (GX 44A Conf(2)-T at 2.) On February 8, Black reiterated to Pok-ross and Labate that for every $1 million *75 that a pension fund introduced by DMN Capital put into Laken’s hedge fund, Black and DMN, collectively, would receive approximately $150,000 a year. (See GX 45B Conf-T at 2.) Black said, what it is, you’re getting basically the majority of the commissions. What happens is, he owns... He’s gonna be managing the Fund. The Fund’s a separate entity. All of the commissions that are generated off the Fund are gonna be done through a clearing firm that he owns. Alright. That’s how he’s gonna pay us. (Id. at 3.) Labate and Black then debated how much DMN Capital would have to pay the corrupt union officials in bribes in order to get them to invest in Laken’s fund. In their conversation on February 7, Labate had speculated that an official would want 60 percent of the amounts generated through churning. (See GX 44A Conf(2)-T at 2.) On February 8, Labate questioned whether the plan would be financially worthwhile for DMN if the bribe amounts had to be as much as 80 percent of what they received from Laken. (See GX 45B Conf-T at 4.) They calculated that at the rate of $150,000 per million dollars invested, an investment of $20 million would get them $3 million from Laken; and if they were required to pay 80 percent of that $3 million, or $2.4 million, in bribes, Black and DMN would be left to share $600,000. (See id. at 5-6.) Black and Labate considered whether they could give the officials a smaller percentage, with Labate cautioning, “we gotta make it sensible for them to do it” (id. at 6): Black: I mean, I think 80’s very sensible for them to do it. For them to get 2.6 million a year... 2.4 million a year. That’s pretty sensible. Labate: Are we happy with the, with... Black: I think we should get a little bit more... Alright... Labate: [ ]How much money... Black: [ ]I mean, not so much you... Labate: [ ]Do we wanna get 30%[?] (Id.) They settled on a proposed aggregate of 30 percent for Black and DMN Capital, amounting to $900,000, to be divided $300,000 for Black and $600,000 for DMN. (See id. at 7-8.) Laken was due to come to New York to meet with Pokross and Labate the next day, February 9, and Black, Pokross, and Labate proceeded to discuss plans for that meeting. (See GX 45B Conf-T at 12.) Pokross told Black that the head of the DEA would be there. (See id. at 13.) In an ensuing conference call in which Black, Labate, Pokross, and Laken participated, Pokross told Laken that the DEA retirement fund assets totaled some $300 million: Pokross: Okay, we have a very, very near and dear friend of ours who runs the Detectives uh, Retirement Fund... that’s got about 300 million dollars in it. Laken: Yup. Pokross: A very, very close friend. Okay? Laken: Right. Pokross: So, keep it quiet. You know, I think John had mentioned that to you. Laken: Yes he did. (Id. at 16.) On February 9, Laken met with Black, Pokross, and Labate in New York at the DMN office to describe his hedge fund. (See Trial Tr. 2969.) Pokross told Laken that “there are a couple of Pension Funds who we happen to be very friendly with the Treasury, the Treasurers and Board of Trustees,” mentioning in particular the “Detective’s [sic ] Endowment Fund [with] 300 million dollars,” and “another particu *76 lar Pension Fund with” “60 million dollars in it.” (GX 46C Conf(l)-T at 3.) Pokross said that “a lot of these particular Pension[]” funds were “mostly in the construction” industry. (Id. at 22.) At that meeting, Laken confirmed Black’s explanation that Laken would clear trades below the normal $9 — $11 cost through a clearing house in which Laken was a partner, stating that “[a]t the end of the day what’s in it for you is this” very substantial “kick back”: My charge will be somewhere around 8 bucks. At 8 bucks, I have the ability to probably kick back, or pay in commission flow as opposed to kick back, any way you want to slice it.[ ] Pokross: []I’m from Brooklyn. Kick back is fine by me. Laken: Okay. Kick... I have the ability to kick back around a buck and a half a round turn. Trading the way that I trade, a buck and a half a round turn can amount to a very, very substantive number very quickly. (GX 46C Conf(l)-T at 12.) Pokross asked Laken to quantify “what the yield” would be, explaining that [s]ome of these guys like to live a little nicer than their means. Laken: I’m sure of it. Pokross: Okay, and we will be responsible for some sharing of those commission arrangements... Laken: I got you. Pokross: .. .With them.[ ] Laken: I’m not at all, I’m not at all surprised. (Id. at 17-18.) Pokross indicated that Laken would not need to be involved in making those sharing arrangements, and Laken indicated that he would make payments to DMN Capital “to do whatever it is you need to do.” (Id. at 18.) Pokross said he would deal with the necessary officials [v]ery quietly. For instance... Without getting specific, there’s a specific individual who runs 300 million dollars. Laken: Yes. Pokross: All these guys, they make 80, a 100 grand a year. Laken: Yes. Pokross: They like to live a little. Laken: Yes. Pokross: Junkets... Gambling... Laken: Yes. Pokross: Whatever.... They, these degenerate (UI) guys. So, obviously, for him to get into something so speculative ... let, let’s say the, the, the grease, the wheels have to be greased a little bit. Laken: Yeah.[] Pokross: But I... They will never wanna deal with you on that. They’ll only deal with me and or Jimmy.[ ] Laken: I, and I’m only too happy for it to be that way because I don’t have an interest in dealing with it. Pokross: No, they’d be reluctant and you’d, you wouldn’t want to. Laken: Yes, precisely. (GX 46C Conf(l)-T at 18-19.) Pressing Laken to “quantify something up front” as to the payments DMN Capital could expect (id. at 19), Pokross explained that what he wanted to be able to do was “say to a guy ‘okay, for every million we’ll give you 80 a year. It’ll be here. Go there on vacation with your family and you can go look at it any time you want’ ” (id. at 20). Laken responded that he was not prepared to give a precise number but that he could say that “it w[ould] be a very generous commission throw back on the monies raised.” (Id. at 21.) Laken pre- *77 dieted that not only would the pension funds make a lot of money, but DMN’s “Mends w[ould] make a lot of money.” (Id.) At that February 9 meeting, Pokross stated that he was friendly with trustees of “a lot of’ pension funds, principally associated with “the construction” industry and “the Detectives” (id. at 22). Pokross asked whether Laken could recommend “a very friendly Investment Advisor” whom the trustees could retain (id. at 23) and who would recommend investing pension fund assets in Laken’s hedge fund, and Black endorsed that approach: Black: That could be done, right? Laken: I believe so. Yes. Pokross: That’s the key to the kingdom. (Id. at 24; see also GX 44B Conf-T at 2-4 (February 7 discussion among Black, Pok-ross, and Labate of union pension fund trustees’ need for, in the words of Black, a “professional Investment Advisor” with “some credibility,” who would recommend “that they put their money in certain deals”).) Laken asked how quickly an investment could be expected “from [the time of] finding a friendly Investment Advisor.” (GX 46C Conf(l)-T at 26.) Pokross responded: Well, if you were making 80 grand a year and you lived a lifestyle that was like you spent 400,000 a year... Laken: Yeah. Pokross: ... How quickly do you think it’s gonna move forward? Laken: Probably very quickly. (Id.) On February 29, 2000, Black telephoned Pokross to say that Black and Laken had enlisted defendant Stephens, a San Francisco-based investment advisor, to be their friendly investment advisor. Pokross testified that Black said, “I have the investment advisor, I spoke to Glenn, Bill Stephens is going to be on board with what we are doing.” (Trial Tr. 2992.) Black had mentioned Stephens to Labate and Pokross on February 7 during the discussion of the need to find someone to serve as an investment advisor to union pension fund trustees and recommend investment vehicles that were controlled by the cocon-spirators. (See GX 44B Conf-T at 3-4.) On March 1, Pokross prepared for a telephone conference call with Stephens by asking Black to “[w]alk [Pokross] through” what Black’s “understanding [wa]s with Bill.” (GX 60D Conf-T at 2.) Black responded: My understanding is, is that, is the Detectives Endowment Fund... alright... Steve Gardella [sic] is the Treasurer. Pokross: Gardell. Black: Gardell. He needs somebody as an investment advisor, alright, that knows that he’s gonna be pushed in the direction of certain investments. Alright, and his job is to say, “yes, that’s a good investment”. Alright... for that, he’s gonna receive some remuneration, which I never disclose... (Id. at 2-3.) Pokross added: We are very friendly with certain labor unions and whatnot, who have pension funds ranging from 60 to 300 million. Black: Go ahead. Pokross: They’re friends of the family, if you understand what I’m saying. Black: Sure. Pokross: Okay? Black: Uh huh. Pokross: We can have carte blanche at these joints, ‘cause we’re all friendly with the trustees, who are hand picked by the wiseguys. Black: Right. *78 (Id. at 5; see also Trial Tr. 2513 (explaining that “ ‘wise guy’ ” is a term for an initiated member of a crime family).) “[WJith the Detectives Union,” Pokross stated, “[a]ll these guys, Gardell, and even... you know, the other one.. .Scot-to,” “[t]hey all wanna earn.” (GX 60D Conf-T at 8.) Pokross reminded Black that, as to Laken’s hedge fund, Pokross and Black “were talking about a 150,000 per million,” and they could just “give Steve [Gardell] a fucking... 30,[ ]40, 50,000 dollars a year... in a bag.” (Id.) On March 2, Laken confirmed to Pok-ross and Labate that Stephens could be relied on to advise union officials to invest in Laken’s hedge fund. Laken said, “I spoke to Bill Stephens at some length last night, and uh, he, he understands.” (GX 61A Conf-T at 2.) Laken said he had emphasized to Stephens, “ ‘you’re getting this job through a friend of mine. And one of the prerequisites is that you’re friendly.’ ” (Id. at 4.) On March 2, Stephens faxed his résumé from California to Pokross in New York. In a telephone conversation on March 8, Pokross and Laken discussed the asset sizes of the various pension funds that were targeted because they were operated by DMN’s “friends” (GX 309-T at 3): Pokross: The biggest union we have is the Detective’s [sic] Pension Fund. Laken: Which is how much? POKROSS: Uh, four hundred and fifty to five hundred mill. Laken: That one alone is that big? Pokross: Yeah. (Id. at 2.) Pokross added: Then we go to the other side of the fence. We got Local... Production Local Number 400. That’s sixty mill. We got the Operating Engineers Union, which is probably about four hundred mill. Okay, and so on and so forth. So we have a whole dichotomy. Laken: [ ]To say the least. Pokross: We have the Detectives to, to, to the Labor Unions. Okay? Laken: Yep. Pokross: But those are all our friends. Laken: Right. (Id. at 3.) Pokross also explained how his “very, very good friend” (id. at 4), referring to (though not naming) Pérsico, had come to have control of Local 400: Pokross: Okay. In regard to the Production Local, okay... Our very, very good friend has that. And he has that on default, because the guy that ran it is, ya know, is ah no longer with us. Laken: Oh, he’s gonzo, huh? Pokross: Yeah, lead poisoning, so... Laken: Lead poisoning. Pokross: Yeah, none the less, Jimmy and I, Jimmy and I uh... Laken: [ ]How many pieces of lead poisoned him? Pokross: Well, I don’t know. Well several. Laken: []Several. Pokross: []I don’t think, I don’t think they found him... but I, you know... whatever. Laken: Who did he piss off? Pokross: I don’t wanna get into what certain cousins... Laken: []Okay. Pokross: [ ]But none the less, one of the cousins now has the Union. He’s Business Manager. So... Laken: Right. (Id. at 4-5.) In. a subsequent telephone conference call on March 8 among Laken, Pokross, and Stephens, Laken told Stephens that Pokross was lining up a number of pension *79 funds that might subscribe to Stephens’s investment advisory services. Laken said, I know, from the discussions that I’ve had with Jeffrey, that your potential advisory services are blooming. That through Jeffrey’s network of individuals and the people that he has spoken to uh, he’s developing and fertilizing a number of potential relationships for you. Stephens: Pre-tenderizing? Laken: Pre-tenderizing. (GX 307-T at 6.) Laken predicted that investment recommendations by Stephens would encounter little resistance from the trustees of the pension funds in question {see id. at 20), “like this Detectives Endowment Fund,” “[a]nd the Operating Engineers” {id. at 21); Pokross added to that list other unions, including “Local 400” {id.). On March 22, Laken and Stephens met with Pokross and others in New York. Pokross emphasized the need to bribe— and the ease of bribing — DEA Treasurer Steve Gardell: You gotta remember something. These guys make about 80, 90,000 dollars a year. Tommy [Scotto] lives in a million dollar house across the street from Jimmy [Labate]. Garden’s got a gambling problem. Okay. He makes about 80-90 grand a year. We take care of Steve. We do what ever we have to do. So Steve lives a lifestyle... he needs 500,-000 a year. Okay? (GX 318-T at 12.) Laken said, “if the money is gonna come to me to do this... you know what I mean, to do this venture ... I’m more than willing to do what I need to do so that everybody gets fed appropriately.” {Id. at 14 (emphasis added).) Pokross continued: [W]ith Steve Gardell... okay... with Jimmy and I giving him 50,000 a year for every million... in a fucking Speed Racer lunch box. That’s what’s important for Steve Gardell. ‘Cause we send him to Atlantic City. We make him reservations. We got him hotel suites... and his play doesn’t deserve that. That’s what’s important to Steve. {Id. at 15.) Pokross reiterated that “Steve wants his 50,000 dollars per million or his 25,000 per million. Whatever we’re gonna pay him,” to which Laken responded, “Right.” {Id.) Pokross compared Gardell’s demands with those that could be expected from others such as Labate’s cousin Ralph Gargiulo (who “was an executive at the Operating Engineers Local in Staten Island” (Trial Tr. 3014; see also GX 74B Conf-T at 18-19)). Pokross told Laken, “a guy like Steve, we gotta kick him back 25, 35 grand. His [Labate’s] cousin Ralphie, with the Operating Engineers [of Staten Island], he gives us 5 million dollars, I gotta give him a fucking bag... a 150,000 in cash.” (GX 318-T at 24.) Laken responded, “Right.” {Id. at 25.) When Stephens asked on March 22 what was needed of him while he was in New York, Labate indicáted that they would try to set up a conference call with “Sig[n]ore[lli]” of “the Wes[t]chester Operating Engineers.” (GX 74B Conf-T at 11-12.) Although it is unclear whether such a call was arranged at that time, Labate sent Calvello materials containing information on Stephens’s firm on March 28 {see GX 849; Trial Tr. 4163), and in an April 11 meeting with Labate, Pokross, Black, and others, Calvello stated that he had spoken by telephone to Stephens and had passed the Stephens materials on to the Signorel-lis {see, e.g., GX 88C Desk-T at 18). On April 18, Calvello reported that Signorelli Jr. had read the Stephens materials {see GX 93A Conf-T at 3) and would try to get Calvello an appointment with Signorelli Sr. {see id. at 5). *80 On April 26, Calvello reported to Pok-ross that he had spoken that day to both Signorellis (see GX 98E Conf-T at 2) about the possibility of investing “ ‘through very dear friends’ ” (id.) at a return rate of “18 or 20 or 30%” (id. at 3 (internal quotation marks omitted)); that “they like[d] what they heard” (id. at 4); and that Signorelli Sr. “was very impressed” (id. at 2). Sig-norelli Sr., who in Calvello’s view was not generally cordial, invited Calvello to come to see him (see id. at 4), which Calvello planned to do in the near future (see id. at 5). Calvello stated that he had not provided details of the investment plan to Signo-relli Sr. that day because Signorelli Jr. was present, and Calvello “would never mention anything with 2 people around” (id.). On May 4, Calvello informed Pokross that Signorelli Jr. thought the plan “look[ed] so good” (GX 104B Conf-T at 6), but that Calvello had not yet been able to meet with Signorelli Sr. alone (see id.). He stated that he was hoping to meet with Signorelli Sr. the following week because Labate had told him Stephens would be in town. (See id.; see also GX 103D Conf-T at 10 (Labate stating to Pokross, Laken, and others on May 3, 2000, that “when Stephens comes in on the 15th, we’re gonna make him meet with the Engineers in Westchester”).) In the meantime, on March 23, Stephens had made a presentation to Gardell to persuade him to retain Stephens as investment advisor for the DEA. At the end of that presentation, Gardell stated, “I can tell you 90% it looks pretty good,” and that he would be able to commence the retention of Stephens around July 1. (GX 75B Conf-T at 20.) Gardell said he would like to meet with Stephens in San Francisco. Stephens agreed, and he arranged and paid for round-trip flights for Gardell and his secretary, as well as hotel accommodations for five days. (See, e.g., GX 925; GX 90C Conf-T at 2; Trial Tr. 3108-11.) On April 13, 2000, Stephens sent Pokross, by fax, a travel itinerary and a receipt for E-tickets for Garden’s trip. (See GX 925; Trial Tr. 3110.) On April 26, Pokross reported to Black that Gardell was then in San Francisco, meeting with Stephens. Black: Have we gotten any word back? Pokross: I’m gonna get it later, or certainly tomorrow. They were out for dinner last night. I don’t need word how their uh... Dungeness crab was. Black: Well, you figure, you know... Pokross: I know how it’s gonna go. Meaning, I know the outcome of it in advance. Black: Alright. So you’re saying it’s a done deal? Pokross: It’s impossible to fuck it up. (GX 98B Conf-T at 2.) Black responded approvingly, stating that he wanted Laken’s hedge fund launched by June. (See id. at 3.) The discussion then turned to other pension funds whose trustees might be persuaded to invest their pension fund assets in Laken’s hedge fund if Gardell so invested DEA funds: Black: And how about the other ones from... Baker and, and Operating. ..? Pokross: We’re working. Black: Alright. Pokross: We got em all lit up. Let him come back, so I can point to him. Black: Alright. Okay. Pokross: And then we have Local 137 in play... up in Westchester. (Id. at 4.) Laken expressed the same views, both as to the likely success of the meeting between Gardell and Stephens and as to the persuasive effect that an agreement with Gardell would have on the other tar *81 geted unions. Although on April 26 Laken said he had not yet received a report from Stephens as to how the meeting with Gar-dell had gone, Laken said he had had an extended chat with Bill on Sunday night at home. Pokross: Yeah, go ahead. Laken: .. .And, and I told him pretty much that. I said, you know... I, I said... you know, “this is pretty much idiot proof. This guy is the Number One domino in a number of dominos.” (GX 98B Conf-T at 13.) Pokross said that before Gardell left for San Francisco to meet with Stephens, Pokross “took a visit to his house early one morning” to ensure that Gardell was “well equipped to do shopping and uh, have spending money.” (Id. at 14.) Laken responded, “Well, I figured he was pre-tenderized.” (Id.) Later on April 26, Gardell telephoned Pokross to say that the meeting with Stephens had gone well and that the investment of DEA assets with Stephens was “99.9 a go.” (GX 98D Conf-T at 3.) On May 3, Laken reported that Gardell had told Stephens that “it was a done deal.” (GX 103D Conf-T at 2.) 3. The Allegations Against Phillips and Rossi The indictment alleged that the scheme to defraud union pension plans and to pay illegal kickbacks to union officials also envisioned use of a second corrupt investment vehicle, to wit, American Realty Trust (“ARB”), a REIT controlled by Basic Capital Management Inc. (“Basic”). Basic was an advisory firm controlled and managed by defendants Phillips and Rossi, respectively. The indictment alleged that the defendants agreed that Phillips would have ARB issue a series of preferred stock that would appear to be suitable for investment by a pension fund; that Stephens would recommend investments in that ARB preferred stock (as well as in Laken’s hedge fund); and that Rossi would structure the offering of the preferred stock to allow a portion of the proceeds to be paid to the coconspirators. The alleged agreement was that out of every $10 million of union pension funds invested in the fraudulently issued ARB preferred stock, the enterprise would secretly be paid some $2 million. A portion of that $2 million was to be used to pay off the corrupt union officials. 4. The End of the Scheme; the Redacted Indictment The scheme came to a halt in June 2000, when the FBI concluded its investigation and arrested Laken and Black (and many others) before any pension fund moneys had actually been invested in the corrupt investment vehicles or diverted. As eventually redacted and submitted to the jury, the pension fund fraud/kickbacks indictment at issue here charged Laken and Black, along with Stephens, Phillips, and Rossi, in seven counts: Count One: RICO conspiracy to violate 18 U.S.C. § 1962(c) by conducting the affairs of an enterprise (described as the association of DMN Capital, the defendant individuals, and others) through a pattern of racketeering activity, to wit, wire fraud and illegal kickbacks, in violation of 18 U.S.C. § 1962(d); Count Two: conspiracy to commit securities fraud, wire fraud, and fraud by an investment advisor, and to pay illegal kickbacks, in violation of 18 U.S.C. § 371; Count Three: wire fraud in connection with the scheme to defraud Local 400, in violation of 18 U.S.C. §§ 1343, 1346, and 2; *82 Count Four: offering or promising illegal kickbacks to officials of Local 400, in violation of 18 U.S.C. §§ 1954 and 2; Count Five: wire fraud in connection with the scheme to defraud the DEA, in violation of 18 U.S.C. §§ 1343 and 2; Count Six: theft of the honest services of a DEA official, specifically Gar-dell, in violation of 18 U.S.C. §§ 1343, 1346, and 2; and Count Seven: offering or promising illegal kickbacks to officials of Local 137, in violation of 18 U.S.C. §§ 1954 and 2. 5. The Plea Allocutions of Lino and Labate The defendants named in the original indictment also included Pérsico, Gardell, Lino, and Labate. Those four defendants entered pleas of guilty prior to trial. Over objection, portions of the plea allocutions of Lino and Labate were introduced at the trial of Laken, Black, Stephens, Phillips, and Rossi. As discussed in greater detail in Part II.A. below, those allocutions stated, to the extent pertinent to the pension fund fraud/kickbacks charges, that there had existed a conspiracy to bribe union pension fund officials and that the DEA and Locals 400 and 137 were targets of that conspiracy. 6. The Verdicts The jury returned verdicts of guilty on all counts as to Laken and Black. Stephens, who presented a defense of entrapment, was acquitted on all counts. Phillips and Rossi were also acquitted on all counts. B. The FWEB Conspiracy and Other Charges Against Reifler FWEB, a small company whose stock was traded over-the-counter, was purportedly engaged in the business of providing investment-related services on the Internet, including information on stocks. One of its featured services, “The Stock Detective,” offered to advise subscribing investors of suspicious circumstances involving the stocks of other companies. The FWEB conspiracy indictment, which was assigned to Judge Stein, alleged that Laken, personally or through nominees, controlled large blocks of FWEB stock. It alleged that Reifler was in the business of promoting stocks through, inter alia, Internet promotions and mass mailings of newsletters to investors and that he had described to Laken a fraudulent newsletter program and his past track record in generating high trading volume in over-the-counter stocks at inflated prices. This indictment alleged that beginning in or about February 2000, Laken sought to sell blocks of FWEB stock under his control, that he and others conspired to inflate the price of FWEB stock artificially in order to permit Laken to sell his shares at a profit, and that Reifler joined the conspiracy in or about April 2000. Count 1 alleged that Laken paid his coconspira-tors by secretly giving them blocks of free-trading FWEB stock, that retail brokers were so paid to induce them to create trading volume in the stock, and that neither the fact of those payments nor the fact that Laken would be the true party to the sales transactions was disclosed to the public. That count charged Laken, Reifler, and others with conspiring to commit securities fraud, wire fraud, commercial bribery, and fraudulent failure to disclose compensation for stock promotion, in violation of 18 U.S.C. § 371. Count 2 of the indictment charged Laken, Reifler, and others with securities fraud; count 5 charged those defendants with wire fraud. Counts 3 and 4 charged Laken and others, not including Reifler, with fraudulent concealment of compensation for stock promotion. *83 After this indictment was made public, the price of FWEB shares plunged. FWEB shareholders lost millions of dollars. In February 2002, following the conclusion of his trial on the pension fund fraud/Mckbacks charges, Laken entered a plea of guilty to Count 1 of the FWEB conspiracy indictment in satisfaction of all of the charges against him in that indictment. In his plea allocution, he stated, “I agreed with others [to] inflate the price of FWEB stock above its market value.” (Laken Plea Transcript, February 25, 2002 (“Laken Plea Tr.”), at 34-35.) Laken also asserted that at the time of that conduct, he “didn’t know it was illegal.” (Id. at 41.) Reifler agreed to the filing of a three-count information against him superseding the FWEB conspiracy indictment. The information charged him with the FWEB conspiracy, in violation of 18 U.S.C. § 371, and two apparently unrelated counts of credit card fraud, in violation of 15 U.S.C. § 1644(a). In March 2002, Reifler pleaded guilty to those three charges. In his plea allocution with respect to the FWEB conspiracy charge, Reifler said: I agreed with others to attempt to artificially raise the price of the F Web stock through internet and other promotions. These individuals were doing this in a manner which failed to disclose that Glen [sic ] Lakin [sic ], a shareholder in F Web, was the driving force behind the promotion and that he planned to sell all his stock at these inflated profits if the profits could be achieved. (Reifler Plea Transcript, March 12, 2002 (“Reifler Plea Tr.”), at 24.) C. The Sentences and the Issues on Appeal All three appellants received Guidelines sentences based on calculations discussed in greater detail in Part III below. Judge Pauley sentenced Black principally to 37 months’ imprisonment. Laken’s convictions of the pension-fund-related offenses following his trial before Judge Pauley and his conviction of the FWEB conspiracy following his plea of guilty before Judge Stein were consolidated for sentencing before Judge Pauley, who sentenced Laken principally to a total of 63 months’ imprisonment and ordered him to pay $6,620,675.33 in restitution to victims of the FWEB conspiracy. Judge Stein sentenced Reifler principally to 63 months’ imprisonment and ordered him to pay $2 million in restitution to victims of the FWEB conspiracy. As discussed in Part II below, Laken and Black challenge their pension-fund-related convictions, alleging constitutional and evidentiary errors at trial and contesting the sufficiency of the evidence on several counts. As set forth in Part III below, all three appellants make a variety of challenges to their sentences, complaining of interpretations of specific guidelines and, in any event, seeking resentencing pursuant to Booker and Crosby on the ground that the district court considered application of the Guidelines to be mandatory. As set forth in Part IV below, Laken and Reifler also make several challenges, including statutory-interpretation and Booker challenges, to the orders for restitution. II. CHALLENGES BY LAKEN AND BLACK TO THEIR CONVICTIONS In challenging their convictions, Laken and Black contend principally (A) that the trial court’s admission of codefendants’ plea allocutions violated their Sixth Amendment rights of confrontation as enunciated in Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004); (B) that the admission of references to organized crime and to additional *84 other-act evidence denied them a fair trial; (C) that the evidence was insufficient to support their convictions on Count Three (wire fraud in connection with Local 400), Count Four (offering or promising illegal kickbacks in connection with Local 400), Count Seven (offering or promising illegal kickbacks in connection with Local 137), and two of the three predicate racketeering acts wire fraud and/or illegal kickbacks with respect to Locals 400 and 137) alleged in the Count One RICO conspiracy-charge; and (D), assuming the merit of their insufficiency challenges, that the convictions on the remaining counts should be vacated on the ground of retroactive mis-joinder. For the reasons that follow, we conclude that these contentions provide no basis for reversal. A. The Crawford Error At the pension fund fraud/kickbacks trial, the government was allowed, over objection, to introduce portions of the allocu-tions given by Lino and Labate in entering pleas of guilty to RICO conspiracy and a substantive RICO violation. Each allocution dealt with the fraudulent operations of DMN Capital from 1995 to 2000 and with the expansion of its operations in late 1999 to include the union pension fund fraud/kickbacks scheme. Lino’s admissions were as follows: “From 1995 up until June 2000, I and others were involved with financial advisory company called DMN Capital Incorporated located in Manhattan. DMN Capital was in the business of promoting stocks of various companies and raising money for those companies. I knew that it was a part of business of DMN Capital to line up brokers to work on these deals and these brokers would receive secret payments, cash under the table, to sell these stocks to their customers. Brokers were supposed to discourage customers from selling in return for these payments. “I was informed of and approved deals with certain groups of brokers at various stock brokerage firms in Manhattan and New Jersey. I also knew that DMN Capital and another secretly controlled firm in Manhattan called Monitor Investment Group in 1995 and 1996. I helped to settle disputes between DMN Capital and various brokers at these firms and others about how much monies they were owed. I also helped settle disputes about failures of brokers to pay money that was owed to DMN. I also occasionally brought deals to DMN Capital and asked the partners to work on them. “Later, in approximately 1997, I helped to arrange DMN Capital control over two branches of First Liberty Investment Group in Manhattan. I knew that the secret payments to brokers were wrong and against the law and the investors were defrauded because they wound up paying too much for these stocks. I didn’t know the names of all these stocks that DMN Capital worked on. I do not dispute that the stocks identified in racketeering acts one through four of Count One of the indictment were DMN Capital deals. “In return for my assistance the manipulation of stocks with DMN Capital and others tha[n] DMN Capital partners paid me a weekly salary in cash. I understood this ... money came from the proceeds of illegal stock sales and that DMN Capital had engaged in financial transactions to generate this cash. I knew that these financial transactions were wrong and against the law. “In late 1999 the business arrangement that I had with DMN Capital and others expanded to include a plan to defraud several unions’ pension *85 funds. We agreed that DMN Capital and others would market fraudulent investments to these pension funds. I understood that DMN Capital and others entered into agreements that would result in large kickbacks, and part of that money woidd be used to pay off union officials to get the pension officials to invest in these deals. “Two of these unions were the Detectives’ Endowment Association and the Local 400. I also knew there were several others. I knew that this plan to defraud the pension funds was wrong and against the law.” (Trial Tr. 2475-77 (quoting GX 855, at 18-21 (emphases ours)).) The admitted portion of the Labate plea allocution was similar: “I was a principal at DMN Capital from ’95 through June of 2000. I, with others, participated in the promotion of the sale of stock of various companies and raised money for those companies. I participated with others in getting stockbrokers to work on these deals, and we paid these brokers secret commissions to sell stock to their customer. We also agreed that these brokers would prevent their customers from selling stock they had purchased. Reclaim, in racketeering act two, was a stock on which we paid secret money to stockbrokers. “DMN, of which I was a principal, controlled the brokerage firm, Monitor Investment Group. In 1995 through 1996 we used Monitor to further our ability to fraudulently sell stock to the public by paying secret commissions to brokers to prevent customers from selling their stock they had purchased. “Monitor and various brokers working with us sold stock in Beachport International Stock named in the racketeering act three and four. Brokers were paid cash for excessive commission. “I knew it was wrong to pay secret payments to brokers and against the law to defraud investors. As to racketeering act nine, we engaged in financial transactions and to hide the illegal activity and unlawful payment for brokers and others. I knew this was wrong and I did it in violation of law. “In 1996 Monitor was shut down and DMN had to look for another retail outlet for the stock deals. In 1996 and early ’97 we negotiated to obtain First Liberty Investment Group in Manhattan. We did this secretly with two stockbrokers acting as a front for DMN. With their help we sold Globus International by manipulating the market for Globus so that customer paid more than the stock was worth. I also knew there was a large commission on Globus at First Liberty. “In early 2000 I, with others at DMN, attempted to defraud various union pension funds. We agreed that DMN and others would market fraudulent investments to these pension funds. We agreed with others who are behind the deal that DMN would get large kickbacks from delivering pension funds as clients would invest in these deals. “We also agreed with the people behind these deals that ive would use part of the kickbacks to pay off union officials to influence pension funds in their investment decision. The unions ivere Production Workers Local 400, Detectives’ Endowment, and Operating Engineers of Local 137. I knew this plan was wrong and in violation of the law.” And in response to a question posed by the Court: “Did you understand that commissions being paid with respect to the Globus International Securities transaction were secret and excessive?” *86 The defendant answered: ‘Tes.” (Trial Tr. 2477-79 (quoting GX 856, at 19-22 (emphases ours)).) The racketeering acts cited by Lino and Labate in the above allocutions referred to an indictment that preceded the redacted indictment; although those acts paralleled certain of the redacted indictment’s allegations as to the means and methods of operation of the RICO enterprise, they were not among the racketeering acts alleged in the redacted indictment. In accordance with this Court’s then-prevailing holdings, see, e.g., United States v. Dolah, 245 F.3d 98, 104-05 (2d Cir.2001); United States v. Petrillo, 237 F.3d 119, 122-23 (2d Cir.2000); United States v. Moskowitz, 215 F.3d 265, 268-70 (2d Cir.2000); United States v. Gallego, 191 F.3d 156, 166-68 (2d Cir.1999), cert. denied, 530 U.S. 1216, 120 S.Ct. 2220, 147 L.Ed.2d 252 (2000), the district court allowed these allo-cution statements to be introduced on the limited issues of whether either conspiracy alleged in the indictment existed and what acts Lino or Labate had performed in furtherance of such a conspiracy if it existed. Upon admitting the allocutions, the court instructed the jury that the statements could be considered for those purposes only: Members of the jury, please understand that you may consider these guilty plea proceedings of Robert Lino and James S. Labate only on the following two issues: First, whether there was a racketeering conspiracy or a conspiracy to defraud union pension funds; and second, what, if anything, a defendant who pled guilty did, in order to further the objects of any of those conspiracies if you find that one or both existed. However, the question of whether any one of the defendants on trial before you was also a member of either one or both of the charged conspiracies is an issue for which you ioill have to rely on other evidence. There is no evidence in these statements naming any other defendant or co-conspirator. (Trial Tr. 2479-80 (emphasis added).) The court emphasized that the matter of “whether any defendant on trial was a part of the alleged conspiracy” was “a separate question” that the jury must decide “based entirely on the other evidence in the case,” and that “[t]here is nothing in these statements from Mr. Lino and Mr. Labate that answers that question one way or the other.” (Id. at 2480.) These limitations were reiterated in the court’s general charge to the jury prior to deliberations (see id. at 8252-53) and again in supplemental instructions when the plea allocutions were among the exhibits requested by the jury during deliberations (see id. at 8514, 8519-20). In 2004, Crawford v. Washington established that, in the trial of a criminal case, the Confrontation Clause of the Sixth Amendment bars the admission of an out-of-court testimonial statement against the defendant unless the declarant is unavailable and the defendant had a prior opportunity to cross-examine him. See 541 U.S. at 68, 124 S.Ct. 1354. While “leav[ing] for another day any effort to spell out a comprehensive definition of ‘testimonial,’ ” the Crawford Court stated that “[wjhatever else the term covers, it applies at a minimum to prior testimony at a preliminary hearing, before a grand jury, or at a former trial; and to police interrogations.” Id. In the wake of Crawford, we have held that a plea allocution is a testimonial statement, “as it is formally given in court, under oath, and in response to questions by the court or the prosecutor.” United States v. McClain, 377 F.3d 219, 221 (2d Cir.2004). “Therefore, a plea allocution by *87 a co-conspirator who does not testify at trial may not be introduced as substantive evidence against a defendant unless the co-conspirator is unavailable and there has been a prior opportunity for cross-examination.” Id. at 222. In the present case, there is no suggestion that Laken or Black had any opportunity to cross-examine Lino or La-bate with respect to their plea allocutions, and the government concedes that, in light of Crawford, the admission of those allocu-tions violated the rights of Laken and Black to confrontation. The government contends, however, that the error provides no basis for relief because it was harmless, see Fed.R.Crim.P. 52(a) (“Any error ... that does not affect substantial rights must be disregarded.”). For the reasons that follow, we agree. Prior to Crawford, it was established that violations of the Confrontation Clause, when preserved for appellate review, are subject to harmless-error review, see, e.g., Coy v. Iowa, 487 U.S. 1012, 1021, 108 S.Ct. 2798, 101 L.Ed.2d 857 (1988); Delaware v. Van Arsdall, 475 U.S. 673, 684, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986), and we have interpreted Crawford as not altering that principle, see, e.g., Gutierrez v. McGinnis, 389 F.3d 300, 302-03 (2d Cir.2004); United States v. McClain, 377 F.3d at 222. In order to disregard an error of constitutional dimension, we must be convinced that the error was harmless beyond a reasonable doubt. See Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). In assessing the error’s likely impact, we consider the nature of the violation and the context in which it occurred, see, e.g., United States v. Casamento, 887 F.2d 1141, 1179 (2d Cir.1989), cert. denied, 493 U.S. 1081, 110 S.Ct. 1138, 107 L.Ed.2d 1043 (1990), taking into account, in this case, the strength of the government’s case, the degree to which the statement was material to a critical issue, the extent to which the statement was cumulative, and the degree to which the government emphasized the erroneously admitted evidence in its presentation of the case. See generally Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431; Gutierrez v. McGinnis, 389 F.3d at 308-09. No one factor is dispositive. See generally id. at 309 (hypothetically erroneous admission was harmless “[gjiven the overall strength of the prosecution’s case” and the fact that “the prosecutor highlighted [the challenged evidence] as only one of several important pieces of evidence ... during his lengthy summation”) (emphasis in original); United States v. McClain, 377 F.3d at 222-23 (erroneous admission of plea al-locutions held to be harmless where “[t]he evidence of ... guilt was overwhelming” and “the plea allocutions were cumulative”). However, “[t]he strength of the prosecution’s case is probably the single most critical factor.” Latine v. Mann, 25 F.3d 1162, 1167-68 (2d Cir.1994) (internal quotation marks omitted), cert. denied, 514 U.S. 1006, 115 S.Ct. 1319, 131 L.Ed.2d 200 (1995). Assessing these factors in the present case, we find no basis for reversal. First, there was little emphasis on the plea allo-cutions of Lino and Labate by the government at trial. The government referred to the allocutions in only one paragraph of its lengthy summation, citing them as evidence consistent with the testimony of Pokross as to the existence of an enterprise and the targeting of the DEA and Locals 400 and 137: The enterprise, as we’ve said, is DMN Capital and the stock fraud business that it was in all the way up from ’95 into 2000. You have heard Jeffrey Pok-ross testify about the business that he was in, and you heard a lot about that on cross-examination, and I think you have *88 a pretty clear idea about the kind of activity that he was involved in with his partners back in ’95 and ’96 and that his partners continued in while he was cooperating. You know the enterprise existed not just from what Mr. Pokross told you. You know it because you heard the plea allocutions of Robert Lino and James Labate. Their statements when they pleaded guilty show that there really was a criminal stock fraud business from ’95 to 2000, that it really was involved in all those deals that Pokross told you about, and that it really was involved in ’99 and 2000 in a criminal scheme to bribe union officials and defraud union members, including to defraud and bribe people at the Detectives Endowment Association, Local WO of the Production Workers and Local 137 of the Operating Engineers union. So there should be no question in any of your minds that there really was an enterprise here, there really was a criminal business. (Trial Tr. 7606-07 (emphases added).) There was no other mention of the plea allocutions in the government’s main summation, which covered more than 110 pages of transcript (see id. at 7592-7645, 7650-7709); and there was no mention of the allocutions in the government’s 52-page rebuttal summation (see id. at 8052-8103). Second, although the plea allocution statements bore on two essential elements of the conspiracy charges — to wit, (1) the existence of a RICO “enterprise,” which is defined to “inelude[ ] any individual, partnership, corporation, association, or other legal entity, and any union or group of individuals associated in fact although not a legal entity,” 18 U.S.C. § 1961(4); and (2) the existence, for purposes of 18 U.S.C. § 371, of an agreement between or among two or more persons to commit a federal offense — and although the plea allocutions identified some of the targets of those alleged conspiracies, they were plainly cumulative. Each fact they stated with respect to these issues was the subject of testimony by Pokross and of recorded conversations that were properly introduced at trial. Third, the government’s permissible evidence supporting the elements alluded to in the admitted portions of the plea allocu-tions was abundant. As set forth in detail in Parts I.A1. and 2. above and summarized below, the trial record included recordings of Laken’s and Black’s own conversations showing that DMN Capital, Laken, Labate, Black, and others constituted an association; that Laken, Labate, Black, and others agreed to defraud union pension funds by, inter alia, bribing and offering or promising kickbacks to union officials; and that the targeted pension funds included those of the DEA, Local 400, and Local 137. As to the existence of a RICO enterprise and of a fraud/kickbacks conspiracy, and as to the membership of Laken and Black in the enterprise and the conspiracy — -leaving aside the identities of the targets — the record included taped evidence — that Black promised that if DMN Capital found investors for Laken’s planned hedge fund, Laken would pay DMN secret commissions amounting to $150,000 to $200,000 a year for every million dollars invested (see, e.g., GX 44A Conf(2)-T at 2); and that when Labate pointed out that “the guy’s gonna want 60%,” Black responded, “we’ll... however, however we gotta take care of it” (id.); — that Black stated that he expected to receive a share of the secret commissions (see GX 44A Conf(2)-T at 2; GX 45B Conf-T at 7); *89 • — ■ that Black viewed himself as participating in a joint venture with DMN and Labate, stating that Laken would generate excess commissions and “[tjhat’s how he’s gonna pay us” (GX 45B Conf-T at 3); — that Black agreed that paying union officials 70 percent of the secret commissions would leave DMN and Black with a share that was worthwhile (see GX 45B Conf-T at 4-8); — that Laken stated to Labate and Black (and to Pokross, who could not be a member of the conspiracy because he was cooperating with the government) that “[a]t the end of the day what’s in it for you” is a “kick back” (GX 46C Conf(l)-T at 12); — that while Laken demurred somewhat from Black’s prediction as to the amount of the kickbacks, Laken stated that he would churn the invested moneys to such an extent that “a buck and a half a round turn c[ould] amount to a very, very substantive number very quickly” (GX 46C Conf(l)-T at 12), and that “it w[ould] be a very generous commission throw back on the monies raised” (id at 21); — that Laken said DMN’s “friends will make a lot of money” (GX 46C Conf(l)-T at 21); — and that, in a discussion as to the amounts of cash that would be expected by various union officials for investing in Laken’s hedge fund, Laken said, “I’m more than willing to do what I need to do so that everybody gets fed appropriately” (GX 318-T at 14). As evidence that three unions whose pension funds were targeted were the DEA (also referred to as the “Detectives” Pension Fund or Endowment Fund or Retirement Fund), Local 400 (also referred to as the “Production Workers” union), and Local 137 (also referred to as the “Operating Engineers” or the “Operating” union), the recorded conversations to which Laken and/or Black were parties showed — that at the outset, Pokross told Laken, “we have a very, very near and dear friend of ours who runs the Detectives uh, Retirement Fund... that’s got about 300 million dollars in it” (GX 45B Conf-T at 16); — that thereafter, Pokross described “the Detective’s [sic] Pension Fund” to Laken as “[t]he biggest union we have” (GX 309-T at 2) and said, in addition, “[w]e got Local ... Production Local Number 400” and “[w]e got the Operating Engineers Union” (id at 3); — that Black stated his “understanding” that one of the targeted funds “[wa]s the Detectives Endowment Fund,” of which “Gardella [sic] [wa]s the Treasurer” (GX 60D Conf-T at 2); — that Black attended a meeting in which Pokross, describing how Stephens would distribute pension fund investments between ARB and “Laken’s” hedge fund (GX 69C Conf(l)-T at 22), stated that they were dealing with the “Production Workers” and the “Operating Engineers” (id at 18), and stated that Stephens was “tickled pink” at the prospect of dealing with the assets of pension funds “like [the] Production Workers[ and the] Operating Engineers” (id at 21); — that after Garden's meeting with Stephens in San Francisco, Black sought and received assurance that the DEA investment was “a done deal” (GX 98B Conf-T at 2); that Black then asked, “[a]nd how about the other ones,” mentioning the “Operating” union (id at 4); and that Pokross stated, “we have Local 137 in play... up in Westchester” (id); — and that Laken, in predicting that Stephens would encounter minimal resistance from the trustees of the tar *90 geted pension funds, mentioned the “Detectives Endowment Fund,” “[a]nd the Operating Engineers” (GX 307-T at 21); and in that conversation Pokross stated that Local 400 too was in that category (see id.). We think it plain, in light of these recorded conversations of Laken and Black, along with the testimony of Pokross described in Parts I.A.1. and 2. above, that the government’s evidence to establish the existence of both the RICO enterprise and the pension fund fraud/kickbacks conspiracy was overwhelming, and that the evidence (a) establishing the targeting of the DEA and Locals 400 and 137, and (b) establishing that Laken and Black were well aware that each of those three unions was a target, was ample without any consideration of the Lino and Labate plea allocutions. Finally, the jury’s verdicts themselves strongly indicate that the plea allocutions played no role in the convictions of Laken and Black. The relevant passages of the allocutions did not name any of the defendants who were then on trial. Nor did they indicate the methods by which the scheme to defraud pension funds and give illegal kickbacks to corrupt union officials was to be carried out. There was no mention of a hedge fund; there was no mention of churning a pension fund’s account; there was no mention of generating excessive commissions. Rather, the allo-cutions were equally applicable to both the plan to use Laken’s hedge fund to generate excessive commissions and the alleged plan to use Basic to siphon off 20 percent of the pension funds’ anticipated investments in the ARB REIT controlled and run by Phillips and Rossi. The jury, however, while convicting Laken and Black, acquitted Phillips and Rossi on all counts. Further, although Stephens, who was recruited by Laken and Black, was alleged to have participated intimately with Laken in the scheme to defraud pension funds by having them invest in, inter alia, Laken’s hedge fund, the jury acquitted Stephens on all counts. The jury returned verdicts of guilty only against Laken and Black, whose incriminating conversations permeated the recorded evidence. The jury’s differentiation among similarly accused defendants in light of the varying evidence presented against each through the testimony of Pokross and the tape recordings plainly indicates that the jury heeded the court’s instructions that the plea allocu-tions — which were admitted equally against all five of these defendants — could not be relied on as proof, on any count, of the guilt of a defendant who was on trial. We thus see no reasonable possibility that the plea allocutions might have contributed to the convictions of Laken and Black. ■ In sum, given the discerning nature of the verdicts, the brevity of the government’s mention of the plea allocutions, the purely cumulative character of the statements, and the strength of the government’s case against Laken and Black, we conclude that the Crawford error was, beyond a reasonable doubt, harmless. B. The Evidentiary Challenges As indicated in Parts I.A.1. and 2. above, Pokross testified that he had been an associate of the Bonanno Crime Family and that Black, Labate, Lino, Pérsico, and others were members or associates of various organized crime families. Pokross explained in general, inter alia, the positions and hierarchy within a crime family and ways in which disputes between or among such families, or between factions within a crime family, are resolved. (See Trial Tr. 2512-13.) In addition, the government was allowed to introduce evidence that Black, contemporaneously with his involvement in the pension fund fraud/kickbacks *91 scheme, was participating in a scheme to manipulate the stock of a company called Motorsports, Inc. (“Motorsports”). (See id. at 3159-66.) Laken and Black contend that they were denied a fair trial by the admission of the organized crime and Mo-torsports evidence. They argue that such evidence “had little or nothing to do with any fact in issue in this case” (Black brief on appeal at 58) and was unfairly prejudicial (see, e.g., id. at 60; Laken brief on appeal at 66). The principles governing such contentions are well established. Evidence is relevant, and hence normally admissible, if it would tend to make the existence of any material fact more probable or less probable than it would be without that evidence. See Fed.R.Evid. 401, 402. Evidence of other acts or crimes, although not admissible to prove a party’s character, may nonetheless be admissible for other purposes, such as proof of knowledge, intent, or absence of mistake. See Fed.R.Evid. 404(b); Huddleston v. United States, 485 U.S. 681, 687-88, 108 S.Ct. 1496, 99 L.Ed.2d 771 (1988); United States v. Gordon, 987 F.2d 902, 908-09 (2d Cir.1993). Even as to evidence that is plainly relevant and not excludable on grounds such as privilege or hearsay, however, the trial judge retains discretion to exclude the evidence “if its probative value is substantially outweighed by the danger of unfair prejudice.” Fed. R.Evid. 403; see, e.g., Huddleston, 485 U.S. at 687-88, 108 S.Ct. 1496; United States v. Gordon, 987 F.2d at 908. Assessment of proffered evidence in light of Rules 401-404 lies within the trial court’s discretion. This court will reverse the court’s evidentiary ruling “only if there is a clear showing that the court abused its discretion or acted arbitrarily or irrationally.” United States v. Salameh, 152 F.3d 88, 110 (2d Cir.1998) (internal quotation marks omitted), cert. denied, 525 U.S. 1112, 119 S.Ct. 885,142 L.Ed.2d 785 (1999); see, e.g., United States v. Valdez, 16 F.3d 1324,1332 (2d Cir.), cert. denied, 513 U.S. 810, 115 S.Ct. 60, 130 L.Ed.2d 18 (1994); United States v. Birney, 686 F.2d 102, 106 (2d Cir.1982). Laken and Black have not met this standard. 1. The Organized Crime Evidence Evidence that a defendant had ties to organized crime may be admissible in a variety of circumstances. In order to prove a RICO offense, for example, the government is required to show that there was a “ ‘pattern of racketeering activity,’ ” 18 U.S.C. § 1961(5), which is interpreted to mean “multiple racketeering predicates — which can be part of a single ‘scheme’ — that are related and that amount to, or threaten the likelihood of, continued criminal activity,” United States v. Coiro, 922 F.2d 1008, 1016 (2d Cir.), cert. denied, 501 U.S. 1217, 111 S.Ct. 2826, 115 L.Ed.2d 996 (1991); see, e.g., H.J. Inc. v. Northwestern Bell Telephone Co., 492 U.S. 229, 239, 109 S.Ct. 2893, 106 L.Ed.2d 195 (1989); United States v. Indelicato, 865 F.2d 1370, 1381-84 (2d Cir.) (en banc), cert. denied, 493 U.S. 811, 110 S.Ct. 56, 107 L.Ed.2d 24 (1989). Evidence that activities such as bribery were conducted on behalf of organized crime is relevant to establish the requisite relatedness and continuity. See, e.g., H.J. Inc., 492 U.S. at 242-43, 109 S.Ct. 2893 (A “threat of continuity is sufficiently established where the predicates can be attributed to a defendant operating as part of a long-term association that exists for criminal purposes. Such associations include ... those traditionally grouped under the phrase ‘organized crime.’ ”). Evidence of a defendant’s ties to organized crime or of his other crimes may also be admissible “to provide background for the events alleged in the indictment,” *92 United States v. Daly, 842 F.2d 1380, 1388 (2d Cir.), cert. denied, 488 U.S. 821, 109 S.Ct. 66, 102 L.Ed.2d 43 (1988); see, e.g., United States v. Tutino, 883 F.2d 1125, 1138-39 (2d Cir.1989), cert. denied, 493 U.S. 1081, 110 S.Ct. 1139, 107 L.Ed.2d 1044 (1990), or to “enable the jury to understand the complete story of the crimes charged,” or “how the illegal relationship between [coconspirators] developed,” United States v. Brennan, 798 F.2d 581, 590 (2d Cir.1986), cert. denied, 490 U.S. 1022, 109 S.Ct. 1750, 104 L.Ed.2d 187 (1989); see also United States v. Salerno, 868 F.2d 524, 536 n. 5 (2d Cir.) (evidence of association with organized crime admissible to show “the background of interfamily relationships and the development of interfam-ily trust in the area of union control”), cert. denied, 493 U.S. 811, 110 S.Ct. 56, 107 L.Ed.2d 24 (1989). “Background evidence may be admitted to ... furnish an explanation of the understanding or intent with which certain acts were performed,” United States v. Daly, 842 F.2d at 1388, to explain, for example, “the basis for the trust between” coconspirators, United States v. Brennan, 798 F.2d at 590; see, e.g., United States v. Salerno, 868 F.2d at 536 n. 5. Even as to a defendant who had no ties to organized crime, evidence that one of the other participants had such ties may be admitted if relevant to rebut the defendant’s claim that he did not know the activity in which he participated was unlawful. See, e.g., United States v. Santoro, 302 F.3d 76, 82-83 (2d Cir.2002). In the present case, the evidence that key individuals were members or associates of organized crime families was relevant in a number of ways. First, the government was required to prove that Laken and Black conducted the RICO enterprise through a pattern of racketeering activity. The evidence that Black, Labate, Lino, and Pérsico were associated with their respective organized crime families was plainly relevant to show a threat of continuity of bribery, wire fraud, and illegal kickbacks, all of which are within the definition of racketeering activity, see 18 U.S.C. § 1961(1). Second, Laken and Black argued to the jury that they had had no intent to participate in any criminal activity and did not know or believe that they were participating in a scheme that was illegal. For example, Laken’s attorney, in his opening statement, said that Laken had “no criminal intent” (Trial Tr. 65), no “intention to do anything wrong” (id. at 58). Black’s attorney argued similarly that, as to Black, the government would “fail to meet [its] burden of proof with respect to establishing the guilty mind, a mind of intent.” (Id. at 149.) The organized crime references in the conversations of Laken and Black, however, belied their claims of guilelessness and ignorance; and some of those references warranted explanatory testimony. For example, when Pokross told Black on March 1, 2000, that “certain labor unions and whatnot” are “friends of the family, if you understand what I’m saying,” Black said, “[s]ure”; when Pokross stated that the targeted funds belonged to unions that would be receptive “ ‘cause we’re all friendly with the trustees, who are hand picked by the wiseguys,” Black’s response was, “[r]ight.” (GX 60D Conf-T at 5.) Pokross’s testimony that “wise guy” is a term for an initiated member of an organized crime family, and that Black himself was a self-described associate of the Luchese Crime Family, was relevant to show that Black was well aware from this conversation (even had there been no others) that investors for Laken’s fund would be recruited through DMN’s contacts with members of organized crime and that the union pension fund trustees they were recruiting were influenced by organized crime. Other evidence confirmed *93 that Laken too understood that the “friends” who were to invest in Laken’s fund and expect kickbacks had ties to organized crime. For example, when Pok-ross told Laken that the predecessor of DMN’s “friend” at Local 400 was “ah[,] no longer with us” due to “lead poisoning,” Laken asked, “[w]ho did he piss off,” and “[h]ow many pieces of lead poisoned him?” (GX 309-T at 4-5.) Further, evidence of Black’s organized crime connection, along with evidence of Labate’s association with the Gambino Crime Family and Pokross’s assumed continued association with the Bonanno Crime Family, provided explanations as to (a) why Black could comfortably approach La-bate and Pokross with a proposal for a scheme that was explicitly fraudulent, (b) why the participants discussed the planned frauds candidly among themselves, without any apparent concern that one of them might inform law enforcement authorities, and (c) why Labate cautioned Black at the outset that Laken must not reveal to others that Black had secured the investment of union pension funds through Labate and his associates (see GX 44B Conf-T at 7 (and why Black responded, “[g]ive me the script”)). Finally, Laken and Black argued at trial that Pokross, having been arrested in 1996, had simply invented scenarios that could be viewed as crimes so that he could cooperate with the government in order to earn a lighter sentence. For example, Laken’s attorney, in his opening statement to the jury, argued that “this case is ... about Pokross’s attempts to manufacture a crime.” (Trial Tr. 57.) The organized crime evidence was also relevant to refute this argument. For example, the evidence (a) that Pérsico, who proposed the plan to defraud Local 400, was an associate of the Colombo Crime Family, (b) that Lino was a Bonanno Crime Family capo who could get confirmation from the Colombo family’s underboss that the Colombo family wished to pursue that plan, and (c) that Black, who proposed the fraudulent scheme with respect to Laken’s hedge fund, was an associate of the Luchese Crime Family and believed that Pokross was associated with the Bonanno Crime Family (see id. at 2692), was relevant to show that the pension fund fraud/kickbacks scheme was not, as Laken and Black contended, simply a figment of Pokross’s machinations. 2. The Motorsports Evidence The contention that the Motor-sports evidence was wrongly admitted does not require extended discussion. Black’s attorney, in his opening statement at trial, argued that Black had had no criminal intent because he simply had “not believe[d] what Jeffrey Pokross was saying” about paying bribes to union officials. (Trial Tr. 140.) The Motorsports evidence, however, showed that during the period of the union pension fund fraud/kickbacks scheme Black was in fact consulting Pok-ross on ways to bribe others in connection with a different matter. Pokross testified that in mid-March 2000, he learned from Black and from Mike Grecco, a Colombo Crime Family associate (see id. at 3159), that there was a dispute between them concerning Motor-sports stock. (See, e.g., id. at 3163-65; GX 98B Conf-T at 8-9.) Black had asked Grecco to bribe a group of stockbrokers to execute a fraudulent transaction in that stock on behalf of Black (see Trial Tr. 3159-60); the transaction, however, had been botched, and as a result, “[t]he bribe wasn’t received” (id. at 3160). Grecco demanded payment; and a “sit down,” or meeting to settle the dispute between the Luchese and Colombo crime families (id. at 3159), was held. As a result, Black *94 sought to generate money to pay Grecco through a new Motorsports transaction, “a particular deal that was available for bribes” (id. at 3164), and Black approached Pokross for advice and assistance in bribing stockbrokers. The Motorsports evidence was thus plainly relevant, as Black’s request for Pokross’s assistance to devise a scheme that involved bribery made it highly unlikely that he did not believe that Pokross was suggesting that the pension fund fraud scheme be implemented through bribery. Black indeed essentially concedes that the Motorsports evidence was relevant, arguing that its probative value was “minimal” (Black brief on appeal at 60), rather than nonexistent, and he contends instead that its probative value was outweighed by its potential for unfair prejudice. Given the wealth of evidence in the record as to other bribery plans, we cannot agree, and we conclude that the trial court did not abuse its discretion in admitting this evidence. C. The Sufficiency Challenges Convicted on all seven counts of the redacted indictment, Laken and Black contend that the evidence was insufficient to support their convictions on four of those counts: Count One (RICO conspiracy), Count Three (wire fraud in connection with Local 400), Count Four (kickbacks in connection with Local 400), and Count Seven (kickbacks in connection with Local 137). They do not challenge the sufficiency of the evidence to support their convictions of conspiracy in violation of 18 U.S.C. § 371 to pay illegal kickbacks and to commit securities fraud, wire fraud, union pension fund fraud, and fraud by an investment advisor (Count Two), or of wire fraud and theft of honest services with regard to the DEA (Counts Five and Six). They contend, however, that if we reverse their convictions on Counts One, Three, Four, and Seven, their convictions on Counts Two, Five, and Six should be vacated on the ground of retroactive misjoinder. “In challenging the sufficiency of the evidence to support his conviction, a defendant bears a heavy burden.” United States v. Hamilton, 334 F.3d 170, 179 (2d Cir.), cert. denied, 540 U.S. 985, 124 S.Ct. 502, 157 L.Ed.2d 378 (2003); see, e.g., United States v. Best, 219 F.3d 192, 200 (2d Cir.2000), cert. denied, 532 U.S. 1007, 121 S.Ct. 1733, 149 L.Ed.2d 658 (2001); United States v. Autuori, 212 F.3d 105, 114 (2d Cir.2000). In considering such a challenge, we must credit every inference that could have been drawn in the government’s favor, see, e.g., United States v. Hamilton, 334 F.3d at 179; United States v. Carson, 702 F.2d 351, 361 (2d Cir.), cert. denied, 462 U.S. 1108, 103 S.Ct. 2457, 77 L.Ed.2d 1335 (1983), and affirm the conviction so long as, from the inferences reasonably drawn, the jury might fairly have concluded guilt beyond a reasonable doubt, see, e.g., United States v. Hamilton, 334 F.3d at 179; United States v. Buck, 804 F.2d 239, 242 (2d Cir.1986). “We defer to the jury’s determination of the weight of the evidence and the credibility of the witnesses, and to the jury’s choice of the competing inferences that can be drawn from the evidence.” United States v. Morrison, 153 F.3d 34, 49 (2d Cir.1998). Pieces of evidence must be viewed not in isolation but in conjunction, see, e.g., United States v. Podlog, 35 F.3d 699, 705 (2d Cir.1994), cert. denied, 513 U.S. 1135, 115 S.Ct. 954, 130 L.Ed.2d 897 (1995); United States v. Brown, 776 F.2d 397, 403 (2d Cir.1985), cert. denied, 475 U.S. 1141, 106 S.Ct. 1793, 90 L.Ed.2d 339 (1986); United States v. Geaney, 417 F.2d 1116, 1121 (2d Cir.1969), cert. denied, 397 U.S. 1028, 90 S.Ct. 1276, 25 L.Ed.2d 539 (1970), and the conviction must be upheld if “any rational *95 trier of fact could have found the essential elements of the crime beyond a reasonable doubt,” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis in original). Applying these principles to appellants’ sufficiency challenges, we conclude that each lacks merit. 1. Wire Fraud Targeting Local WO (Count Three) The federal wire fraud statute makes it unlawful for any person, “having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises,” to “transmit[ ] or cause[ ] to be transmitted by means of wire, radio, or television communication in interstate or foreign commerce, any writings ... or sounds for the purpose of executing such scheme or artifice.” 18 U.S.C. § 1343. In addition to encompassing schemes to obtain money and property, “the term ‘scheme or artifice to defraud’ includes a scheme or artifice to deprive another of the intangible right of honest services.” Id. § 1346. In interpreting § 1343, we look not only to cases decided under that section but also to cases involving 18 U.S.C. § 1341, the mail fraud statute, as § 1341 uses the same relevant language in prohibiting the furtherance of fraudulent schemes by use of the mails. See, e.g., Carpenter v. United States, 484 U.S. 19, 25 n. 6, 108 S.Ct. 316, 98 L.Ed.2d 275 (1987); United States v. Slevin, 106 F.3d 1086, 1088 (2d Cir.1996) (§§ 1341 and 1343 “are analyzed in the same way”). In order to convict a given defendant of violating § 1343, the government must show, inter alia, (a) that there was a scheme or artifice to defraud, (b) that the defendant participated in the scheme with fraudulent intent, (c) that there was a wire transmission, (d) that the wire transmission was in furtherance of the scheme, and (e) that the defendant caused that transmission. See, e.g., Schmuck v. United States, 489 U.S. 705, 710-12, 109 S.Ct. 1443, 103 L.Ed.2d 734 (1989) (construing § 1341); United States v. Guadagna, 183 F.3d 122, 129-30 (2d Cir.1999) (construing § 1343); United States v. Altman, 48 F.3d 96, 101 (2d Cir.1995) (construing § 1341); United States v. D'Amato, 39 F.3d 1249, 1256-57 (2d Cir.1994) (construing § 1341). These requirements are not to be given a cramped or narrow interpretation. Rather, we “consider[ ] the scope of [the] fraudulent scheme,” Schmuck, 489 U.S. at 711, 109 S.Ct. 1443, and give appreciation to its “full flavor,” id. at 712, 109 S.Ct. 1443. The scheme-to-defraud element is construed broadly to encompass “ ‘everything designed to defraud by representations as to the past or present, or suggestions and promises as to the future.’ ” United States v. Altman, 48 F.3d at 101 (quoting Durland v. United States, 161 U.S. 306, 313, 16 S.Ct. 508, 40 L.Ed. 709 (1896)). To be in furtherance of the fraud, the wire transmission “need not be an essential element of the scheme”; rather, “[i]t is sufficient” if that transmission was “ ‘incident to an essential part of the scheme,’ ... or ‘a step in [the] plot.’ ” Schmuck, 489 U.S. at 710-11, 109 S.Ct. 1443 (quoting Badders v. United States, 240 U.S. 391, 394, 36 S.Ct. 367, 60 L.Ed. 706 (1916) (emphasis ours)). Nor need the wire communication itself have been false; even “ ‘innocent’ ” transmissions, i.e., “ones that contain no false information — may supply the [transmission] element.” Schmuck, 489 U.S. at 715, 109 S.Ct. 1443; see, e.g., Parr v. United States, 363 U.S. 370, 390, 80 S.Ct. 1171, 4 L.Ed.2d 1277 (1960). *96 The requirement that the defendant have been the cause of the wire transmission is also interpreted liberally. “Where one does an act with knowledge that the use of the [wires] will follow in the ordinary course of business, or where such use can reasonably be foreseen, even though not actually intended, then he ‘causes’ the [wires] to be used.” Pereira v. United States, 347 U.S. 1, 8-9, 74 S.Ct. 358, 98 L.Ed. 435 (1954) (construing § 1341); see, e.g., United States v. Kenofskey, 243 U.S. 440, 443, 37 S.Ct. 438, 61 L.Ed. 836 (1917) (construing predecessor to § 1341); United States v. Altman, 48 F.3d at 103. Moreover, to violate the statute, the defendant need not have completed or succeeded in his scheme to defraud, and the scheme need not have resulted in actual injury to the scheme’s victims. See, e.g., United States v. D'Amato, 39 F.3d at 1257. Further, where a necessary consequence of the scheme, if it were successful, would be injury to others, “fraudulent intent may be inferred from the scheme itself.” United States v. Guadagna, 183 F.3d at 130 (internal quotation marks omitted). Section 2 of Title 18 provides, in part, that whoever aids or abets the commission of an offense against the United States is punishable as a principal. See 18 U.S.C. § 2(a). “Under 18 U.S.C. § 2, a defendant may be convicted of aiding and abetting a given crime where the government proves that the underlying crime was committed by a person other than the defendant, that the defendant knew of the crime, and that the defendant acted with the intent to contribute to the success of the underlying crime.” United States v. Hamilton, 334 F.3d at 180; see, e.g., United States v. Pipola, 83 F.3d 556, 562 (2d Cir.), cert. denied, 519 U.S. 869, 117 S.Ct. 183, 136 L.Ed.2d 122 (1996); United States v. Labat, 905 F.2d 18, 23 (2d Cir.1990). To prove that the defendant acted with that specific intent, the government must show that he knew of the crime, see, e.g., United States v. Gallishaw, 428 F.2d 760, 763 (2d Cir.1970); but it need not show that he knew all of the details of the crime, see, e.g., United States v. Grubczak, 793 F.2d 458, 463 (2d Cir.1986), so long as the evidence shows that he “joined the venture, [that he] shared in it, and that his efforts contributed towards its success,” United States v. Wiley, 846 F.2d 150, 154 (2d Cir.1988) (internal quotation marks omitted); see, e.g., United States v. Aiello, 864 F.2d 257, 263 (2d Cir.1988), cert. denied, 525 U.S. 932, 119 S.Ct. 342, 142 L.Ed.2d 282 (1998); United States v. Grubczak, 793 F.2d at 463. A defendant may not properly be convicted of aiding and abetting a crime that was completed before his accessorial acts were performed. See, e.g., United States v. Hamilton, 334 F.3d at 180; United States v. Daly, 842 F.2d at 1389; United States v. Shulman, 624 F.2d 384, 387 (2d Cir.1980). However, where the crime has more than one stage, the defendant may be convicted of aiding and abetting even if he did not learn of the crime at its inception but knowingly assisted at a later stage. See, e.g., United States v. James, 998 F.2d 74, 79-81 (2d Cir.) (a defendant who learned of a bank robbery only during the escape phase and assisted in the escape may be convicted of aiding and abetting that robbery), cert. denied, 510 U.S. 958, 114 S.Ct. 415, 126 L.Ed.2d 362 (1993). The latter principle has been applied to charges of wire fraud, allowing a defendant to be convicted of that offense on an aiding-and-abetting theory even if the wire transmission preceded his conduct, so long as the fraudulent scheme was ongoing at the time of his conduct. See, e.g., United States v. Westbo, 746 F.2d 1022, 1025 (5th Cir.1984); United States v. Phillips, 688 *97 F.2d 52, 54-55 (8th Cir.1982); United States v. Conte, 349 F.2d 304, 306 (6th Cir.), cert. denied, 382 U.S. 926, 86 S.Ct. 313, 15 L.Ed.2d 339 (1965). In United States v. Phillips, for example, the court ruled that the defendant’s act of cashing a money order that had been fraudulently wired aided and abetted the wire fraud, stating that actions taken after the scheme has been devised and after the wire transmission are sufficient to constitute aiding and abetting where, as here, the acts were an integral part of the fraudulent scheme. 688 F.2d at 55. See also United States v. Westbo, 746 F.2d at 1025 (“Once membership in a scheme to defraud is established, a knowing participant is liable,” on “ ‘at least’ ” an aiding-and-abetting theory, “for any wire communication which subsequently takes place or which previously took place in connection with the scheme.” (emphasis added)). Further, the wire fraud statute prohibits a wire transmission for the purpose of executing a fraudulent scheme by a person who either “ha[s] devised” a scheme “or [is] intending to devise” a scheme. 18 U.S.C. § 1343 (emphasis added). Under the latter clause, therefore, a defendant may be convicted of wire fraud even if the wire transmission in furtherance of the fraud occurred while the scheme was still in a formative stage or was incomplete in design. In the present case, Count Three alleged that Laken and Black violated §§ 1343, 1346, and 2 by participating in a fraudulent scheme to obtain money from the Local 400 pension fund by having its trustees invest pension fund assets in, inter alia, Laken’s hedge fund, from which kickbacks would be made and bribes would be paid to union pension fund fiduciaries, and by causing an interstate wire transmission in furtherance of that scheme. The wire transmission was the faxing of Stephens’s resumé from San Francisco to DMN Capital’s offices in New York on or about March 2, 2000. Laken and Black contend that the evidence was insufficient to convict them of wire fraud in connection with Local 400 on the basis of the March 2 fax, arguing principally that that transmission occurred before Laken and Black knew that Local 400 was a target of the scheme; hence, they argue that that transmission was not made for the purpose of executing the scheme to defraud Local 400. (See, e.g., Black brief on appeal at 48.) They also argue that they never met with Pérsico, who was in control of the pension fund assets of Local 400, or even heard his name (see, e.g., Laken brief on appeal at 42-46); that the last “recorded” conversation with Pérsico was on February 3, 2000, prior even to Black’s February 7 introduction of Laken to the DMN Capital principals (id. at 40^41); and that Pérsico had made it clear prior to that introduction that he wanted nothing more to do with “[ ]Pokross[ ]” (id. at 42). These arguments land far from the mark. Taking them in reverse order, we note first that the record belies the notion that any crime with regard to Local 400 had been either abandoned or completed prior to the involvement of Laken and Black. Although there had been a hiatus in DMN’s negotiations with Pérsico for the corrupt investment of Local 400 pension fund assets, the record contains, inter alia, a conversation recorded on March 2 in which Lino reported to Labate and Pok-ross that the Colombo Crime Family, with which Pérsico was associated, remained interested in pursuing the fraudulent scheme. (See GX 61C Desk-T at 3.) And Pokross testified that Pérsico confirmed at a meeting on April 25 “[t]hat the scheme *98 was going to continue to move forward.” (Trial Tr. 3151-52.) Further, the government was not required, in order to prove Laken and Black guilty of wire fraud with respect to Local 400, to show that they had met with Pérsi-co or that they knew Persico’s identity as the corrupt official to whom the planned kickbacks were to be offered, promised, or paid. As discussed above, a defendant who acts with intent to contribute to the success of a crime may be convicted of aiding and abetting that crime even if he did not know all of its details. Thus, Laken and Black could have been convicted of wire fraud with respect to Local 400 on an aiding and abetting theory even if the government had not proven that they were integrally involved in the scheme. Finally, even if the March 2 fax was sent before Laken and Black knew that Local 400, in particular, was one of the targets of their fraudulent scheme, that sequence in this case is immaterial. Laken and Black were not merely aiders and abetters; they were prime movers of the scheme. The evidence permitted the jury to find that Black approached Labate in early February 2000 with the proposal, confirmed by Laken, that DMN Capital find investors for Laken’s hedge fund in return for Laken’s churning the invested funds to such an extent that he could pay DMN “kick back[s]” (GX 46C Conf(l)-T at 12) of many thousands, and perhaps millions, of dollars each year (see, e.g., GX 45B Conf-T at 2; GX 44A Conf(2)-T at 2). From the very first conversation between Black, Pokross, and Labate, the focus was on “[ujnions.” (GX 44B Conf-T at 4.) In order to implement the scheme, Pokross and Black urged Laken to find “a very friendly Investment Advisor” (GX 46C Conf(l)-T at 23) who could be recommended to union pension fund trustees and who would advise • the trustees to invest pension fund assets in Laken’s hedge fund (see id. at 23-24); having such an advisor was termed “the key to the kingdom” (id. at 24). On February 29 and March 2, respectively, Black and Laken reported that they had found such an advisor, Stephens. (See Trial Tr. 2991-92; GX 61A Conf-T at 2.) And on March 2, Stephens faxed his re-sumé from San Francisco to DMN in New York. Plainly, the fraudulent scheme did not end with the transmission of Stephens’s resumé; the very purpose of that transmission was to facilitate his retention by corrupt union pension fund trustees who could be bribed to permit the bilking of their funds. As Black had stated, trustees “need[ ] somebody as an investment advis- or, alright, that knows that he’s gonna be pushed in the direction of certain investments. Alright, and his job is to say, ‘yes, that’s a good investment.’” (GX 60D Conf-T at 2-3.) Use of Stephens as an investment advisor was thus an integral part of an ongoing scheme, as his advice would induce investment decisions that would generate profits for the enterprise and the corrupt officials for years to come. Local 400 (as well as Local 137, see Part II.C.3. below) was, along with the DEA, explicitly identified as a target for investment in Laken’s hedge fund at least as early as March 8 in two conversations between Pokross and Laken and March 15 in a conversation among Pokross, Black, Rossi, and Labate. In the first conversation on March 8, Pokross told Laken, “We got Local... Production Local Number 400. That’s sixty mill.” (GX 309-T at 3.) In the second conversation on that date, Laken told Stephens that officials of certain unions had been “[p]re-tenderiz[ed]” (GX 307-T at 6), and Pokross listed among those unions “Local 400” (id. at 21). The unions discussed in the March 15 conversation with Black similarly included the “Production Workers.” (GX 69C Conf(l)- *99 T at 18, 21.) Pokross stated that, with Stephens as investment advisor, the unions’ “investments w[ould] be split up between” Rossi’s seemingly conservative ARB preferred stock and “this particular Managed Fund of Glenn Laken’s” (id. at 22-23), and that “Stephens is uh, is tickled pink” at the prospect of investments by pension funds “like [the] Production Workers” (id. at 21). Thus, the targets of the pension fund fraud/kiekbacks scheme of Laken, Black, and DMN explicitly included the Production Workers Local 400, and Stephens’s retention was plainly an integral part of the scheme. The fact that Local 400 was not mentioned by name in the recorded conversations until several days after Stephens faxed his resumé from California to New York is of no consequence. Laken and Black having asked DMN Capital to find investors who could be defrauded, having discussed from the start the targeting of unions, and having caused a wire transmission for the express purpose of facilitating investments by corrupt union pension fund trustees, they cannot escape liability for wire fraud by arguing that they did not yet know, at the moment they caused that transmission, precisely which unions they would be defrauding. In sum, the evidence was ample to show that Laken and Black knew in the early stages of their scheme that Local 400 was a target and that the credentials of Stephens would help them achieve their goal. Taking into account the scope of the fraudulent scheme, and appreciating its full flavor, we find the evidence ample to support the convictions of Laken and Black on the Count Three charge of wire fraud with respect to Local 400. 2. Illegal Kickbacks Targeting Local 400 (Count Four) The illegal-kickback statute that was the subject of Count Four is violated by “any person who directly or indirectly gives or offers, or promises to give or offer, any ... kickback, commission, ... money, or thing of value” to “an administrator, officer, trustee, custodian, counsel, agent, or employee of any employee welfare benefit plan” covered by the Employee Retirement Income Security Act of 1974 (“ERISA”), “with intent to ... influence! ] ... any of the actions, decisions, or other duties relating to any question or matter concerning such plan,” 18 U.S.C. § 1954 (emphases added). This section may be violated even if a bribe or kickback has had no actual effect on the ERISA plan’s assets. See United States v. Glick, 142 F.3d 520, 524 (2d Cir.1998). It was stipulated at trial that the pension funds at issue here were covered by ERISA. (See GX 1001.) Laken and Black contend, however, that their convictions on Count Four should be reversed because there was no evidence that they actually offered a bribe or kickback to any pension fund official (see, e.g., Laken brief on appeal at 47-48), or that they intended to make any payments to Local 400 or Pérsico, who controlled its pension fund, or that they had even heard of Pérsico (see, e.g., id. at 42). The record reveals, however, ample evidence that both Laken and Black were aware that the scheme was to be accomplished through kickbacks to union officials and that Local 400 was one such union. The evidence as to Local 400 was that Pérsico wanted an investment advisor who would agree to “commission sharing” (Trial Tr. 2753) in order to give Pérsico a substantial sum of money annually (see GX 30A Conf-T at 5 (“We’ll tell them we want 200,000,” “[e]very year though!”)). Although the January 2000 conversations with Pérsico took place prior to any in *100 volvement by Laken and Black, Persico’s proposition dovetailed with the scheme for commission sharing that was proposed some three weeks later by Laken and Black (which Laken gratuitously referred to as “kick back[s]”); Laken and Black then recruited Stephens to be the investment advisor who would have the pension fund trustees invest in Laken’s hedge fund; and, as discussed in the preceding section, Laken and Black expressly discussed the targeting of Local 400. That the scheme was to function through the payment of kickbacks to union officials was overtly acknowledged by Laken and Black from the outset. Black began to discuss the amounts of those kickbacks on the very day he asked DMN to find investors for Laken’s hedge fund. When Labate stated that “the guy’s gonna want 60%,” Black said, “we’ll... however, however we gotta take care of it. You know?” (GX 44A Conf(2)-T at 2 (emphasis added).) On the following day, Black and Labate discussed whether they might have to pay the union officials as much as 80 percent of the amounts to be generated by Laken and, if so, whether the remaining 20 percent would be worth their while. When Labate asked Black’s view, Black said, “What am I gonna say? It’s your guy Jim ....” (GX 45B Conf-T at 6.) Black stated that if Laken generated $3 million, 80 percent would make it “very sensible for them to do it. For them to get 2.6 million a year... 2.4 million a year.” (Id.) Laken, in his recorded conversations, likewise acknowledged that the scheme would be accomplished through kickbacks to union officials. In his February 9 meeting with Black, Pokross, and Labate, when Pokross said that “some sharing of ... commission arrangements” would be needed for “[s]ome of these guys [who] like to live a little nicer than their means” (GX 46C Conf(l)-T at 17), Laken responded that he was “sure of it” (id.) and “not at all surprised” (id. at 18). When Pokross stated that he would take care of making the necessary sharing arrangements with pension fund officials, sparing Laken the task of dealing with the officials directly, Laken indicated his relief at that division of responsibility and stated that he would make “pay[ments]” to DMN Capital “to do whatever it is you need to do” (id. at 18). In a later conversation, Laken stated, “I’m more than willing to do what I need to do so that everybody gets fed appropriately.” (GX 318-T at 14.) Finally, in his March 8 telephone call with Pokross and Stephens, Laken told Stephens, “Jeffrey’s ... developing and fertilizing a number of potential relationships for you,” a developmental process that both Stephens and Laken referred to as “Pre-tenderizing.” (GX 307-T at 6.) And if there had been any question as to what Laken meant by that metaphor, he later dispelled any doubt when Pokross described giving Gardell a bag of cash for Gardell’s trip to meet Stephens in San Francisco. Laken responded, ‘Well, I figured he was pre-tenderized.” (GX 98B Conf-T at 14.) In sum, the record provided abundant evidence from which the jury could infer that Labate and DMN Capital had promised Pérsico kickbacks on the Local 400 pension fund investments, that Laken and Black knew that Local 400 was targeted for investment in Laken’s hedge fund, and that the plan was to pay kickbacks to “the guy” at Local 400. Given that § 1954 prohibits even promises to give or offer kickbacks, the evidence was sufficient to support the convictions of Laken and Black for aiding and abetting the violation of that section with respect to Local 400. 3. Illegal Kickbacks Targeting Local 1S7 (Count Seven) Although the discussions with Local 137 officials had not progressed as far as those *101 with Pérsico for Local 400 or Gardell for the DEA before the June arrests put an end to the scheme, and the Local 137 discussions had been conducted only through an intermediary, the evidence was nonetheless sufficient to support the convictions of Laken and Black under § 1954 with respect to Local 137, for that section prohibits an offer or a promise to give or offer kickbacks whether it is made “directly or indirectly,” 18 U.S.C. § 1954. The record includes evidence that after Black asked DMN Capital to find investors for Laken’s hedge fund, and Laken and Black introduced Stephens as an investment ad-visor who could be relied on to tout that fund, DMN Capital sent offers of kickbacks to officials of Local 137, using Cal-vello as an intermediary. Less than a week after Stephens was brought in to serve as a friendly investment advisor, Pokross told Laken, “We got the Operating Engineers Union” (GX 309-T at 3; see also id. at 6). In his March 15 conversation with Black, Rossi, and La-bate, Pokross similarly stated that the “client list” included “the Operating Engineers Union” (GX 69C Conf(l)-T at 4), and that Stephens was “tickled pink” at the prospect of investment by the “Operating Engineers” (id. at 21; see also id. at 17, 18). Both Laken (see GX 307-T at 21) and Black (see GX 98B Conf-T at 4) expressly mentioned Local 137 in their own statements discussing the targets of the fraudulent scheme. In recruiting Local 137, Labate sent Calvello copies of materials describing Stephens’s firm; Calvello passed the materials on to the Signorellis, Local 137’s president and business manager. Calvello himself discussed Local 137 with Stephens. (See GX 88C Desk-T at 18.) On April 11, as described in Part I.A.I.C. above, Calvello discussed with- Pokross and Labate the possibility of getting $100 million from the Local 137 pension fund, with $10 million of that to be invested with Laken; with $1 million of the $10 million to be diverted for the enrichment of Black and the DMN associates (see id. at 6-8); and with 40 percent of the $1 million to be paid as kickbacks to the Signorellis, who could, Labate predicted, “walk away with 200,000 apiece” (id. at 8). A week later, Calvello stated that Signo-relli Jr. had read the Stephens materials and was trying to set up an appointment for Calvello to see Signorelli Sr. (See GX 93A Conf-T at 3, 5.) Calvello was optimistic; he stated that at Christmas time, “contractor guys” routinely gave Signorelli Sr. at least $25,000 in cash “in an envelope.” (Id. at 14-15.) Calvello said that Signorelli Sr. “loves to earn. He loves to earn money.” (Id. at 14.) A few days later, Calvello reported that both Signorel-lis “like[d] what they heard” (GX 98E Conf-T at 4) about the possibility of investing “ ‘through very dear friends’ ” (id. at 2). Given the evidence (1) that Laken and Black (a) had recruited DMN Capital to find corrupt fiduciaries to invest in Laken’s hedge fund, (b) had been informed that they needed to have a “friendly” investment advisor to tout Laken’s fund, (c) had introduced Stephens as an investment advisor to perform that function, and (d) acknowledged that one of the funds being recruited to invest in Laken’s fund was Local 137, (2) that Labate (a) sent materials describing Stephens’s firm to officials of Local 137 via Calvello, and (b) told Calvello that each of the Signorellis could walk away with $200,000, and (3) that Cal-vello (a) spoke with Stephens about Local 137, (b) spoke with each of the Signorellis about Stephens and the proposed plan, and (c) stated that the Signorellis had read Stephens’s materials and were interested in investing “ ‘through very dear friends,’ ” *102 it was entirely permissible for the jury to find that Laken and Black violated § 1954 by aiding and abetting Labate’s promise, communicated through Calvello, of an offer of kickbacks to officials of Local 137. 4. RICO Predicate Acts 1 and 3 (Count One) Finally, Laken and Black contend that their convictions of RICO conspiracy should be reversed on the ground that, in order to establish a RICO violation, the government was required to, but did not, prove the commission of at least two predicate acts of racketeering activity. In Count One, the redacted indictment alleged three racketeering act (“RA”) predicates. RA-1 alleged both wire fraud and kickbacks with respect to Local 400, alleging that a finding that either crime had been committed would suffice to establish RA-1; RA-2 alleged wire fraud with respect to the DEA; and RA-3 alleged both wire fraud and kickbacks with respect to Local 137, alleging that a finding that either of those crimes had been committed would suffice to establish RA-3. The jury returned a special verdict in which it answered 10 questions with respect to the alleged predicate acts: five questions as to whether the government had proven against Laken each of the offenses alleged as racketeering activity (i.e., kickbacks and wire fraud against Local 400, kickbacks and wire fraud against Local 137, and wire fraud against the DEA), and five questions as to whether the government had proven those offenses by Black. As to each of those two defendants, the jury found that each offense that could be considered a racketeering act had been proven. (See Trial Tr. 8647-49.) The findings that Laken and Black committed wire fraud against the DEA, as alleged in RA-2, are unchallenged, and the evidence amply supported those findings. However, Laken and Black contend that there was insufficient evidence to establish RA-1 and RA-3, and thus that the requirement that the government prove at least two predicate acts was not met. We reject this contention. As to RA-1, the acts of wire fraud and kickbacks with respect to Local 400 were also alleged as separate substantive offenses in Counts Three and Four, respectively. Since we have concluded in Parts II.C.l. and 2. above that the evidence was sufficient to support the convictions of Laken and Black on Counts Three and Four, the evidence was necessarily sufficient to support the jury’s verdict that the acts alleged in RA-1 had been proven. Similarly, the predicate act of illegal kickbacks to officials of Local 137 in RA-3 was alleged as a separate substantive offense in Count Seven. As we have concluded in Part II.C.3. above that the evidence was sufficient to support the convictions of Laken and Black on Count Seven, the evidence was likewise sufficient to support the jury’s verdict that RA-3 had been proven. We need not address whether the evidence was also sufficient to support the jury’s findings that Laken and Black committed wire fraud with respect to Local 137, which was not alleged as a separate substantive offense, since RA-3 could be established by a finding of either illegal kickbacks or wire fraud with respect to that union. In sum, the evidence against Laken and Black was sufficient with respect to all three alleged racketeering acts, and their challenges to .their convictions on the Count One charge of RICO conspiracy are meritless. 5. The Claim of Retroactive Misjoin-der The contentions of Laken and Black that their convictions on Counts Two, Five, and *103 Six should be vacated on the ground of retroactive misjoinder were contingent on a ruling that the evidence was insufficient to support guilty verdicts on the other counts. As we have found the evidence sufficient on all of the challenged counts, the claim of retroactive misjoinder is moot. III. CHALLENGES TO THE APPLICATION OF THE GUIDELINES In sentencing Laken and Black, Judge Pauley stated that he would employ the 1998 version of the Guidelines; that version is not materially different from the 2000 version, which was used by Judge Stein in sentencing Reifler, and which all parties cite on these appeals as applicable to appellants’ offense conduct, all of which took place in 2000. Accordingly, unless otherwise specified, we refer here to the 2000 version of the Guidelines. With respect to Black, the district court found that his base offense level was 6 and that this should be increased by a total of 15 steps: 2 steps pursuant to Guidelines § 2Fl.l(b)(2)(B) because the offenses involved a scheme to defraud more than one victim; 2 steps pursuant to § 2Fl.l(b)(5)(C) because the scheme used sophisticated means; and 11 steps pursuant to § 2Fl.l(b)(l)(L) for an intended loss of $900,000 with respect to the DEA. In calculating the loss amount, the court found that the trial record, along with evidence presented by the government at a Fatico hearing, indicated that the DEA was to invest approximately $159 million with Stephens, of which 10 percent, or roughly $15 million, was to go to Laken’s proposed hedge fund; and that at least six percent of the moneys to be invested in Laken’s hedge fund was to be used as illegal kickbacks. (See Sentencing Transcript, August 8, 2003 (“Blaek/Laken S.Tr.”), at 91.) Black’s total offense level was thus 21. As his criminal history category (“CHC”) was I, the Guidelines-recommended range of imprisonment was 37-46 months. The court imposed a prison term of 37 months. With respect to Laken, whose sentenc-ings for the pension fund fraud/kickbacks offenses and the FWEB conspiracy were consolidated, the court similarly found that the base offense level was 6. The court found that Laken’s offense level was to be increased by a total of 20 steps: 2 steps pursuant to Guidelines § 2Fl.l(b)(6)(C) because the pension fund fraud/kickbacks scheme involved sophisticated means; 2 steps pursuant to § 2Fl.l(b)(3) because the FWEB offense was committed through mass marketing; 2 steps pursuant to § 2F1.1(b)(2)(A) because the FWEB offense involved more than minimal planning; and 14 steps pursuant to § 2Fl.l(b)(l)(0) for a total loss amount of more than $5 million but not more than $10 million. This loss amount aggregated the $900,000 attributable to the pension fund fraud/kickbacks scheme and more than $5 million in losses suffered by FWEB shareholders. (See Black/Laken S.Tr. at 94, 97-98, 105; Sentencing Transcript, September 3, 2003 (“Laken S.Tr. II”), at 61.) Laken’s total offense level was thus 26. (See id. at 65.) As his CHC was I, the Guidelines-recommended range of imprisonment was 63-78 months. Dealing with imprisonment, and postponing its determination of the amount Laken would be required to pay in restitution (see Part IV.B. below), the court sentenced Laken to a total of 63 months’ imprisonment for his FWEB and pension fund fraud/kickbacks convictions. With respect to Reifler, who pleaded guilty to the FWEB conspiracy in violation of 18 U.S.C. § 371, and two credit card fraud offenses in violation of 15 U.S.C. § 1644, Judge Stein found that his *104 total offense level was 20, beginning from a base offense level of 6, adjusted by the following: an increase of 2 steps pursuant to Guidelines § 2Fl.l(b)(2)(A) because the FWEB offense required more than minimal planning; an increase of 2 steps pursuant to § 2F1.1 (b)(4)(C) because that offense involved the violation of a prior injunction obtained by the Securities and Exchange Commission (“SEC”) prohibiting Reifler from violating the securities laws; an increase of 13 steps pursuant to § 2Fl.l(b)(l)(N), based on a finding that Reifler was responsible for more than $2.5 million, but not more than $5 million, of the loss suffered by FWEB shareholders; and a decrease of 3 steps pursuant to §§ 3El.l(a) and (b) for acceptance of responsibility. Reifler had a record of numerous prior felony convictions. (See Part III.B.6. below.) However, because of their vintage, most of those convictions were disregarded in the strict Guidelines computation of his criminal history category, and Reifler’s Guidelines-calculated CHC was III. The district court, finding that category III significantly underrepresented both the seriousness of Reifler’s record and the likelihood that he would commit future crimes, departed upward to category V pursuant to Guidelines § 4A1.3. (See Sentencing Transcript, March 21, 2003 (“Rei-fler S.Tr.”), at 35-38.) Given a total offense level of 20 and a CHC of V, the Guidelines-recommended range of imprisonment for Reifler was 63-78 months. Because the statutory maximum prison term for conspiracy in violation of § 371 is five years and the statutory maximum for a § 1644 violation is ten years, the court sentenced Reifler to 63 months on the § 1644 counts, and to 60 months on the § 371 count to run concurrently with that 63-month term. The court postponed its determination of the amount that Reifler would be required to pay in restitution (see Part IV.B. below). All three appellants make a variety of challenges to their prison terms. We find potential merit only in the Booker challenge. A. The Booker Challenges to the Mandatory Use of the Guidelines Reifler, Laken, and Black contend principally that they are entitled to be reSentenced because the district court sentenced them under the then-mandatory Guidelines regime that was thereafter invalidated by Booker, 543 U.S. at 244, 259, 125 S.Ct. 738. None of the appellants challenged the mandatory application of the Guidelines in the district court. Accordingly, their present Booker argument is subject to plain-error analysis. In accordance with the procedure adopted by this Court in Crosby in the aftermath of Booker, we will remand for the district judges to determine, as to each appellant sentenced by that judge, whether a nontri-vially different sentence would have been imposed if, at the time of sentencing, the Guidelines had been advisory, see Crosby, 397 F.3d at 117-18. See also United States v. Garcia, 413 F.3d 201, 226-29 (2d Cir.2005) (Crosby determination may be made by a different judge if the sentencing judge is unavailable).- B. Challenges to the District Court’s Guidelines Interpretations Appellants also challenge the district court’s interpretation of certain guidelines. As the district court is required to take the Guidelines into account on an advisory basis in deciding whether to resentence, see, e.g., Booker, 543 U.S. at 264, 125 S.Ct. 738 (“The district courts, while not bound to apply the Guidelines, must consult those Guidelines and take them into account when sentencing.”); Crosby, 397 F.3d at *105 111, we here address those contentions briefly, bearing in mind that sentences imposed by the district court are now to be reviewed under a standard of “ ‘reasonableness,’ ” Booker, 543 U.S. at 262, 125 S.Ct. 738. 1. Offense Level for Conspiracy In the district court, Laken and Black requested that their base offense levels be reduced by three steps pursuant to Guidelines § 2X1.1(b)(2) on the ground that the pension fund fraud/kickbacks conspiracy was inchoate, ie., did not achieve its objective. The district court reasonably rejected this request. In general, the Guidelines provide that, in calculating the base offense level for an inchoate offense such as a conspiracy or an attempt, if that offense is not covered by a specific offense guideline the court should refer to the base offense level stated in the guideline for the substantive offense that was the objective of the conspiracy or attempt. See Guidelines § 2X1.1(a). Taking that offense level, the court is then to decrease the base offense level for a conspiracy conviction by three steps, see id. § 2Xl.l(b)(2), unless [1] the defendant or a co-conspirator completed all the acts the conspirators believed necessary on their part for the successful completion of the substantive offense or [2] the circumstances demonstrate that the conspirators were about to complete all such acts but for apprehension or interruption by some similar event beyond their control, id. (the “unless clause”) (emphases added). Where the “tmless clause” is applicable, the court is to use the “greater [ of] the offense level for the intended offense minus 3 levels ... or the offense level for the part of the offense for which the necessary acts ivere completed,” Guidelines § 2X1.1 Application Note 4 (“Application Note 4”) (emphases added). In United States v. Downing, 297 F.3d 52 (2d Cir.2002), we held that where a defendant was convicted only of conspiracy, and was not charged with a substantive offense that was an objective of the conspiracy, the § 2Xl.l(b)(2) three-step downward adjustment should be made even if, in the course of the incomplete conspiracy, the defendant technically committed a substantive offense that was not the objective of the conspiracy. See id. at 62-64. We stated that the relevant question for purposes of determining how that section is to be applied “is whether the conspiracy ‘ripen[ed] into [a] substantially completed offense[ ]’ or ‘c[a]me close enough to fruition,’ ” id. at 62 (quoting United States v. Amato, 46 F.3d 1255, 1262 (2d Cir.1995), cert. denied, 517 U.S. 1126, 116 S.Ct. 1365, 134 L.Ed.2d 531 (1996) (emphasis in original)). In the present case, the district court rejected the contentions of Laken and Black that Downing required that they be granted the § 2Xl.l(b)(2) three-step decrease. The court noted, inter alia, that Laken and Black had been charged with and convicted of not only conspiracy but also several substantive offenses that were among the objectives of the conspiracy, including defrauding the DEA. Thus, the court concluded that, under Application Note 4, the proper base offense level was the level for the substantive offense of fraud against the DEA, ie., 6, rather than the offense level for an inchoate conspiracy whose objectives included that fraud, ie., 6 minus 3. (See Black/Laken S.Tr. at 94.) Given the convictions of Laken and Black of substantive offenses that were objectives of their conspiracies, the district court properly concluded that the requested offense-level reductions were not required by Douming. *106 Nor was the district court’s refusal to grant the reductions otherwise unreasonable. Insofar as the DEA was one of the targets of the pension fund fraud/kickbacks conspiracy, the evidence permitted a determination that the second part of § 2Xl.l(b)(2)’s “unless clause” was applicable here, i.e., that a fraudulent investment of DEA pension fund assets in Laken’s hedge fund was about to be completed but for the coconspirators’ arrests in June 2000. Stephens had made a formal presentation to DEA Treasurer Gardell, and Gardell’s response was that he was 90 percent certain to retain Stephens as the DEA’s investment advisor; Gardell had then been further persuaded by a free five-day trip for two to San Francisco and a “pre-tenderiz[ing]” bag of cash; Black sought and received assurance that, as a result, the desired DEA investment in Laken’s hedge fund was essentially “a done deal”; Laken characterized the deal “[a]s pretty much idiot proof’; and Gardell himself characterized it as “99.9 a go” and “a done deal.” Gardell said the DEA’s retention of Stephens would begin near the beginning of July. The record thus easily permits the inference that the planned July diversion of DEA funds was thwarted by the arrests in mid-June. We cannot conclude that the court’s refusal to grant an inchoate-conspiracy decrease in offense level was unreasonable. 2. The Amount of Loss Laken and Reifler also challenge the district court’s calculation of their Guidelines offense levels with respect to the amount of loss caused by their participation in the FWEB conspiracy. That stock manipulation scheme, like the union pension fund conspiracy/kiekbacks scheme, came to an end with the June 2000 arrests. After the FWEB and pension fund conspiracy/kickbacks indictments were filed, the government issued a 12-page press release describing the indictments. With respect to the alleged FWEB' conspiracy, the release stated, in part, that [i]n United States v. Laken, et al., 00 Cr. 651, it is alleged that, from February 2000 to June 2000, GLENN B. LAKEN, a hedge fund manager and commodities trader on the Chicago Mercantile Exchange, held a large position in FWEB stock, and enlisted others to fraudulently inflate the price of FWEB stock, and to conceal his identity as the seller. (FBI, New York Office, Press Release dated June 14, 2000, at 6.) After identifying some of Laken’s alleged coconspirators and their respective Internet websites, the release stated that, LAKEN also allegedly agreed to use the services of LIONEL REIFLER, President of Fortune Investments, Inc., who allegedly offered a fraudulent newsletter program used to generate high trading volume in OTC securities at inflated prices. According to the Indictment, it was agreed that [DAVID W.] BRUNO, [ADAM] KRIFTCHER and [MICHAEL] PORRICELLI would feature FWEB on websites that they controlled, would promote FWEB by sending bulk E-mails to their website subscribers, and that BRUNO and KRIFTCHER would prepare and post on their websites promotional materials describing FWEB’s business and its common stock. LAKEN allegedly agreed to pay BRUNO, KRIFTCHER, REIFLER, and PORRICELLI for their promotional efforts with FWEB stock, and to conceal that fact, as well as LAKEN’s involvement in those efforts. (Id.) After the indictments were made public, the price of FWEB stock plummeted. Selling at $8 a share on June 13, FWEB *107 fell to less than $3 a share on June 15, and to $1.38 a share by June 22. The district court determined the FWEB shareholder losses for which Laken and Reifler were responsible after conducting Fatico hearings at which the government called various witnesses, introduced recordings of Laken’s conversations with coconspirators, and produced charts listing shareholder losses (see Part IV.B. below). At the Fatico hearing with respect to Reifler, Michael Porricelli, a cooperating codefendant, testified that he was brought into the FWEB scheme in 2000 by a codefendant who introduced him to Pokross and Laken. (See Hearing Transcript, December 10, 2002 (“Reifler Fatico Dec. 2002 Tr.”), at 22.) Porricelli testified that Laken “appeared to be a large shareholder who had a very large controlling position in the company” (id.), and “[h]e basically wanted us to participate in a pump and dump” (id.), ie., to inflate the price of FWEB shares so that Laken could sell his stock at a large profit (see id. at 18). Participants in the scheme were to be compensated by Laken’s secretly giving them blocks of FWEB stock. (See id. at 27-30). Porri-celli himself received 32,500 shares of FWEB stock for his participation (see id. at 29-30), which he promptly sold (see id. at 54-55). Porricelli testified that Laken indicated that he “ha[d] somewhere in the range of 1.5 to 2 million shares that he was looking to dump into the market” (id. at 25), pursuing an “ ‘exit strategy for [him]self and a couple of [his] cohorts’ ” (id. at 23). Porri-celli testified that the price of FWEB shares in the spring of 2000 was as low as $5 a share; Laken sought to sell his FWEB stock for more than $10 a share. (See id. at 24.) Chapter Two, Part F, of the 2000 Guidelines (“Part F”), which was eliminated from the Guidelines in 2001, with the substance of many of its provisions being moved to Chapter Two, Part B, see Guidelines Appendix C, Vol. II, Amendment 617, at 131-86 (eff.Nov. 1, 2001) (“Amendment 617”), provided that the base offense level for a fraud offense was 6, see Guidelines § 2Fl.l(a). If the loss resulting from that offense exceeded $2,000, the district court was to increase the defendant’s offense level; the amount of the increase depended on the amount of the resulting loss. See id. § 2Fl.l(b)(l). Commentary to § 2F1.1 incorporated by reference the valuation-of-loss commentary to § 2B1.1 and defined “loss” as “the value of the money, property, or services unlawfully taken.” Guidelines § 2F1.1 Application Note 8. Other commentary to § 2F1.1 stated that “[f]or purposes of subsection (b)(1), the loss need not be determined with precision. The court need only make a reasonable estimate of the loss, given the available information.” Guidelines § 2F1.1 Application Note 9; see, e.g., United States v. Carboni, 204 F.3d 39, 46 (2d Cir.2000). The § 2F1.1 commentary also provided that, “[consistent with the provisions of § 2X1.1” with regard to conspiracy, inter alia, if the defendant intended to inflict a greater loss than was actually inflicted, and if that intended amount could be determined, “this [intended loss] figure will be used if it is greater than the actual loss.” Guidelines § 2F1.1 Application Note 8 (“For example, if the fraud consisted of selling or attempting to sell $40,000 in worthless securities, ... the loss would be $40,000.” (emphasis added)). The district court determined the loss amounts to be attributed to Laken and Reifler under the Guidelines both by estimating actual shareholder losses as shown by the government’s charts and by estimating the loss intended to be inflicted on shareholders by reason of Laken’s pump *108 and dump scheme. As indicated above, the district judges increased the offense levels of Laken and Reifler by 14 and 13 steps, respectively, pursuant to Guidelines §§ 2Fl.l(b)(l)(0) and (N) after finding that they were responsible for $5-10 million and $2.5-$5 million in shareholder losses, respectively. Laken and Reifler contend that the shareholder losses were the direct result of the government’s press release and only an indirect consequence of the conduct of the coconspirators, and that they should not have been held accountable for consequential damages. Consequential damages are generally defined as damages for a loss or injury that does not flow directly and immediately from the act of the party but flows only from some of the consequences or results of the party’s act or from the intervention of ordinarily unpredictable special circumstances. See Black’s Law Dictionary 390 (6th ed.1990); see also Amendment 617, at 182 (likening the distinction between direct and consequential damages to the “civil law distinction between direct and indirect harms”). Laken and Reifler argue that the 2000 Guidelines barred consideration of consequential damages in cases of securities fraud such as this one. For that proposition, they rely on Guidelines § 2F1.1 Application Note 8(c), which stated, in part, that “[ijn contrast to other types of cases, loss in a procurement fraud or product substitution case includes not only direct damages, but also consequential damages that were reasonably foreseeable,” id. (emphasis added), and on the rulings of some courts that Application Note 8(c)’s explicit inclusion of consequential damages in the loss determination for contract procurement and product substitution cases implied that only nonconsequential or direct damages were to be included in all other cases, see, e.g., United States v. Thomas, 62 F.3d 1332, 1346-47 (11th Cir.1995), cert. denied, 516 U.S. 1166, 116 S.Ct. 1058, 134 L.Ed.2d 202 (1996). This interpretation of § 2F1.1 Application Note 8(c), however, provides no basis for excluding FWEB shareholder losses from consideration, given the Guidelines provision for sentencing a defendant based on his “Relevant Conduct,” Guidelines § 1B1.3. Under § lB1.3(a), the court, in calculating a defendant’s offense level, was to take into account, inter alia, the defendant’s own acts and omissions, see id. § lB1.3(a)(l)(A), as well as “all reasonably foreseeable acts and omissions of others in furtherance of the jointly undertaken criminal activity,” id. § lB1.3(a)(l)(B), and “all harm that resulted from the acts and omissions specified in subsection[] (a)(1) ... above, and all harm that was the object of such acts and omissions,” id. § lB1.3(a)(3) (emphasis added). These provisions required the district court to take into account injuries that were the outcome of the defendant’s own offense conduct or of foreseeable acts by his co-conspirators in furtherance of the conspiracy. See, e.g., United States v. Molina, 106 F.3d 1118, 1123-24 (2d Cir.) (reversing district court’s failure to take into account the wounding of a bystander by a guard, a reasonably foreseeable outcome of defendant’s coconspirators’ “attempt to rob an armored car protected by armed guards on a busy street during the middle of the day”), cert. denied, 520 U.S. 1247, 117 S.Ct. 1859, 137 L.Ed.2d 1060 (1997); see also id. at 1122 (“Even if Molina hoped that the original plan would be carried out and that no shooting would occur, it was nonetheless reasonable for him to foresee that, in an encounter between armed robbers and armed guards protecting an armored car, a shooting was likely to occur.”). As used in § lB1.3(a)(3), the term “ ‘[h]arm’ includes” “monetary loss.” Guidelines § 1B1.3 Application Note 4. *109 In the present case, Laken owned or controlled substantial blocks of FWEB stock that he wanted to sell at a large profit, and in his plea allocution he admitted that he had “agreed with others [to] inflate the price of FWEB stock above its market value” (Laken Plea Tr. at 34-35). Reifler, for his part, admitted that he had “agreed with others to attempt to artificially raise the price of F Web stock” and had agreed to conceal the fact that the coconspirators’ goal was to allow Laken to sell his stock and receive “inflated profits.” (Reifler Plea Tr. at 24.) Necessarily, therefore, the coconspirators intended that FWEB shareholders would suffer some amount of loss — the inflated price paid minus the unmanipulated market value of the shares. Porricelli testified that in the spring of 2000, with the market price of FWEB shares was as low as $5, the coconspira-tors’ plan was to inflate the price to more than $10 so that Laken could sell his shares for “ ‘double digits’ ” (Reifler Fatico Dec. 2002 Tr. at 24). That planned inflation by $5 a share, given Laken’s plan to dump “1.5 to 2 million shares” (id. at 25) at the inflated price, indicated an intended loss to shareholders of $7.5 million to $10 million. It was thus not an unreasonable interpretation of the Guidelines’ loss provisions to find that Laken should be held responsible for more than $5 million intended loss in connection with the FWEB conspiracy. Nor do we find unreasonable the district judges’ findings that the total collapse of FWEB stock was reasonably foreseeable to the coconspirators. As a general matter it is not ordinarily unpredictable that law enforcement authorities will learn of unlawful stock manipulation, put a halt to it, prosecute those accused, and so inform the public. A sell-off is foreseeable when stockholders learn that the prevailing share price may be artificially inflated to some unknown extent. Although such a sequence may not usually put the company whose stock was the target of the manipulation out of business, that consequence was the likely result here, given the nature of FWEB’s business. FWEB was a small company that held itself out as being able to help investors discern when the stock of a small company was being manipulated. It was reasonably foreseeable that FWEB would collapse if it were disclosed that FWEB had apparently been unable to recognize manipulation of even its own stock. The district judges who sentenced Laken and Reifler found that the defendants’ conduct, not the government’s press release, was the cause of the collapse of FWEB’s share price. Judge Stein noted that Reifler’s contention was, essentially, that “everybody would be better off if only the government hadn’t blown the whistle on the fraud” (Reifler S.Tr. at 30), and dismissed it. In rejecting the equivalent argument by Laken, Judge Pauley stated: as to the proximate cause issue, this Court finds that the fraud that Laken pled guilty to was the cause of the collapse of FWEB’s share price---- It was reasonably foreseeable to defendant Laken that disclosure of this fraud involving FWEB’s stock would cause the company’s stock price to plummet, particularly due to FWEB’s reliance on its credibility as an asset, if not its most important asset. The government’s disclosure of that fraud is not an intervening cause of the collapse. The argument that the government caused the losses, or that if only the government had not disclosed the losses as they did then the company would not have been ruined, is absurd. (Blaek/Laken S.Tr. at 96-97.) Judge Pau-ley concluded, “this Court finds, as Judge Stein did [in] sentencing [Reifler] in the *110 FWEB fraud, that the fraud itself, and not the government or anything else, was the cause of the decline in the company’s stock price and thus the cause of FWEB’s shareholder losses.” (Id. at 97.) We cannot conclude that these rulings, or the methods by which shareholder losses were estimated, were unreasonable. Laken and Reifler intended that FWEB shareholders would suffer losses by purchasing Laken’s shares at artificially inflated prices, and they either knew or should have foreseen that losses would also result if their manipulations were exposed. The argument that the shareholder losses were not caused by the conduct of the coconspir-ators but were instead attributable to the government is merely an attempt to ignore the message and blame the messenger. 3.Acceptance of Responsibility Laken contends that the district court erred in refusing to reduce his offense level by three steps pursuant to Guidelines §§ 3El.l(a) and (b) for acceptance of responsibility. This contention merits swift rejection. In the union pension fund fraud/kickbacks case, Laken earned no acceptance-of-responsibility credit as he insisted on going to trial and proclaimed his innocence every step of the way, despite his own recorded statements promising kickbacks and acknowledging past and anticipated bribery. See Guidelines § 3E1.1 Application Note 2 (“This adjustment is not intended to apply to a defendant who puts the government to its burden of proof at trial by denying the essential factual elements of guilt[ and] is convicted,” even if he “then admits guilt and expresses remorse.”). Further, although Laken pleaded guilty to the FWEB conspiracy, sparing the government the need to conduct a trial in that case, this experienced securities trader (who had completed a year of law school) repeatedly stated in his plea allocution that he had no idea that it was unlawful to manipulate the prices of securities (see Laken Plea Tr. at 35-37), and he continues to maintain that any losses to FWEB shareholders were caused by the government’s accusation of his price manipulation, rather than by his own unlawful conduct. The court properly denied Laken any acceptance-of-responsibility credit. 4. Requested Downward Departure for Overlapping Adjustments Finally, as to the prison term imposed, Laken contends that the Guidelines upward adjustments in his offense level for mass marketing, more than minimal planning, and use of sophisticated means are closely related and that their overlap caused his total offense level to be unwar-rantedly high. He asks that we remand so that the district court may consider granting him a downward departure on this ground. Although Laken did not move for a departure on this basis in the district court, his present request for a remand to permit him to make such a motion is mooted by our Crosby remand. On remand, the court is to determine whether it would have imposed a nontrivially different sentence had the Guidelines not, at the time of sentencing, been mandatory. That determination may include the court’s assessment of whether it would have applied all of the adjustments that allegedly overlap. 5. Disparities Among Codefendants as to FWEB Loss Amounts The FWEB indictment named as defendants not only Laken, Reifler, and Porri-celli, but also David W. Bruno, Adam Kriftcher, and Peter J. Worrell. Prior to February 2004, Bruno, Kriftcher, and Worrell entered into plea agreements with the government and into stipulations as to *111 the amount of loss caused by the FWEB conspiracy, ranging from $32,000 to $100,000. Those amounts were used in determining the sentences of those three defendants, and Reifler contends that in light of those amounts, the district court could not properly find that he was responsible for losses in the range of $2.5 million to $5 million. We disagree. When a defendant has pleaded guilty, the court sentences him on the basis of his plea allocutions and the record as it exists at that time. If another defendant is sentenced later, and there has been an intervening evidentiary hearing at which additional information has come to light, the court is entitled, in sentencing the second defendant, to take into account information it credits from the intervening hearing. See generally United States v. O’Neil, 118 F.3d 65, 75 (2d Cir.1997) (“where some co-defendants plead guilty and others go to trial, sentencing disparity may well occur because the relevant sentencing information available to the judge after [a] plea will usually be considerably less than that available after a trial.” (internal quotation marks omitted)), cert. denied, 522 U.S. 1064, 118 S.Ct. 728, 139 L.Ed.2d 666 (1998); United States v. Perez, 904 F.2d 142, 147 (2d Cir.) (same), cert. denied, 498 U.S. 905, 111 S.Ct. 270, 112 L.Ed.2d 226 (1990); cf. Alabama v. Smith, 490 U.S. 794, 801, 109 S.Ct. 2201, 104 L.Ed.2d 865 (1989) (applying this principle to a single defendant who succeeded in having his plea of guilty vacated, went to trial, and thereafter received a sentence more severe than that imposed on the basis of his guilty plea). Here, after Bruno, Kriftcher, and Wor-rell had entered into their plea agreements with the government and the stipulations as to loss amounts, Porrieelli entered into a cooperation agreement. Evidence that was previously inaccessible to the government thereby became available in time for the sentencing of Reifler. Porrieelli testified at Reifler’s Fatico hearing and provided details as to the operation of the FWEB scheme as a whole and as to Rei-fler’s role in it. The court was entitled to rely on that evidence in sentencing Reifler. Given the increased information provided by Porrieelli, we conclude that the disparities between Reifler’s sentence and those imposed on Bruno, Kriftcher, and Worrell were not unwarranted. 6. Reifler’s Objection to the CHC Departure As indicated above, the district court placed Reifler in criminal history category V, an upward departure from the Guidelines-caleulated CHC of III. Reifler contends that this departure was an abuse of discretion. We disagree. The Guidelines provisions governing consideration of a defendant’s record of past criminal conduct assign specified numbers of points for, inter alia, prior sentences imposed on the defendant, varying principally with the length of the sentence. See generally Guidelines § 4A1.1. However, points are not assigned for a sentence imposing a prison term of more than one year and one month if that sentence was imposed more than 15 years before the defendant’s commencement of the instant offense, see id. §§ 4A1.2(e)(l) and (3), unless the defendant’s incarceration extended into this 15-year period, see id. § 4A1.1 Application Note 1. Nor are points assigned for a sentence imposing any shorter prison term if that sentence was not imposed within 10 years of the defendant’s commencement of the instant offense. See Guidelines §§ 4A1.2(e)(2) and (3). Nonetheless, the Guidelines encourage the court to consider an upward departure from a criminal history category *112 that has been computed strictly pursuant to §§ 4A1.1 and 4A1.2 “[i]f reliable information indicates that the criminal history category does not adequately reflect the seriousness of the defendant’s past criminal conduct or the likelihood that the defendant will commit other crimes.” Id. § 4A1.3. Such information includes “prior sentence(s) not used in computing the criminal history category.” Id. § 4A1.3(a). Thus, if reliable, evidence of sentences imposed more than 15 years prior to the instant crime may be the basis for such a departure. See, e.g., United States v. Delmarle, 99 F.3d 80, 85 (2d Cir.1996) (upholding departure based on 25-year-old conviction), cert. denied, 519 U.S. 1156, 117 S.Ct. 1097, 137 L.Ed.2d 230 (1997). Further, where serious crimes that were committed on different occasions were consolidated for sentencing, thereby resulting in the Guidelines assignment of points for only a single sentence, “the assignment of a single set of points may not adequately reflect the seriousness of the defendant’s criminal history,” and on this basis too “an upward departure may be warranted.” Guidelines § 4A1.2 Application Note 3. Reifler’s CHC, calculated under §§ 4A1.1. and 4A1.2(e), was III, based solely on sentences imposed on him in 1991 for conspiracy to commit securities fraud (18 months’ imprisonment), and in 1993 for two counts of making false statements on a loan application to a bank in Louisiana, and one count of making false statements to influence a savings and loan association in New York (two years’ imprisonment, concurrently). However, Reifler’s criminal record also included five additional sentences, imposed in 1970, 1972, 1975, and 1976, for a variety of offenses: mail fraud (five counts), making false statements in tax matters, sale of unregistered stock (five counts), selling stock without being a registered dealer or salesman (five counts), fraudulent stock transactions (five counts), interstate transportation of stolen property, and wire fraud. None of these sentences figured in Reifler’s Guidelines-calculated CHC because they were beyond the 10-and 15-year periods specified in §§ 4A1.2(e)(2) and (1). Looking at Reifler’s record as a whole, the district court stated that “we have a 30-year history of significant felonies and convictions from the time the man was in his very ... early 30s” and that Reifler could “be fairly characterized as engaging in financial crimes as a way of life.” (Reifler S.Tr. at 37.) The court observed that for many of his crimes, Rei-fler had received lenient punishment as a result of his cooperation with the government, including concurrent sentences or sentences of probation, which had had no apparent deterrent effect. {See id. at 36.) The court also noted, inter alia, that Rei-fler had been enjoined three times in civil enforcement proceedings brought by the SEC and had violated those injunctions. {See id.) The court concluded both that a CHC of III significantly underrepresented the seriousness of Reifler’s criminal history and that there was a “substantial likelihood that [Reifler would] commit other crimes.” {Id. at 37.) We see no error in this conclusion; in light of Reifler’s record, the court’s decision to depart to CHC V was reasonable. 7. The Sentence for Credit Card Fraud Finally, Reifler contends that the district court erred in imposing a 63-month sentence on him for credit card frauds in violation of 15 U.S.C. § 1644 in the absence of any evidence that the credit card frauds occasioned any loss. In the circumstances of this case, this contention is mer-itless. As indicated above, under the Guidelines, Reifler’s total offense level was 20, *113 and his CHC was V, making the Guidelines-recommended prison range 63-78 months. The statutory maximum prison term for conspiracy in violation of § 371, however, is 60 months, whereas the statutory maximum prison term for violation of § 1644 is 120 months. The Guidelines provide that where the Guidelines-recommended sentence exceeds the statutory maximupi on some counts but not others, the court should impose no more than the statutory maximum on any one count but should impose the sentences consecutively to the extent necessary to reach the recommended Guidelines range. See Guidelines § 5G1.2(d); United States v. Gordon, 291 F.3d 181, 195 (2d Cir.2002), cert. denied, 537 U.S. 1114, 123 S.Ct. 866, 154 L.Ed.2d 788 (2003). This was the procedure followed by the district court with respect to Reifler. No calculation of loss with respect to the credit card frauds was necessary, and we see no error in the court’s interpretation of the pertinent guidelines. IV. CHALLENGES BY LAKEN AND REIFLER TO RESTITUTION The Mandatory Victims Restitution Act (“MVRA”), see Part IV.B. below, provides, in part, that in sentencing a defendant convicted of a felony committed through fraud or deceit, the court must order the defendant to pay restitution to any identifiable person directly and proximately harmed by the offense of conviction. See 18 U.S.C. § 3663A(a)(2). The procedures to be followed in determining whether, and to what extent, to order restitution pursuant to the MVRA are those set out in 18 U.S.C. § 3664. See id. § 3663A(d). Section 3664 requires, inter alia, that the sentencing court direct the probation officer to prepare a presentence report containing “information sufficient for the court to exercise its discretion in fashioning a restitution order,” including, “to the extent practicable, a complete accounting of the losses to each victim.” Id. § 3664(a). Section 3664 provides that “[i]n each order of restitution, the court shall order restitution to each victim in the full amount of each victim’s losses as determined by the court and without consideration of the economic circumstances of the defendant.” Id. § 3664(f)(1)(A). In connection with any proposed order of restitution, the sentencing court may refer any issue ... to a magistrate judge or special master for proposed findings of fact and recommendations as to disposition, subject to a de novo determination of the issue by the court. Id. § 3664(d)(6). “Any dispute as to the proper amount or type of restitution shall be resolved by the court by the preponderance of the evidence.” Id. § 3664(e). As indicated in Part I.C. above, the district court ordered Laken and Reifler to pay totals of $6,620,675.33 and $2 million, respectively, in restitution to the shareholders of FWEB whose stock became worthless sometime after the filing of the FWEB indictment. Laken and Reifler challenge these orders on the principal grounds (1) that in light of Booker, the district court’s entry of such restitution orders in the absence of their own admissions, or of findings by a jury beyond a reasonable doubt, that they caused shareholder losses in these amounts constituted plain error, and (2) that the restitution orders were not authorized by the MVRA. For the reasons that follow, we reject the Booker contention, but we find merit in the contention that the restitution orders did not comply with the MVRA. A. The Booker Challenges to the Restitution Orders Laken and Reifler, who were sentenced in 2003, contended in their initial appellate *114 briefs, filed in 2004 and 2003, respectively, that the district court’s restitution orders based on factual findings made by the district judges by a preponderance of the evidence, rather than on findings by a jury beyond a reasonable doubt or on the defendants’ own admissions, violated Sixth Amendment principles as enunciated in Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004). In the wake of the Supreme Court’s 2005 decision in Booker, the parties filed supplemental briefs addressing the application of Booker to orders of restitution. Defendants concede that, because they did not argue to the district court that restitution orders based on judge-made findings constituted error under Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), the forerunner to Blakely and Booker, their present contentions are subject to plain-error analysis. A plain error is one that prejudicially affects the defendant’s “substantial rights” and “seriously affect[s] the fairness, integrity or public reputation of judicial proceedings.” United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (internal quotation marks omitted). For the reasons that follow, we conclude that the imposition of restitution orders based on the district judges’ findings by a preponderance of the evidence did not constitute error under Apprendi, Blakely, and Booker, much less “plain error.” Apprendi involved two New Jersey sentencing statutes, one authorizing a maximum of 10 years’ imprisonment for conviction of possession of a firearm for an unlawful purpose, and the other authorizing an increase of the maximum imprisonment to 20 years if the sentencing judge found, by a preponderance of the evidence, that the crime was committed with a purpose to intimidate because of race, color, gender, handicap, religion, sexual orientation, or ethnicity. The defendant had pleaded guilty to possession but had denied any motivating bias; the sentencing judge found against him and imposed a prison term of 12 years. The United States Supreme Court ruled that the imposition of the higher sentence based on the judge’s finding violated the defendant’s rights under the Due Process Clause, stating that “[ojther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt,” 530 U.S. at 490, 120 S.Ct. 2348. See also Jones v. United States, 526 U.S. 227, 243 n.- 6, 119 S.Ct. 1215, 143 L.Ed.2d 311 (1999) (“[Ujnder the Due Process Clause of the Fifth Amendment and the notice and jury trial guarantees of the Sixth Amendment, any fact (other than prior conviction) that increases the maximum penalty for a crime must be charged in an indictment, submitted to a jury, and proven beyond a reasonable doubt.”). In Blakely, decided four years after Ap-prendi, the Court dealt with Washington State’s sentencing guidelines, which allowed the trial court to impose an “ ‘exceptional’ ” sentence above the standard prescribed range if it found that there were factors — other than the factors used in computing the standard range for the offense — that constituted substantial and compelling reasons justifying an exceptional sentence. 542 U.S. at 299, 124 S.Ct. 2531. The defendant had pleaded guilty to kidnaping, for which the standard range, based on “[t]he facts admitted in his plea,” was 49 to 53 months. Id. at 298, 124 S.Ct. 2531. The state trial court imposed an “ ‘exceptional’ ” sentence of 90 months— more than three years longer than the top of the standard range — after making a judicial determination that the defendant had acted with “ ‘deliberate cruelty.’ ” Id. *115 at 299-300, 124 S.Ct. 2531. The Blakely Court concluded that the imposition of that sentence violated the defendant’s Sixth Amendment right to a jury trial. “[A]p-ply[ing] the rule [it had] expressed in Apprendi,” id. at 301, 124 S.Ct. 2531, the Blakely Court clarified that the “statutory maximum” for Apprendi purposes is the maximum sentence a judge may impose solely on the basis of the facts reflected in the jury verdict or admitted by the defendant .... In other words, the relevant “statutory maximum” is not the maximum sentence a judge may impose after finding additional facts, but the maximum he may impose without any additional findings, id. at 303-04, 124 S.Ct. 2531 (emphases in original). The Blakely Court stated that “[w]hen a judge inflicts punishment that the jury’s verdict alone does not allow, the jury has not found all the facts which the law makes essential to the punishment, ... and the judge exceeds his proper authority.” Id. at 304, 124 S.Ct. 2531 (internal quotation marks omitted). In Booker, the Court held that the Sixth Amendment, as construed in Blakely, applies to the federal Sentencing Guidelines, stating that “[a]ny fact (other than a prior conviction) which is necessary to support a sentence exceeding the maximum authorized by the facts established by a plea of guilty or a jury verdict must be admitted by the defendant or proved to a jury beyond a reasonable doubt.” 543 U.S. at 244, 125 S.Ct. 738. The Booker Court concluded that the constitutional flaw in the Guidelines lay in the provisions of the Sentencing Reform Act (“Act” or “SRA”) that made the application of the Guidelines mandatory, and it analyzed “the question of which portions of the sentencing statute we must sever and excise as inconsistent with the Court’s constitutional requirement.” Id. at 258,125 S.Ct. 738 (emphasis in original). Bearing in mind that it should “refrain from invalidating more of the statute than is necessary,” and should “retain those portions of the Act that are (1) constitutionally valid, ... (2) capable of functioning independently, ... and (3) consistent with Congress’ basic objectives in enacting the statute,” id. at 258-59, 125 S.Ct. 738 (internal quotation marks omitted), the Court concluded that the appropriate remedy for the unconstitutional aspect of the Guidelines was to sever and invalidate the statutory provisions that made application of the Guidelines mandatory. See, e.g., id. at 259, 125 S.Ct. 738 (“ ‘[E]veryone agrees that the constitutional issues presented by these cases would have been avoided entirely if Congress had omitted from the [SRA] the provisions that make the Guidelines binding on district judges.’ ” (Breyer, J., opinion of the Court (quoting id. at 233, 125 S.Ct. 738 (Stevens, J., opinion of the Court)))). The Court accordingly severed 18 U.S.C. § 3553(b)(1), which had “require[d] sentencing courts to impose a sentence within the applicable Guidelines range (in the absence of circumstances that justify a departure),” along with 18 U.S.C. § 3742(e), which had imposed a standard of review that was premised on application of the Guidelines being mandatory. Booker, 543 U.S. at 259, 125 S.Ct. 738. The matter of whether the substantive holding of Booker applies to orders of restitution is not entirely clear from some of the language of Blakely and Booker. When a defendant has been convicted of an offense covered by the MVRA, additional proceedings are normally required in order for the sentencing court to determine the identity of the victims of the offense and the amounts of loss to each that were directly and proximately caused by the defendant’s commission of the offense. The procedural provisions incorpo *116 rated in the MVRA require that, after a defendant is convicted, the court order the probation officer to gather the facts necessary to permit the judge to fashion an appropriate restitution order, including, for example, “to the extent practicable, a complete accounting of the losses to each victim,” 18 U.S.C. § 3664(a). As indicated above, however, Blakely stated that “[wjhen a judge inflicts punishment that the jury’s verdict alone does not allow, the jury has not found all the facts which the law makes essential to the punishment, ... and the judge exceeds his proper authority.” 542 U.S. at 304, 124 S.Ct. 2531 (internal quotation marks omitted). And in Booker, the Court stated that “the Sixth Amendment as construed in Blakely does apply to the Sentencing Guidelines,” 543 U.S. at 226-27, 125 S.Ct. 738, and that a defendant’s Sixth Amendment right “is implicated whenever a judge seeks to impose a sentence that is not solely based on ‘facts reflected in the jury verdict or admitted by the defendant,’ ” id. at 232, 125 S.Ct. 738 (quoting Blakely, 542 U.S. at 303, 124 S.Ct. 2531 (emphasis omitted by Booker)). It might seem from these statements that the district court would exceed its proper authority in making the posttrial determinations that are prerequisites to a valid order of restitution. These statements, however, must be read in the context of Booker as a whole, rather than in isolation. Booker’s analysis of the nature of the Sixth Amendment flaw in the Sentencing Reform Act, and of what is required to cure that flaw, indicates that there is no constitutional requirement that the facts needed for the district court’s fashioning of a restitution order be found by a jury or found beyond a reasonable doubt. First, we note that the Booker Court stated that “[mjost of the statute is perfectly valid,” 543 U.S. at 258,125 S.Ct. 738, and that, omitting the excised sections, “[t]he remainder of the Act function[s] independently,” id. (internal quotation marks omitted), and hence need not be invalidated. Among the provisions that the Court considered to be independent and of continued validity, the Court listed the requirement that the sentencing judge “consider ... the need to provide restitution to victims,” id. at 259-60, 125 S.Ct. 738 (citing 18 U.S.C. § 3553(a)(7) (in imposing sentence, the court “shall consider ... the need to provide restitution to any victims of the offense”)). Second, the Booker Court pointed out that “Congress’ basic statutory goal” in enacting the Sentencing Reform Act, “a system that diminishes sentencing disparity!!,] depends for its success upon judicial efforts to determine, and to base punishment upon, the real conduct that underlies the crime of conviction.” 543 U.S. at 250, 125 S.Ct. 738 (emphasis in original). Determination of a defendant’s “real conduct” is particularly important in the federal system where crimes defined as, for example, “obstructing], delaying], or affecting] commerce or the movement of any article or commodity in commerce, by ... extortion,” 18 U.S.C. § 1951(a), or, say, using the mail “for the purpose of executing” a “scheme or artifice to defraud,” § 1341 (2000 ed., Supp. II), can encompass a vast range of very different kinds of underlying conduct. 543 U.S. at 250-51, 125 S.Ct. 738. Determination of “real conduct” often depends on the development of facts after trial: Consider!! for example] a complex mail fraud conspiracy where a prosecutor may well be uncertain of the amount of harm and of the role each indicted individual played until after conviction— when the offenders may turn over financial records, when it becomes easier to determine who were the leaders and *117 who the followers, when victim interviews are seen to be ivorth the time. Id. at 253, 125 S.Ct. 738 (emphases added). The Booker Court stated that engrafting a Sixth Amendment right of jury trial onto the sentencing statutes ... would create a system far more complex than Congress could have intended.... Would the indictment in a mail fraud case have to allege the number of victims, their vulnerability, and the amount taken from each? .... How would a jury measure “loss” in a securities fraud case — a matter so complex as to lead the Commission to instruct judges to make “only ... a reasonable estimate”? § 2B1.1, comment., n. 3(C). Booker, 543 U.S. at 254-55, 125 S.Ct. 738 (emphases added). If all such facts were required to be developed at trial, such a system could produce complexities that are unnecessary and “put a defendant to a set of difficult strategic choices as to which prosecutorial claims he would contest.” Id. at 256, 125 S.Ct. 738. Instead, [jludges have long looked to real conduct when sentencing. Federal judges have long relied upon a presentence report, prepared by a probation officer, for information (often unavailable until after the trial) relevant to the manner in which the convicted offender committed the crime of conviction, id. at 251,125 S.Ct. 738 (emphasis in original), “Congress expected this system to continue,” and the “[Supreme] Court’s earlier opinions assumed that this system would continue,” id. The Booker Court noted that [t]o engraft the Court’s constitutional requirement onto the sentencing statutes ... would destroy the system. It would prevent a judge from relying upon a presentence report for factual information, relevant to sentencing, uncovered after the trial. In doing so, it would, even compared to pre-Guidelines sentencing, weaken the tie between a sentence and an offender’s real conduct. It would thereby undermine the sentencing statute’s basic aim of ensuring similar sentences for those who have committed similar crimes in similar ways. Id. at 252, 125 S.Ct. 738. The Court concluded that “patching]” “[t]he Court’s constitutional jury trial requirement” onto the Act would, inter alia, “effectively” and inappropriately “deprive the judge of the ability to use post-verdict-acquired real-conduct information.” Id. at 256,125 S.Ct. 738. Finally, we note that the Apprendi principle as applied in Blakely and Booker dealt with “determinate” sentencing systems. In a determinate sentencing regime, a jury finds facts that support a conviction. That conviction, in turn, authorizes the imposition of a sentence within a specified range, established either by statute or administrative guideline, which we call a determinate sentence. Under Booker, a Sixth Amendment violation occurs when a judge increases the punishment beyond that range based upon facts not found by a jury beyond a reasonable doubt. United States v. Fruchter, 411 F.3d 377, 383 (2d Cir.) (noting that criminal forfeiture provisions are not a determinate scheme, and rejecting a Booker challenge to a forfeiture order entered under 18 U.S.C. § 1963 based in part on facts found by the district judge by a preponderance of the evidence), cert. denied, ■— U.S. -, 126 S.Ct. 840, 163 L.Ed.2d 708 (2005). Thus, in Booker, the Court had stated that it must decide whether or to what extent, as a matter of severability analysis, the *118 Guidelines as a whole are inapplicable ... such that the sentencing court must exercise its discretion to sentence the defendant within the maximum and minimum set by statute for the offense of conviction. 543 U.S. at 245, 125 S.Ct. 738 (internal quotation marks omitted) (emphasis added). And the Blakely and Booker opinions repeatedly stated that the Apprendi principle is violated when the judge relies on facts not reflected in the jury verdict or admitted by the defendant to impose a sentence above the “maximum” authorized for the admitted or jury-established facts. E.g., Blakely, 542 U.S. at 303, 124 S.Ct. 2531 (“the ‘statutory maximum’ for Ap-prendi purposes is the maximum sentence a judge may impose solely on the basis of the facts reflected in the jury verdict or admitted by the defendant,” quoted in Booker, 543 U.S. at 228, 232, 125 S.Ct. 738 (emphases ours) (other emphasis omitted)); Blakely, 542 U.S. at 303-04, 124 S.Ct. 2531 (“[T]he relevant ‘statutory maximum’ is not the maximum sentence a judge may impose after finding additional facts, but the maximum he may impose without any additional findings.” (emphases ours) (other emphasis omitted)); Booker, 543 U.S. at 242, 125 S.Ct. 738 (“ ‘The constitutional safeguards that figure in our analysis concern not the identity of the elements defining criminal liability but only the required procedures for finding the facts that determine the maximum permissible punishment ....’” (quoting Jones, 526 U.S. at 243 n. 6, 119 S.Ct. 1215) (emphasis ours)). The MVRA, in contrast to the sentencing provisions at issue in Blakely and Booker, is an indeterminate system. Although it makes the imposition of restitution mandatory for a defendant convicted of a felony covered by the MVRA, see 18 U.S.C. § 3663A(a)(l) (the court “shall,” unless infeasible or unduly burdensome to the sentencing process, see id. § 3663A(c)(3), order restitution to the victims of the offense), the MVRA fixes no range of permissible restitutionary amounts and sets no maximum amount of restitution that the court may order. Thus, we conclude that the Booker-Blakely principle that jury findings, or admissions by the defendant, establish the “maximum” authorized punishment has no application to MVRA orders of restitution. We note that thus far all of our Sister Circuits that have considered similar challenges to restitution orders entered under the MVRA — or under the Victim and Witness Protection Act (“VWPA”), 18 U.S.C. § 3663(a)(1)(A), pursuant to which the sentencing court “may” order restitution to victims of offenses not covered by the MVRA — have concluded that Booker does not apply. Most recently, the Third Circuit, sitting en banc, has concluded that “restitution under the VWPA and the MVRA is not the type of criminal punishment that evokes Sixth Amendment protection under Booker,” and hence that “the amount a defendant must restore to his or her victim need not be admitted by the defendant or proved to a jury beyond a reasonable doubt.” United States v. Leahy, 438 F.3d 328, 331 (3d Cir.2006) (en banc). Dissenting members of the court argued that “[a] finding of loss necessarily is a condition precedent to an order of restitution, and under [the MVRA and VWPA], it is the judge who makes the finding,” and that “the imposition of this additional criminal penalty based on a fact not found by a jury violates the Sixth Amendment.” Id. at 348 (McKee, J., concurring in part and dissenting in part). The Leahy majority, however, reasoned that, as to a defendant convicted of certain specified offenses, the VWPA and the MVRA authorize an order of restitution “as a matter of course ‘in the full amount *119 of each victim’s losses.’ 18 U.S.C. § 3664(f)(1)(A),” and “the full amount of loss” is therefore the amount of restitution that is “authorized by a guilty plea or jury verdict.” United States v. Leahy, 438 F.3d at 337. Thus, the court concluded that, although judicial fact-finding determines what that full amount is, the sentencing court is “by no means imposing a punishment beyond that authorized by jury-found or admitted facts,” or “beyond the ‘statutory maximum’ as that term has evolved in the Supreme Court’s Sixth Amendment jurisprudence.” Id. (“[W]e see the conviction as authorizing restitution of a specific sum, namely the ‘full amount of each victim’s loss’; when the court determines the amount of loss, it is merely giving definite shape to the restitution penalty born out of the conviction.”); see also id. at 338 (“[E]ven though restitution is a criminal punishment, it does not transform a defendant’s punishment into something more severe than that authorized by pleading to, or being convicted of, the crime charged.”). Accord United States v. Miller, 419 F.3d 791, 792-93 (8th Cir.) (“the preponderance-of-evidence burden in [MVRA] restitution cases is unchanged by the United States Supreme Court’s recent decision in United States v. Booker”), cert. denied, — U.S. -, 126 S.Ct. 1379, 164 L.Ed.2d 85 (2006); United States v. Sosebee, 419 F.3d 451, 461 (6th Cir.) (“Booker does not apply to restitution” under the VWPA), cert. denied, - U.S. -, 126 S.Ct. 843, 163 L.Ed.2d 718 (2005); id. at 454 (“restitution is not subject to Booker analysis because the statutes authorizing restitution, unlike ordinary penalty statutes, do not provide a determinate statutory maximum”); United States v. Garza, 429 F.3d 165, 170 (5th Cir.2005) (“We agree with our sister Circuits, who have uniformly held that judicial fact-finding supporting restitution orders does not violate the Sixth Amendment.”), cert. denied, — U.S.-, 126 S.Ct. 1444, 164 L.Ed.2d 143 (2006). See also United States v. King, 414 F.3d 1329, 1330-31 & n. 1 (11th Cir.2005) (holding that if there was Booker error it was not plain error, given that neither the Supreme Court nor the Eleventh Circuit had addressed the question and that “[e]very circuit that has addressed this issue directly has held that Blakely and Booker do not apply to restitution orders”); United States v. Gordon, 393 F.3d 1044; 1051 n. 2 (9th Cir.2004) (“a ‘restitution order made by the district court [under the MVRA] ... is unaffected by Blakely ’ ”), cert. denied, — U.S.-, 126 S.Ct. 472, 163 L.Ed.2d 359 (2005); United States v. Wooten, 377 F.3d 1134, 1144-45 & n. 1 (10th Cir.) (rejecting Blakely and Apprendi challenges to restitution orders under the MVRA because “the amount of the restitution award does not exceed any prescribed statutory maximum”), ce rt. denied, 543 U.S. 993, 125 S.Ct. 510, 160 L.Ed.2d 381 (2004); United States v. Ross, 279 F.3d 600, 609 (8th Cir.2002) (Apprendi does not apply to orders of restitution because, although the pertinent statutes require that in each order of restitution “[t]he district court must order restitution ‘in the full amount of each victim’s losses as determined by the court’ ” (quoting 18 U.S.C. § 3664(f)(1)(A)) (emphasis in Ross), “the full amount authorized by statute will vary,” and thus “there isn’t really a ‘prescribed’ maximum.” (other internal quotation marks omitted)); United States v. Vera, 278 F.3d 672, 673 (7th Cir.) (“[r]estitution, an[ ] openended component of both criminal and civil judgments, is not affected by Appren-di because there is no ‘statutory maximum’ ” (citing United States v. Behrman, 235 F.3d 1049, 1054 (7th Cir.2000) (holding that restitution is not affected by Appren-di on the additional ground that the Seventh Circuit views restitution as essentially *120 a civil remedy rather than a criminal penalty))), cer t. denied, 536 U.S. 911, 122 S.Ct. 2372, 153 L.Ed.2d 191 (2002); United States v. Syme, 276 F.3d 131, 159 (3d Cir.) (“[T]he appropriate place to look for the statutory maximum as that term applies in the Apprendi context, is the restitution statute itself. But section 3663 does not specify a maximum amount of restitution that a court may order. The statute provides guidelines that a sentencing judge may use to determine the amount of restitution, but does not prescribe a maximum amount. The Apprendi rule therefore does not apply to restitution orders made pursuant to 18 U.S.C. § 3663, because Ap-prendi applies only to criminal penalties that increase a defendant’s sentence ‘beyond the prescribed statutory maximum.’ ” (quoting Apprendi, 530 U.S. at 490, 120 S.Ct. 2348)), cert. denied, 537 U.S. 1050, 123 S.Ct. 619, 154 L.Ed.2d 525 (2002). In sum, Booker saw no Sixth Amendment requirement that the indictment allege and that the jury find beyond a reasonable doubt such facts as “the number of victims” of the defendant’s offense or the amount of “loss” in a securities fraud case, or that those facts be admitted by the defendant, in order for those facts to be used by the court in fashioning punishment. And as one of the “perfectly valid” provisions of the SRA the Booker Court cited the requirement that the district court consider the need for restitution — a remedy that manifestly requires findings as to the number and identities of victims and the amount of loss, which are frequently unavailable at the time of trial, are collected by a probation officer after the defendant’s conviction, and are not subject to any monetary ceiling. We thus reject the contentions of Laken and Reifler that the orders requiring them to make restitution for loss amounts not admitted in their plea allocutions violated them rights under the Sixth Amendment as enunciated in Booker. We see no Booker error. B. The Challenges to the Application of the MVRA Finally, Laken and Reifler contend that the restitution orders entered against them must be vacated because the orders did not comply with the requirements of the MVRA. We review a district court’s order of restitution generally for abuse of discretion. See, e.g., United States v. Luden, 347 F.3d 45, 52-53 (2d Cir.2003). Where there are challenges to the court’s findings of fact, we review for clear error; insofar as the order rests on interpretations of law, we review those interpretations de novo. See, e.g., id. at 53. 1. The Provisions of the MVRA The MVRA, codified largely at 18 U.S.C. §§ 3663A and 3664, requires the sentencing court, with limited exceptions, to order restitution to the victims of certain crimes. Section 3663A(a) provides, in pertinent part, that (1) Notwithstanding any other provision of law, when sentencing a defendant convicted of an offense described in subsection (c), the court shall order, in addition to, or in the case of a misdemeanor, in addition to or in lieu of, any other penalty authorized by law, that the defendant make restitution to the victim of the offense .... (2) For the purposes of this section, the term “victim” means a person directly and proximately harmed as a result of the commission of an offense for which restitution may be ordered including, in the case of an offense that involves as an element a scheme, conspiracy, or pattern of criminal activity, any person directly harmed by the defendant’s criminal conduct in the course of the scheme[ or] conspiracy .... *121 18 U.S.C. § 3663A(a) (emphases added). Section 3663A(a)(l) does not authorize the court to order a defendant to pay restitution to any person who was not a victim of the offense of which the defendant was convicted. See, e.g., United States v. Rand, 403 F.3d 489, 493-94 (7th Cir.2005); see generally Hughey v. United States, 495 U.S. 411, 417-20, 110 S.Ct. 1979, 109 L.Ed.2d 408 (1990) (so interpreting authorization in the VWPA for a discretionary order of restitution to the “victim of such offense,” 18 U.S.C. § 3663(a)(1)(A)). Subsection (c) of § 3663A, during the period of the FWEB conspiracy, provided that the MVRA applies to, inter alia, “an offense against property under this title, including any offense committed by fraud or deceit,” 18 U.S.C. § 3663A(c)(l)(A)(ii) (Supp. IV 1998) (current version at 18 U.S.C. § 3663A(c)(l)(A)(ii) (2000)), “in which an identifiable victim or victims has suffered a ... pecuniary loss,” id. § 3663A(c)(l)(B). We have held that this subsection encompasses offenses involving pump-and-dump schemes. See, e.g., United States v. Catoggio, 326 F.3d 323, 327-28 (2d Cir.) (MVRA applicable to a defendant convicted of conducting a RICO enterprise in violation of 18 U.S.C. § 1962(c) to perpetrate frauds against the investing public in connection with the purchase and sale of certain stocks by creating artificial market demand for those stocks and then selling them at inflated prices), cert. de nied; 540 U.S. 939, 124 S.Ct. 264, 157 L.Ed.2d 252 (2003). Subsection (c) also provides, however, that [t]his section shall not apply in the case of an offense described in paragraph (l)(A)(ii) if the court finds, from facts on the record, that— (A) the number of identifiable victims is so large as to make restitution impracticable; or (B) determining complex issues of fact related to the cause or amount of the victim’s losses would complicate or prolong the sentencing process to a degree that the need to provide restitution to any victim is outweighed by the burden on the sentencing process. 18 U.S.C. § 3663A(c)(3) (emphases added). Section 3663A provides that “[a]n order of restitution under this section shall be issued and enforced in accordance with section 3664.” Id. § 3663A(d). Section 3664 places responsibility for identifying the victims of the defendant’s offense on the government. The sentencing court is required to “order the probation officer to obtain and include in its [sic ] presentence report, or in a separate report, as the court may direct,” inter alia, “to the extent practicable, a complete accounting of the losses to each victim.” Id. § 3664(a); see also Fed.R.Crim.P. 32(c)(1)(B) (“If the law requires restitution, the probation officer must conduct an investigation and submit a report that contains sufficient information for the court to order restitution.”). The probation officer, in turn, is to obtain victim information from the government’s attorney, who is required to “consult[ ], to the extent practicable, with all identified victims” and “promptly provide the probation officer with a listing of the amounts subject to restitution.” 18 U.S.C. § 3664(d)(1). “If the number or identity of victims cannot be reasonably ascertained, or other circumstances exist that make this requirement clearly impracticable, the probation officer shall so inform the court.” Id. § 3664(a). If victim losses cannot be ascertained by 10 days before sentencing, “the attorney for the Government or the probation officer shall so inform the court, and the court shall set a date for the final determination of the victim’s losses, not to exceed 90 days after sentencing.” Id. § 3664(d)(5). *122 Section 3664(e) provides that “[t]he burden of demonstrating the amount of the loss sustained by a victim as a result of the offense shall be on the attorney for the Government.” Id. § 3664(e). Section 3664(f) provides that, regardless of the defendant’s economic circumstances, the court, in its order of restitution, “shall order restitution to each victim in the full amount of each victim’s losses as determined by the court.” Id. § 3664(f)(1)(A). The district judges here, in connection with both restitution and the Guidelines loss calculations, held a number of Fatico hearings. At those hearings, the government presented several versions of charts purporting to show the losses suffered by victims of the FWEB conspiracy, which the indictment alleged began in or about February 2000 and ended at or about the time of the filing of the indictments, which were announced on June 14, 2000. However, the government “never claimed, nor ha[d] it sought to prove, that Laken actually inflated FWEB’s stock price, or that any victim bought stock as a result of representations made by Laken or his co-conspirators.” (Government Sentencing Memorandum with respect to Laken, dated May 30, 2003 (“Government May 30 Sentencing Memorandum”), at 70.) Rather, the government’s theory was that anyone who held FWEB stock when the indictment was announced was a victim of the conspiracy; it contended that the victims’ losses occurred “when [the] fraud was revealed” (id. at 71) because, after the FWEB conspiracy indictment was announced, the price of FWEB shares declined, and the company was eventually liquidated, with the expenses of liquidation consuming all of its assets and leaving the shareholders nothing. Accordingly, the government presented charts, prepared by the SEC at the request of the United States Attorney’s Office, based on broker-dealer records referred to as “blue sheets” (so-called because of the medium in which such records were maintained prior to the electronic record-keeping age). The blue sheets showed, inter alia, customers’ names and addresses; trade dates, settlement dates, and whether the transactions were purchases or sales; and the stock symbol, number of shares, and purchase or sale price. As described in greater detail below, the government represented that the charts listed all persons who had held FWEB common stock at any time during the conspiracy period and showed the amount each person lost as a result of the conspiracy. On these appeals, Laken and Reifler argue principally (a) that the government did not sufficiently identify the supposed victims of their offense or prove the victims’ alleged losses, and hence that the restitution orders were beyond the authority conferred by the MVRA, and (b) that FWEB shareholders were not directly harmed by the conduct admitted by Laken and Reifler and hence are not entitled to restitution. For the reasons that follow, we conclude that defects in the government’s identification of victims and quantification of losses require that the restitution orders entered against Laken and Reifler be vacated. 2. Victim Identification and the Amended Judgment Against Reifler At the Fatico hearing before Judge Stein in December 2002 with respect to Reifler, the government introduced a chart identified as Government Exhibit 3, which it described as “detailing the loss to each investor in FWeb as a result of the scheme charged in the indictment.” (Reifler Fati-co Dec. 2002 Tr. at 6.) According to Government Exhibit 3, the losses suffered by FWEB shareholders totaled $6,092,174. The government stated that Exhibit 3 dis *123 played “information for each person that the SEC could determine held [FWEB common stock] at any time during the fraud” (id. at 7) and that it not only provided “an actual loss figure or allow[ed] the Court to derive an actual loss figure as a result of the fraud,” but also provided “a detailed accounting and identification of each of the victims as to whom restitution is appropriate” (id. at 6). The Assistant United States Attorney (“AUSA”) stated that Government Exhibit 3 showed that “people lost between 5 and 6 million dollars on the publicly traded common stock of FWeb as a result of this fraud.” (Id. at 12.) He explained that for Exhibit 3 an arbitrary cutoff date of June 30, 2000, had been used, with hypothetical losses calculated as of that date. All of the totals shown included as loss the number of shares held by each shareholder on June 30 times the cost of those shares. The two loss totals emphasized by the government were calculated on the assumption that on that date the FWEB shares had a market value of $0; those shareholder loss totals were $5,870,952.73, representing unrealized loss without consideration of prior sales, and $6,092,174.46 representing unrealized loss plus any realized profits or losses. In addition, Exhibit 3 showed lower shareholder loss totals ($4,510,639.07 and $4,727,983.71) that took into account the fact that on June 30, the closing market price of FWEB shares was $1.4063 per share. (See Government Exhibit 3, at 1, 11; Reifler Fatico Dec. 2002 Tr. at 9,12.) The government added that some of the accounts shown on Exhibit 3 belonged to participants in the FWEB conspiracy, who should not be considered victims, including some nominee accounts ... we think, that belong to Glenn Laken. We have taken the position that although this is the actual loss and it is over $5 million, because some of the people who lost money may have been co-conspirators, we don’t think that it is fair to tag Mr. Reifler with the entire $5 million, so we have taken the position that it is around $3 million.... Our position is just that it is over $3 million. (Reifler Fatico Dec. 2002 Tr. at 12 (emphases added).) These monetary references were clarified somewhat as follows: The Court: Are you saying it is 6,092,000 minus whatever the co-conspirators’ profits were in that, or losses? [AUSA] Clark: Losses, that’s right, your Honor. It is our position that to the extent that his co-conspirators lost money, that is not something that his sentence should be enhanced by. The Court: It shouldn’t be part of the loss calculation? Mr. Clark: That’s right. The Court: How do you quantify that? Mr. Clark: There are identifiable within these names very few but some persons, including Mr. Reifler, nominees, accounts controlled by Mr. Reifler, Mr. Porricelli, and other entities like that such that we know that they are not victims. The rest of the individuals in here are in fact victims. The Court: Have you quantified the Porricelli and Reifler accounts here? Mr. Clark: Yes. What we have, it is nowhere near a million dollars. Just trying to be conservative and accounting for the possibility that there are other nominees that we didn’t discover in our investigation, we thought that the safest loss estimate was over 3 million. (Id. at 14-15 (emphases added).) Reifler’s attorney inquired: Your Honor, I would like to clarify one thing with Mr. Clark, if I might. He said that he is excluding from his loss *124 calculation losses by Mr. Reifler and Mr. Porricelli. I want to make sure that is also excluding losses by ■ Mr. Laken and/or his nominees. Mr. Clark: Your Honor, we actually had discussions with counsel for Mr. Laken. To the extent that we could identify persons on this list that were Mr. Laken’s nominees, we have excluded them. My recollection of those discussions with counsel for Mr. Laken is there wasn’t, I don’t want to quote them, there wasn’t a substantial amount of shareholders or shares represented on here that represented nominees of Mr. Laken or Mr. Laken himself, which was a surprise to me. But that is my recollection. (Id. at 16-17 (emphasis added).) Government Exhibit 3 was further discussed at Reifler’s March 21, 2003 sentencing hearing, when Reifler objected to entries totaling some $675,000 in losses on the ground that they represented persons who purchased FWEB stock after the indictments were announced, i.e., after the conspiracy had ended. The government immediately agreed that persons who bought FWEB shares with knowledge of the fraud allegations were not to be considered victims of the fraud. (See Reifler S.Tr. at 6-7.) The AUSA also stated that the $3 million figure he had mentioned at the February hearing was intended to reflect a conservative number that was lower than the actual total losses: [I]n using 3 million as a term, obviously that was less than was indicated on our [E]xhibit[ 3], and it was simply me trying to be conservative and accurate. I wasn’t saying and never have said the government’s position is investor losses in this case were limited to $3 million. (Id. at 41.) In announcing Reifler’s custodial sentence as calculated pursuant to the Guidelines, the court estimated that the loss attributable to Reifler under § 2Fl.l(b)(l) was more than $2.5 million but less than $5 million, stating that “it’s an inexact science, and I don’t have to determine the loss with precision” (Reifler S.Tr. at 33). In estimating the loss to be less than $5 million, the court stated, I do credit Exhibit S from the Fatico hearing, which shows an actual loss of — that’s in the third column of approximately $6 million, but you have to take away from that, let’s say, something less than a million. We’ll call it a million of coconspirator loss, so that by itself brings it down to 5 million and a little less [sic ] than 5 million. So under actual loss, that’s true. And crediting the information that I’ve just been given [by the defense], ... the loss to investors [who purchased] after the government announcement is approximately 675,-000, and I do think it’s appropriate that we take that out of the mix. So then it’s definitely under 5 million, closer to I million of the actual loss .... (Id. at 33-34 (emphases added).) The court asked the parties to submit additional briefing on the restitution issues within 14 days, noting that “[t]his sentencing has gone on for so long, it’s time to bring it to a close” (id. at 21). Reifler, in his supplemental memorandum, made no further objection to the accuracy of Government Exhibit 3, arguing only that any restitution order should recognize that Reifler had a substantial negative net worth and should not impose restitution obligations disproportionate to those that Judge Stein had imposed on other FWEB conspiracy participants, ranging from $32,000 to $100,000. The government’s supplemental submission principally stated its “position that Reifler should be ordered *125 to pay restitution in the amount of $3.5 [sic ] million (the lowest loss amount corresponding to the offense level found by the Court at sentencing) to the victims of the offense identified in Government Exhibit 3 (the FWEB investor loss chart).” (Letter from AUSA Clark to Judge Stein dated April 3, 2003 (“Government’s April 2003 Letter”), at 1 (emphases added).) Judge Stein ordered Reifler to make restitution in the amount of $2 million. In entering that order, the court stated, in pertinent part, that it had considered all of the materials set forth at defendant’s sentencing as well as the two subsequent submissions ..., the amount of the losses sustained by the victims as a result of the offense, the financial resources of the defendant, the financial needs and earning ability of the defendant and his dependents, and defendant’s future earning ability. It Is Hereby Ordered that defendant Reifler pay restitution in the amount of $2 million. Restitution shall be paid to the victims of the offense identified in Government Exhibit 3 at the hearing and sentencing — the list of investors who lost money due to defendant’s scheme — excluding the co-conspirators. Order dated June 23, 2003, at 1 (emphases added). This second paragraph was incorporated in the amended judgment entered on June 23, 2003 (“Reifler Amended Judgment”). We have several difficulties with the use of Government Exhibit 3 as identification of the persons to be considered FWEB conspiracy “victims” within the meaning of the MVRA. First, although Exhibit 3 does not reveal the dates on which any of the shares were purchased, it seems clear that notwithstanding Reifler’s objection and the government’s concession in March 2003, Government Exhibit 3 continues to include as victims those persons who lost a total of $675,000 by purchasing FWEB stock after the indictments were announced, i.e., after the conspiracy had ended and the fraud charge was a matter of public knowledge. We see no indication that Exhibit 3 was amended to exclude those post-conspiracy-period purchasers— or indeed any of the other persons the government conceded could not be considered victims. As presented to the district court in December 2002, Exhibit 3 showed total shareholder losses of $6,092,174; as filed with the Reifler Amended Judgment in June 2003, it shows the same total. Second, the government acknowledged at the Reifler Fatico hearing that Government Exhibit 3 included some “accounts controlled by Mr. Reifler, Mr. Porricelli, and other entities like that ... that we know ... are not victims.” (Reifler Fati-co Dec. 2002 Tr. at 14 (emphases added).) According to the government, those accounts were “identifiable” and had been “quantified” by the government at “nowhere near a million dollars.” (Id.) The Reifler Amended Judgment’s order of restitution contains the phrase “excluding the co-conspirators,” but we see no indication in the record that the government ever in fact identified the entries for coconspira-tors for the court or removed them from Exhibit 3. Rather, Exhibit 3 retains its original totals for shareholder losses, and it includes, inter alia, at least four entries for persons with the surname “Porricelli,” two of which are for “Mike Porricelli” (Government Exhibit 3, at 2, 6, 7, 10). Third, the government acknowledged that Government Exhibit 3 also included “some nominee accounts ... we think, that belong to Glenn Laken.” (Reifler Fatico Dec. 2002 Tr. at 12 (emphases added).) The AUSA stated that “[t]o the extent that we could identify persons on this list that were Mr. Laken’s nominees, we have excluded them.” (Id. at 17 (emphasis add *126 ed).) Although this statement could be interpreted as indicating that the government had excluded Laken’s nominees from Government Exhibit 3, we infer that the government instead meant only that it was conceptually excluding them from consideration by requesting that Reifler be held accountable for losses of only $3 million, rather than the $6 million shown. We infer that the government had not actually excluded Laken’s identifiable nominees from Exhibit 3, given that it had not excluded from Exhibit 3 an entry for Laken himself. (See Government Exhibit 3, at 4 (“Glenn B Laken”).) The record contains no indication that the government either specified for the court which of the listed entries — “that [the government] could identify” — were nominees of Laken or amended Exhibit 3 to remove them. Finally, even if all of the inappropriate entries discussed above had been omitted from Government Exhibit 3, the record undercuts the government’s assertion that “[t]he rest of the individuals in here are in fact victims” (Reifler Fatico Dec. 2002 Tr. at 14). The government argued to the district court at Reifler’s Fatico hearing that the total loss to victims of the FWEB conspiracy (assuming the total worthlessness of FWEB stock) was the $6,092,174 shown on Government Exhibit 3 minus $1 million in identified coconspirator losses. (See Reifler Fatico Dec. 2002 Tr. at 12-14; but see Part IV.B.3. below with respect to the Laken Fatico hearings, at which the government called Exhibit 3, inter alia, incomplete). Yet a combination of factors in the record suggests that the quantification of coconspirator losses at just $1 million is implausible. First, the government contended (and Laken’s own statements to coconspirators indicated) that “Laken ... controlled] ... the vast majority of FWEB’s publicly traded shares.” (Government May 30 Sentencing Memorandum at 55.) Citing surveillance recordings of Laken’s conversations with his coconspira-tors, the government pointed out that Laken himself estimated that out of a publicly traded float of 2.5 million shares, he controlled approximately 2 million shares. (See FWEB GX 93D Conf, at 2; see also FWEB GX 84D Conf, at 63 (Laken states that he controls all but 350,000 of FWEB’s publicly traded shares); id. at 56 (Laken estimates “trading float” of FWEB to be 2.4 million shares); FWEB GX 327, at 4 (Laken states that he controls a “gigantic slug” of FWEB stock)). (Government May 30 Sentencing Memorandum at 55-56 (emphasis added).) The record offers no reason to believe Laken had sold any substantial portion of that stock; indeed, the government disavowed any suggestion that Laken had succeeded in inflating the price of FWEB stock (see id. at 70 (the government has “never claimed, nor has it sought to prove, that Laken actually inflated FWEB’s stock price”)), and such inflation was to be the precursor to his selling (see, e.g., Reifler Plea Tr. at 24 (“Lakin [sic ] ... planned to sell all his stock at these inflated profits if the profits could be achieved” (emphasis added))). Porricelli testified that Laken wanted to sell “north of $10,” or for “ ‘double digits,’ ” and that the price never got that high. (Reifler Fatico Dec. 2002 Tr. at 24.) Thus, it seems highly unlikely that, of the $6 million in shareholder losses that the government contends were incurred when the indictments were announced, only one-sixth would have been suffered by Laken and his nominees, given Laken’s control of four-fifths of the stock. Second, Laken “sought to sell FWEB stock under his secret control without disclosing that he was the true party to the sales transactions.” (FWEB Conspiracy Indictment ¶ 10 (emphasis added); see also Laken Plea Tr. at 37-38 (Laken’s *127 acknowledgement that part of the conspiracy entailed promotions in which his FWEB stake would not be disclosed).) Given Laken’s intent to conceal his ownership or control of the stock to be sold, it is highly likely that much of his stock was held not in his own name but in the names of nominees. Thus, the government’s ability to link only $1 million of losses out of the total of $6 million to accounts held by coconspirators suggests to us that the government had simply not succeeded in identifying all of Laken’s nominees. The government based its $1 million quantification of coconspirator losses in part on its view that the Reifler and Porri-celli accounts’ losses totaled “nowhere near a million dollars” (Reifler Fatico Dec. 2002 Tr. at 14), and in part on its apparent acceptance of the representation by Laken’s counsel that “there wasn’t a substantial amount of shareholders or shares represented on [Government Exhibit 3] that represented nominees of Mr. Laken or Mr. Laken himself’ (id. at 17). The government had found this representation to be “a surprise” (id.), and it acknowledged “the possibility that there are other nominees that we didn’t discover in our investigation” (id. at 14). That possibility was offered to explain why, despite its assertion that the losses of actual victims (after the subtraction of $1 million for coconspir-ator losses) totaled more than $5 million, the government thought it “safest” to “estimate” the loss instead as approximately $3 million. (Id. at 14-15.) However, while such an estimate sufficed for purposes of Guidelines calculations, it did not serve to winnow out coconspirators for purposes of an order of restitution. The record before us gives no indication that the government investigated further in order to determine, given its continued belief that Laken controlled the vast majority of FWEB’s publicly traded shares, whether Government Exhibit 3 in fact included additional persons who were not victims of the conspiracy but rather were Laken’s collaborators. In sum, the Reifler Amended Judgment orders Reifler to pay restitution to the persons listed in Government Exhibit 3; but Exhibit 3 includes persons who were not FWEB conspiracy victims within the meaning of the MVRA, either because their losses resulted from purchases they made after the conspiracy had ended or because they were coconspirators. And while the order of restitution contains the phrase “excluding the co-conspirators,” Reifler Amended Judgment at 2, the co-conspirators were not in fact deleted from Exhibit 3. Thus, Reifler is now ordered to pay “restitution” to, among other cocon-spirators, Laken. Although the precise issue of the continued presence of coconspirators on the lists of “victims” to whom restitution has been ordered was not raised by any of the parties to these appeals, any order entered under the MVRA that has the effect of treating coconspirators as “victims,” and thereby requires “restitutionary” payments to the perpetrators of the offense of conviction, contains an error so fundamental and so adversely reflecting on the public reputation of the judicial proceedings that we may, and do, deal with it sua sponte. For the reasons discussed above, we conclude that the order of restitution imposed on Reifler was beyond the authority conferred by the MVRA. As the federal courts have no inherent power to order restitution, see, e.g., United States v. Casamento, 887 F.2d at 1177; United States v. Elkin, 731 F.2d 1005, 1010 (2d Cir.), cert. denied, 469 U.S. 822, 105 S.Ct. 97, 83 L.Ed.2d 43 (1984), the amended judgment entered against Reifler must be vacated. *128 3. Victim Identification and the Amended Judgment Against Laken Judge Pauley held Fatico hearings with respect to Laken on January 28, February 19, and April 30, 2003. At the January 28 hearing, the government introduced Government Exhibit 3, which it had introduced at Reifler’s December 2002 Fatico hearing and which Judge Stein would eventually, in June 2003, credit in ordering restitution by Reifler. However, at the February 19, 2003 hearing with respect to Laken, the government informed the court that Exhibit 3 was “wrong,” “incomplete,” and “irrelevant,” and contained “bad data.” (Hearing Transcript, February 19, 2003 (“Laken Fatico Feb. 2003 Tr.”), at 3.) Thus, the government stated that it would present new charts. It explained that the new charts would expand the period that the government considered relevant for the identification of the FWEB conspiracy victims, thereby increasing the total that the government viewed as shareholders’ losses; but the government indicated that because it had previously contended that the losses totaled the amount shown on Exhibit 3, it would not seek to have Laken sentenced on the basis of the higher amounts to be shown in the new charts. [AUSA] ESSEKS: ... [W]e proffered] to the Court Government Exhibit 3, a spreadsheet of loss analysis on FWeb[ t]hat, it turns out, is in fact an incomplete analysis. It does not have all - of the data — it appears to be an incomplete date range and that is simply an administrative foul-up .... We had ... additional information that we are prepared to back up by calling a witness from the SEC, but we inadvertently provided the Court with, essentially, bad data without understanding exactly what the problem was. Government Exhibit 3, we submit to the Court, is wrong and irrelevant with one exception that I will explain in a moment. What we have since identified, and these documents are not yet before the Court but we are proposing to put them before the Court supported by a witness, a full loss analysis for a particular period that we will put in the record that we think was a relevant period of trading in FWeb that is along the same lines of type of analysis that the Court saw in Government Exhibit 3, and that comes to much larger real loss figures for investors in FWeb. On this sheet as there were in Government Exhibit 3, there are categories for realized loss, unrealized loss of 100 percent and then an arbitrary end of data date and some different math, taking people out of positions, hypothetically, at the market price at the end of the data run. So it is similar in structure because it includes, we think, a different starting and ending date and a fuller set of blue sheet information from a full set — -at least a much fuller set of market makers that [sic ] were reflected in Government Exhibit 3. We think that’s why the numbers are different. We have more data. And then, your Honor, we have a revision of those numbers that, in a somewhat complicated way, that we will explain in more detail at another time, adjusts some of the investors’ purchase prices downward in order to address some issues raised by the defense and somewhat by the Court the last time that we were here, in an attempt to adjust the numbers and clarify where the loss is coming from. Those numbers are lower than the all [sic ] end numbers but higher than the numbers in Government Exhibit 3. *129 Our proposal is as follows. We are not contending that the Court should sentence the defendants on losses from common stock at any number higher than the highest number in Government Exhibit 3. It has always been our position — it is our position and we think has been-consistently our position — -that all the investor losses on FWeb stock are more than $10 million comprised of investor losses on common stock, which we are luilling to cap at the roughly $6 million and change that we gave notice of in Government Exhibit 3, plus I think on the order of another 4 or 6 million dollars of private placement stock that we think is appropriately attributable to the defendant as loss caused by the charged scheme. That puts actual loss, if my numbers are right, over $10 million. That’s been our position. Our position is that intended loss was over $10 million. (Laken Fatico Feb. 2003 Tr. at 3-5 (emphases added).) Retreating from its characterization of Government Exhibit 3 as “wrong” and supplying “bad data,” the government stated, [w]e don’t think that the entries on [Exhibit 3] are inaccurate. We think that, as a picture of the total losses by the investors in FWeb, it is incomplete. We don’t want the Court to rely on it as a basis to find out what the losses were, but we do accept that the Court and counsel should rely on it as a cap of the amount of loss that the Court, given how this proceeding has evolved, ought to look for when calculating loss on FWeb arising from the kinds of transactions that are reflected in these sheets. (Id. at 6-7 (emphases added).) The AUSA added, we are going to put before the Court on a couple of different scenarios, numbers bigger than the numbers in Government Exhibit 3. We are going to ask the Court to accept those numbers as real, as appropriate, accurate descriptions of loss that could be used by the Court in sentencing the defendant. The relevance of Exhibit 3 is that, because of notice issues, we are not going to argue that the Court should ulti-mateíy use a number based on the kind of stock transactions that are reflected in Government Exhibit 3 higher than the highest number here. We think that the truth is — let’s say, that the result of that, the Court accepting some of defense arguments [challenging the government’s methodology], is that the biggest number in our spreadsheet, which is roughly $13 million, gets discounted by some amount. We think, given the truth that the Court then would have found — let’s say, that the Court finds that the losses to investors caused by the scheme, of the kind of transactions reflected in these spreadsheets is $8 million. We are then going to say to the Court, [y]ou found it 8, you should only include 6 because of the fact that we told the Court and the defense that the number was 6, and that we don’t want to change the position. We do want the Court to see all the facts, and that is why we don’t want to simply say, [flake Exhibit 3, and then have us defending Exhibit 3 as the truth because it is just not accurate, it is not complete, but it does provide a cap of how much loss of this type we are going to argue that the Court should look to. (Laken Fatico Feb. 2003 Tr. at 8-9 (emphases added).) The government concluded that, because of its erroneous presentation of Government Exhibit 3, *130 we are not asking the court to sentence the defendants based on the true numbers, we are asking the court to look to the true numbers, find out what they are and if they are higher than the numbers that we put forth [in Exhibit 3], cap it at that. (Id. at 17 (emphases added).) At the April 30 hearing, the government introduced its two new charts, Government Exhibits 102 and 103, and presented the testimony of the assistant regional director in the SEC’s enforcement division, whose staff had prepared all of the charts. Government Exhibits 102 and 103 included hundreds more entries than Exhibit 3. Unlike Exhibit 3, which did not reveal the beginning of the time period it covered, the government’s new charts clearly included persons who had purchased FWEB shares as early as January 7, 1999 — more than a year before the February 2000 start of the conspiracy as alleged in the FWEB Indictment. And unlike Exhibit 3, which used a cutoff date of June 30, 2000, the new charts adopted a cutoff date of August 1, 2000. (See Hearing Transcript, April 30, 2003 (“Laken Fatico Apr. 2003 Tr.”), at 42, 47, 55.) Government Exhibit 102, proceeding on the assumption that FWEB stock was worthless on August 1, showed losses for FWEB shareholders totaling $13,755,133.83. However, using the actual closing market price of FWEB shares on August 1, 2000 — which was $0.78125 a share — Exhibit 102 showed losses for FWEB shareholders totaling $12,712,035.15. Government Exhibit 103, like Exhibit 102, covered the period January 7, 1999, through August 1, 2000, but bore a heading “Contains Adjusted Prices for Trades Prior to 3/1/00.” The government had instructed the SEC that in Exhibit 103, for persons who on August 1, 2000, held FWEB shares that had been bought before March 1, 2000, the SEC should use $8.25 — which apparently was the market price of FWEB shares on March 1, 2000— as an arbitrary cost basis for any shares bought at a price higher than $8.25. (See Laken Fatico Apr. 2003 Tr. at 51-52.) Using the assumption that FWEB stock was worthless on August 1, Exhibit 103 showed FWEB shareholder losses totaling $8,270,779.93. Using that assumption but excluding losses on purchases made after June 13, 2000, Exhibit 103 showed FWEB shareholder losses totaling $7,539,259.22. Excluding those losses but using the actual $0.78125 market price of FWEB shares on August 1, Exhibit 103 showed losses for FWEB shareholders totaling $6,816,531.09. At the April hearing, Laken’s attorney questioned the SEC witness on the government’s new charts, and in particular on three Exhibit 103 entries that purported to show shareholders who had held their FWEB stock until it was worthless and thus lost their entire investments. That cross-examination was based on the blue sheets from which the exhibits had been compiled, and it elicited admissions from the witness that in those three cases the blue sheets revealed that the shareholder in fact had not retained his stock but had sold it, and had not suffered a loss but had enjoyed a profit. Laken’s attorney represented that those three errors had been discovered as a result of a sampling of just 21 names. (See Laken Fatico Apr. 2003 Tr. at 102 (“only 21 names were looked at”).) The government agreed to eliminate the accounts of those three individuals from Government Exhibit 103. Thereafter, Laken offered evidence that Government Exhibit 103 contained errors in its calculation of losses for other accounts as well. Based on a review of 24 accounts and the corresponding blue sheets, Laken contended that the SEC in *131 various instances had, inter alia, included post-conspiracy-period purchasers, failed to recognize and account properly for short sales, and included duplicate transactions. (See Affidavit of Sheryl E. Reich dated July 3, 2003, ¶ 9.) Laken contended that this relatively small sample showed errors totaling more than $215,000 and called into question Exhibit 103’s entire loss calculation. (See id. ¶ 12.) At the first sentencing hearing for Laken, the court asked the government for its view as to the accuracy of Government Exhibit 103. The government, taking “a stab in the dark,” responded that it did not think the total could be off by more than 10 percent. (Black/Laken S.Tr. at 48.) In its final written submission in support of restitution, the government proffered Government Exhibit 105, a version of Exhibit 103 that was described as having been redacted to eliminate the erroneous entries identified by Laken at the April 30 hearing and any additional errors that Laken had identified by October 3, 2003. The government stated that, with those deletions, it “believe[d] that this loss schedule identifies, with accuracy and particularity, the losses suffered by victims of Laken’s criminal conduct, and accordingly, the Court should order restitution to the victims identified on the schedule in the amounts specified thereon.” (Letter from AUSA Clark to Judge Pauley dated October 7, 2003 (“Government’s October 2003 Letter”), at 2.) On December 2, 2003, Judge Pauley entered an amended judgment (“Laken Amended Judgment”) based on Exhibit 105’s loss figure of $7,539,259.22, which was further reduced by a handwritten amendment subtracting “182,953.30” for “Laken-Identified Errors” and resulting in total losses of “$7,356,305.92.” Apparently adopting the government’s shot-in-the-dark estimate of a 10 percent margin for error, and thus reducing the $7,356,305.92 figure by 10 percent to $6,620,675.33, the court ordered restitution by Laken as follows: It is ordered that the defendant make restitution in the amount of $6,620,675.33, to the Clerk, U.S. District Court, for disbursement to the various investors listed in the attached victim list, (government exhibit 105 attached) .... The compensable injury for each individual investor is equal to the amount associated unth that investor in Government Exhibit 105 less 10%, for a total of $6,620,675.33. Laken Amended Judgment at 7 (emphases added). We have two principal difficulties with the Laken Amended Judgment’s adoption of Government Exhibit 105 as the FWEB conspiracy victim list. First, Exhibit 105 fairly clearly includes accounts belonging to at least one coconspirator. For example, although the government appears to have deleted the three entries in Government Exhibit 3 that show losses for Michael Porricelli and Laken, there are numerous new entries for Por-ricelli in Exhibit '105. In the 40-page Exhibit 105, page 6 alone contains 46 entries — grouped by the government to indicate a single investor — showing transactions in FWEB stock, beginning in April 2000, by “Core Financial LLC” for the accounts of persons with the surname “Porricelli” or “Poricelli” or “Parri-celli,” 40 of them with the first name “Mike.” In those 46 transactions, the number of FWEB shares purchased totaled 9,460; the number sold totaled 41,-460. Thus, the number of shares shown sold exceeded the number shown purchased by 32,000, almost exactly the number of shares (32,500) that Porricelli testified Laken had given him in the *132 spring of 2000 for participating in the FWEB conspiracy. Apparently disregarding the sales of the 32,000 shares, page 6 of Government Exhibit 105 indicates that the remaining Por-ricelli transactions resulted in a net loss, and it thus includes Porricelli as a supposed victim of the FWEB conspiracy. In addition, Exhibit 105 contains other entries for “Mike Porricelli,” as well as entries for another investor with the surname “Porri-celli” at an address on the same street in Denver, Colorado, that was shown for Michael Porricelli on Government Exhibit 3. (See, e.g., Government Exhibit 105, at 24, 20; Government Exhibit 3, at 7.) Second, we note that despite the government’s earlier acknowledgement of the possibility that Exhibit 3 included entries for “other nominees that we didn’t discover” (Reifler Fatico Dec. 2002 Tr. at 14), and its “surprise” that there were supposedly so few accounts belonging to nominees of Laken (id. at 17), the government’s bottom-line explanation of the need for the new charts was that Exhibit 3 was incomplete, not that it was overinclusive (see Laken Fatico Feb. 2003 Tr. at 3-4). At no point in the proceedings, so far as we have been able to ascertain, did the government indicate that its new charts omitted the “identifiable” (but unspecified) accounts of coconspirators’ nominees (which it had estimated as totaling $1 million); nor did it indicate that it had investigated further to determine whether its charts still included other Laken nominees. Yet, given Laken’s control of some 80 percent of FWEB’s publicly traded common stock, it seems highly unlikely, if the losses to FWEB shareholders totaled $7,356,305.92, or even $6,620,675.33, that only $1 million of those losses would have been in accounts controlled by Laken and his cohorts. In its final submission to the court as to a proper restitution order for Laken, the government stated that it had rectified only the errors pointed out by Laken. Laken had made no objection whatever to the inclusion of coconspirators among those to whom restitution would be ordered; nor is that surprising, as the inclusion of coconspirators’ accounts would be in Laken’s interest if he were to be found unable to pay the full amount of restitution ordered. In that event, assuming pro rata distributions, some of Laken’s payments would be diverted from victims to cocon-spirators. In sum, because Laken is ordered to pay restitution to the persons listed in Government Exhibit 105, and we conclude that Exhibit 105 includes persons who were not FWEB conspiracy victims within the meaning of the MVRA because they were instead coconspirators, the order of restitution was beyond the authority conferred by the MVRA. Accordingly, the amended judgment entered against Laken must be vacated. 4. The Government’s Quantifications of Loss The amended judgments entered against Laken and Reifler are also flawed in that they do not comply with the MVRA’s provision that “[i]n each order of restitution, the court shall order restitution to each victim in the full amount of each victim’s losses as determined by the court,” 18 U.S.C. § 3664(f)(1)(A) (emphasis added). We assume that the government’s failure to provide the district court with any victims list containing only victims, notwithstanding its statement that Government Exhibit 3 provided “a detailed accounting and identification of each of the victims as to whom restitution is appropriate” (Reifler Fatico Dec. 2002 Tr. at 6), may be explained in part by the government’s focus on the meaning of loss under the Guidelines, which provide that loss *133 need not be established “with precision[; t]he court need only make a reasonable estimate of the loss,” Guidelines § 2F1.1 Application Note 9. For example, at Rei-fler’s Fatico hearing, the government stated that it believed the “actual loss [was] over $5 million” but that Reifler should be charged with only $3 million (Reifler Fati-co Dec. 2002 Tr. at 12), explaining that this was the government’s “loss estimate ” (id. at 15 (emphasis added)). Likewise with respect to Laken, the government stated that “all that is required” is “a fair estimate of loss.” (Government May 30 Sentencing Memorandum at 74.) Focus solely on the Guidelines likely also explains why the government, though arguing that the “actual,” “real,” “accurate,” and “tru[e]” figures as to shareholder losses were $10-$13 million (Laken Fatico Feb. 2003 Tr. at 3-5, 8-9), believed the court could properly “cap it at” the $6,092 million figure presented in Exhibit 3 (id. at 17). Such a cap for restitution purposes, however, plainly contravenes the MVRA’s requirement that any restitution order compensate the victims in “full.” Both sentencing judges recognized that they were not required to determine loss with precision in order to calculate defendants’ offense levels under the Guidelines. (See, e.g., Reifler S.Tr. at 33; Laken S.Tr. II at 61.) However, after making their reasonable estimates of the shareholder losses resulting from the FWEB conspiracy for purposes of applying the Guidelines and imposing the custodial portions of the sentences on Laken and Reifler, both judges asked for additional briefs on the question of restitution. The government, in response, neither made any presentation tailored to the issue of loss amounts for purposes of restitution nor cited any authority to indicate that an artificial “cap” on losses could be appropriate for purposes of a restitution order under the MVRA. To the contrary, with respect to Reifler, the government argued expressly that his restitutionary amount should be “the lowest loss amount corresponding to the [Guidelines] offense level found by the Court” (Government’s April 2003 Letter at 1 (emphasis added)). And with respect to Laken, the government advanced a “total restitution number” of $7,356,305.92, making no mention whatever of its prior arguments to the court that the actual losses to FWEB shareholders totaled $10 — $13 million. (Government’s October 2003 Letter at 2.) Further, the government offered no amendment, refinement, or limitation of Government Exhibits 3 and 105 to include only victims within the meaning of the MVRA, and that failure in itself impeded the court’s ability to order restitution “in the full amount” of the losses of the victims. For example, Reifler was ordered to pay only $2 million in restitution. This may have represented a decision by Judge Stein to apportion restitution liability between Reifler (who entered the conspiracy several weeks after Laken initiated it) and Laken, who, though he was to be sentenced by Judge Pauley, had pleaded guilty before Judge Stein. See 18 U.S.C. § 3664(h) (“If the court finds that more than 1 defendant has contributed to the loss of a victim, the court may make each defendant liable for payment of the full amount of restitution or may apportion liability among the defendants to reflect the level of contribution to the victim’s loss and economic circumstances of each defendant.”). But the order that Reifler pay only $2 million to the persons listed in Government Exhibit 3, whose total losses are listed at more than $6 million, means that the maximum amount of restitution to be received from Reifler by each person on that list — victims and nonvictims alike — is less than one-third of the specified loss. Judge Stein, however, in imposing Rei- *134 fler’s custodial sentence, found that the “actual loss” total for FWEB conspiracy- victims — i.e., excluding the $675,000 lost by post-conspiracy-period investors and the estimated $1 million “of coconspirator loss” — was “closer to 4 million.” (Reifler S.Tr. at 34.) If the losses of persons properly found to be victims within the meaning of the MVRA totaled $4 million, and the victims list included only those persons, an order requiring Reifler to pay $2 million in restitution would mean that a victim could instead receive from Reifler as much as 50 percent of his loss. Thus, even as to a defendant who is permissibly, by reason of an authorized apportionment, ordered to pay a sum less than the full amount of the listed losses, the presence of nonvictims on the list of persons to whom restitution is to be paid has the effect of diluting the amount the victims will receive. We note also, as to both of the restitution orders at issue here, that Exhibits 3 and 105, in stating individual shareholders’ total loss amounts, appear to deduct any profit the shareholder had made on a sale of some of his shares. (See, e.g., Government Exhibit 3, at 1; Government Exhibit 105, at 12.) Needless to say, this issue has not been raised by the parties, given that it is the government’s own calculation and that the treatment is favorable to the defendants. But we question whether that treatment is allowed by the MVRA. The government has not contended that the conspiracy had any inflationary effect on the market price of FWEB shares, and we do not see any explanation in the record as to why the MVRA should have been interpreted to give Laken and Reifler credit for a shareholder’s profitable sale, in an uninf-lated market, to offset the losses that, by the government’s theory, were caused by the conspiracy. Giving a defendant such credit appears to deviate from § 3664(f)(l)(A)’s requirement that any restitution order award the victim’s loss “in ... full.” Finally, as to the Laken Amended Judgment, the district court clearly was skeptical of the government’s quantification of victims’ losses — a skepticism well deserved in light of the errors in Government Exhibit 103 pointed out by Laken, the lack of evidence of any relevant securities transactions within the period of the conspiracy to anchor the government’s various explanations, and the government’s acknowledge-ments, inter alia, that the assumptions underlying Exhibits 102 and 103 included factors that were hypothetical and arbitrary (see, e.g., Laken Fatico Feb. 2003 Tr. at 4 (“an arbitrary end of data date and some different math, taking people out of positions, hypothetically”)). The district court understandably stated, “I have a sense that the government is just sort of inventing this as they go along, because everything has changed continuously with respect to the government’s theory of loss in this case.” (Laken Fatico Apr. 2003 Tr. at 17.) Neither the specific errors in the government’s chart nor any general skepticism on the part of the court could be offset properly, however, by an order that the amounts shown on Government Exhibit 105 “for each individual investor,” Laken Amended Judgment at 7, simply be reduced by 10 percent. To the extent that Exhibit 105 was accurate, the Laken Amended Judgment’s 10 percent reduction violated the MVRA requirement that the order of restitution award restitution in the full amount of the victims’ losses. And if Exhibit 105 was not accurate, and even if the total losses reported on that chart were in fact exactly 10 percent too high, it is rather unlikely that the loss amounts shown for individual shareholders were uniformly 10 percent too high. Without such uniformity, some of the restitution *135 awards cannot represent the full amount of the victims’ losses. 5. Issues Relating to Causation Finally, we note that questions relating to causation are particularly bedeviling here, because the MVRA defines victims as persons who were “directly and proximately harmed as a result of the commission of an offense for which restitution may be ordered including,” where the offense is conspiracy, “any person directly harmed by the defendant’s criminal conduct in the course of the ... conspiracy,” 18 U.S.C. § 3663A(a)(2) (emphasis added), and because Congress, in the interest of providing speedy resolution of restitution issues, made the MVRA inapplicable where “determining complex issues of fact related to the cause or amount of the victim’s losses would complicate or prolong the sentencing process,” id. § 3663A(c)(3)(B). In light of § 3663A(c)(3)(B)’s limitation on the scope of the MVRA, we view the requirement that the harm have been “proximately” caused as a reflection of Congress’s interest in maintaining efficiency in the sentencing process, as the term “ ‘proximate cause’ ” is sometimes used “to label generically the judicial tools used to limit a person’s responsibility for the consequences of that person’s own acts. At bottom, the notion of proximate cause reflects ‘ideas of what justice demands, or of what is administratively possible and convenient,’ ” Holmes v. Securities Investor Protection Corp., 503 U.S. 258, 268, 112 S.Ct. 1311, 117 L.Ed.2d 532 (1992) (quoting W. Keeton, D. Dobbs, R. Keeton, & D. Owen, Prosser and Keeton on Law of Torts § 41, at 264 (5th ed.1984) (emphasis ours)). The requirement that the harm have been “directly” caused doubtless reflects the same interest in efficiency, because “the less direct an injury is, the more difficult it becomes to ascertain the amount of a plaintiffs damages attributable to the violation,” Holmes, 503 U.S. at 269, 112 S.Ct. 1311. In the circumstances of the present case, we see difficult questions as to both the causation requirement and the requirements for determining the timing and the amounts of the losses caused. As indicated above, the district court cannot properly order restitution under the MVRA unless the victim’s harm resulted from the offense of conviction, including, with respect to a conspiracy offense, the defendant’s conduct in the course of the conspiracy. The offense to which Laken and Reifler pleaded guilty was conspiracy, in violation of 18 U.S.C. § 371, to inflate artificially the price of FWEB common stock in violation of § 10(b) of the Securities Exchange Act of 1934 and SEC Rule 10b-5. It is not clear, however, that even the innocent' persons listed in the government’s charts should be considered harmed as a result of violations of § 10(b) and Rule 10b-5, for it is questionable whether they would be entitled to recover in civil actions under those provisions. Rule 10b-5 prohibits uses of fraudulent communications or manipulative devices “in connection with the purchase or sale of any security.” 17 C.F.R. § 240.10b-5. To prevail in a civil action under this Rule, a plaintiff is required to prove, inter alia, that he was a buyer or a seller, of the securities in question and that the defendant made a material misrepresentation, or omitted a material fact as to which disclosure was required, on which the plaintiff relied. See, e.g., Blue Chip Stamps v. Manor Drug Stores, 421 U.S. 723, 749, 95 S.Ct. 1917, 44 L.Ed.2d 539 (1975). Quaere whether the persons listed in Exhibits 3 and 105 could meet this test. Many of them had purchased their shares as early as January 7, 1999, more than a *136 year before the conspiracy to which Laken and Reifler pleaded guilty had begun. None of them were shown to have made FWEB stock purchases in reliance on any misrepresentation or omission of Laken or Reifler. Rather, the government stated that it had “never claimed, nor ha[d] it sought to prove, that Laken actually inflated FWEB’s stock price, or that any victim bought stock as a result of representations made by Laken or his coconspirators.” (Government May 30 Sentencing Memorandum at 70.) Thus, there has been no showing that any of the persons listed in Exhibit 3 or Exhibit 105 could prove that they were purchasers meeting the Rule 10b-5 criteria. Moreover, most of the persons listed apparently also were not sellers. Although the government contends that FWEB shareholders were damaged because their unsold shares became worthless, Rule 10b-5, so far as we are aware, has not been extended to allow suits by persons who were neither buyers in reliance on a defendant’s material misrepresentation/omission nor sellers at all, but rather were persons who simply held their stock until it became worthless. See generally Blue Chip Stamps, 421 U.S. at 737-38, 95 S.Ct. 1917 (even a shareholder who claims to have relied on a false statement as a basis for not selling his shares has no standing under § 10(b) or Rule 10b-5, because he was not a seller); Holmes, 503 U.S. at 285, 112 S.Ct. 1311 (O’Connor, J., concurring in part (“In Blue Chip Stamps, we adopted the purchaser/seller standing limitation in § 10(b) cases as a prudential means of avoiding the problems of proof when no security was traded .... ” (emphasis added))). Further, although some persons listed in Exhibits 3 and 105 are shown to have sold shares after the announcement of the FWEB conspiracy indictment, i.e., after the conspiracy had ended, the government has not advanced any theory on which those persons could be found to have sold in reliance on any statement, omission, or conduct of the defendants. We thus question whether in a civil action, any of the persons listed in Exhibits 3 or 105 would have purchaser/seller standing to sue these defendants for violations of § 10(b) and Rule 10b-5. It would, of course, be within Congress’s power to require the sentencing court to order a convicted defendant to pay restitution to a person injured by the defendant’s offense even if that person lacked purchaser/seller standing to recover for injuries resulting from that offense in a civil action, thus leading to the problems of proof that that standing requirement is designed to avoid. If Congress had intended to impose such a requirement here, however, we would have expected that intent to be expressed in clear terms. We see nothing in the language of the MVRA to indicate that Congress had such an intention. Instead, Congress plainly intended that sentencing courts not become embroiled in intricate issues of proof, as it provided that the MVRA is to be inapplicable if the court finds that the determination of complex factual issues related to the cause or amount of the victims’ losses would unduly burden the sentencing process. See 18 U.S.C. § 3663A(c)(3)(B). This provision reflects Congress’s intention that the process of determining an appropriate order of restitution be “streamlined,” Senate Report at 20, 21, reprinted in 1996 U.S.C.C.A.N. at 933, 934, and that the restitution “determination be made quickly,” id. at 20, reprinted in 1996 U.S.C.C.A.N. at 933. Accordingly, the Senate Report stated that cases “in which the victim’s loss is not clearly causally linked to the offense, should not be subject to mandatory restitution,” id. at 19 (emphasis added), reprinted in 1996 U.S.C.C.A.N. at 932, and expressed the *137 intent that courts order full restitution to all identifiable victims of covered offenses, while guaranteeing that the sentencing phase[s] of criminal trials do not become fora for the determination of facts and issues better suited to civil proceedings, id. at 18 (emphasis added), reprinted in 1996 U.S.C.C.A.N. at 931. Thus, the provisions of §§ 3663A(c)(3)(B) and 3664(j)(2) and the statements in the legislative history do not seem to reflect any congressional intent that the persons eligible to receive restitution under the MVRA would include persons who lack standing to sue, based on the conduct underlying the offense of conviction, in a civil action. Indeed, giving an overview of the purpose of the MVRA, the Senate Report stated, “[t]his legislation is needed to ensure that the loss to crime victims is recognized, and that they receive the restitution that they are due.” Id. at 12 (emphasis added), reprinted in 1996 U.S.C.C.A.N. at 925. We interpret the phrase “that they are due” to refer to the victims’ entitlement to recover under some law other than the MVRA. If compensation were due only by reason of the MVRA, this rationale would be circular. In short, we see nothing in the statute or the legislative history to suggest that Congress meant in the MVRA to make restitution — a traditional civil remedy-mandatory in a criminal proceeding for a person who would have no right to recover in a civil action. Had Congress so intended, we would not expect it to have implemented that intent sub silentio. In addition, assuming that FWEB non-selling shareholders may properly be considered victims within the meaning of the MVRA, the MVRA provision governing the calculation of loss is not easily applied in this case. Section 3663A(b) provides that in ordering monetary restitution to the victim of an offense that resulted in injury to property, the court is to award “the value of the property on the date of the damage, loss, or destruction,” 18 U.S.C. § 3663A(b)(l)(B)(i)(I), or “the value of the property on the date of sentencing,” id. § 3663A(b)(l)(B)(i)(II), whichever is greater. Obviously the value of the FWEB shares on the dates Laken and Reifler were sentenced was zero; thus the court would be required to award the “value” of those shares “on the date of the damage, loss, or destruction.” It is hardly clear, however, what would be meant in circumstances such as these by, for example, “the date of ... destruction.” The government’s stated theory was that “the market value of FWEB was forever destroyed” “when [Laken’s] fraud was revealed.” (Government May 30 Sentencing Memorandum at 71 (emphasis added).) Yet Laken’s fraud was revealed on the date the indictments were announced, June 14, 2000; and on that day, the price of FWEB shares “went up” (Laken Fatico Feb. 2003 Tr. at 149). Further, Government Exhibit 3 indicated that, although the price of the shares thereafter fell sharply, the stock did not immediately become worthless: Its market price per share was $1.4063 on June 30, 2000. And Government Exhibit 105 revealed that the FWEB shares had a market price of $0.78125 on August 1, 2000. The shares plainly were worthless when the company eventually was liquidated; but their market value had not in fact been “destroyed,” according to the government’s own evidence, either on the date when the fraud was revealed or for at least several weeks thereafter. Moreover, the valuation premise of Exhibits 3 and 105 is inconsistent with the government’s stated theory that the FWEB shares were destroyed “when [Laken’s] fraud was revealed,” because those charts in fact measure shareholder *138 losses not by any market value of FWEB shares at or about the time of that revelation, but rather by what each shareholder’s shares cost. The use of cost to measure “value” for MVRA purposes in this case has several absurd consequences. The cost of the shares obviously reflected their value to the purchasing shareholder on the date of their purchase. But given the MVRA requirement that the restitution order award the value of the shares “on the date of’ their “destruction,” an award of the purchase-date value holds, in effect, that a shareholder’s shares were destroyed on the date he bought them. This, in turn, would mean that there was a different date of destruction for each day’s purchases. And it would mean that the shares of many of the shareholders listed in Exhibits 3 and 105, having been purchased as early as January 7, 1999, became worthless before the FWEB conspiracy even began. Finally, even if a particular date were settled on as the date of damage, loss, or destruction, it is not clear — -in circumstances where the property is a security retained by the victim, the value of which has first plunged, has then been further eroded over a period of weeks or months, and has finally ceased to exist entirely— what Congress would have meant by the “value” of the property on the date of damage, loss, or destruction. The difficulty in determining the “value” to be awarded is perhaps best reflected in the fact that, in order to produce the loss figures shown in its exhibits, many of the factors used by the government were hypothetical or arbitrary assumptions. For example, in order to have Government Exhibit 105 show the losses allegedly caused by this conspiracy that began in February 2000 and ended in mid-June 2000, the government arbitrarily — chose January 7, 1999, as the earliest date of purchase of shares for which losses would be calculated, notwithstanding that this date (a) bore no relationship to the conspiracy period, and (b) may have excluded persons who had held FWEB shares since before that date; — decided, despite its hypothesis that loss equaled cost, not to use the actual cost basis for any shareholder who, on August 1, 2000, held shares that he had purchased prior to March 1, 2000, at a price higher than $8.25 per share; ■ — ■ chose $8.25 as the hypothetical cost basis for such a shareholder because $8.25 was the share price on March 1, 2000, a date that has no apparent relationship to the start or the end of the conspiracy, and whose choice was unexplained; — chose August 1, 2000, as the date on which to calculate FWEB shareholders’ losses, notwithstanding the fact that Exhibit 105 was prepared 2}£ years later and presumably could have provided data for transactions occurring after that date; and — chose August 1, 2000, as the date on which it sought to have FWEB shares assumed to be entirely worthless, notwithstanding the fact that on that date FWEB’s market price per share was $0.78125, and presumably some shareholders could have sold their shares for approximately that price after August 1, 2000, thereby lowering their losses to amounts less than those shown in Exhibit 105. Perhaps it was unduly difficult, in this criminal prosecution — in which the government apparently could not show any artificial inflation of the price of the stock or any purchases or sales in reliance on any statement or conduct of the defendants— to attempt to determine a victim’s actual loss on the basis of dates and prices that *139 were not hypothetical, assumed, or arbitrary. But that difficulty clearly implicates § 3663A(c)(3)(B)’s exclusion from the reach of the MVRA those cases in which causation and loss determinations will unduly prolong the sentencing process. Accordingly, we leave these questions as to causation and valuation for another day, given that the restitution orders must in any event be vacated because they awarded restitution to persons who, for the reasons discussed in Parts IV.B.2. and 3. above, are clearly beyond the MVRA’s definition of victims. We remand to the district court for consideration of what further proceedings may be appropriate with respect to restitution, bearing in mind both (a) the inapplicability of the MVRA if the court finds, in accordance with § 3663A(c)(3)(B), that the factual issues as to causation and loss quantification will unduly burden the sentencing process, and (b) the seemingly inordinate length of time already consumed — intervals between guilty plea and restitution order stretching to 15 months for Reifler and 22 months for Laken, in each case including no less than the MVRA-permitted 90 days after sentencing — in the production of victims lists that remained arbitrary and inappropriate. CONCLUSION We have considered all of defendants’ contentions on these appeals and have found in them no basis for reversing the convictions. In light of the Supreme Court’s decision in Booker and this'Court’s decision in Crosby, we remand to the district court for consideration by the sentencing judges, in conformity with Crosby, of whether any of these defendants would have received custodial or supervisory sentences that are nontrivially different from those that were imposed if the Guidelines had been advisory, and if so, for the resen-tencing of that defendant. , Insofar as the amended judgments against Laken and Reifler ordered restitution, the amended judgments are vacated, and the cases against Laken and Reifler are remanded for further proceedings on restitution not inconsistent with this opinion.