United States of America, Plaintiff-Appellee/cross-Appellant v. Michael D. Andreas and Terrance S. Wilson, Defendants-Appellants/cross-Appellees

KANNE, Circuit Judge. For many years, Archer Daniels Midland Co.’s philosophy of customer relations could be summed up by a quote from former ADM President James Randall: “Our competitors are our friends. Our customers are the enemy.” This motto animated the company’s business dealings and ultimately led to blatant violations of U.S. antitrust law, a guilty plea and a staggering criminal fine against the company. It also led to the criminal charges against three top ADM executives that are the subject of this appeal. The facts involved in this case reflect an inexplicable lack of business ethics and an atmosphere of general lawlessness that infected the very heart of one of America’s leading corporate citizens. Top executives at ADM and its Asian co-conspirators throughout the early 1990s spied on each other, fabricated abases and front organizations to hide their activities, hired prostitutes to gather information from competitors, lied, cheated, embezzled, extorted and obstructed justice. After a two-month trial, a jury convicted three ADM officials of conspiring to violate § 1 of the Sherman Antitrust Act, 15 U.S.C. § 1, which prohibits any conspiracy or combination to restrain trade. District Judge Blanche M. Manning sentenced defendants Michael D. Andreas and Terrance S. Wilson to twenty-four months in prison: They now appeal several issues related to their convictions and sentences, and the government counter-appeals one issue related to sentencing. We find no error related to the convictions, but agree with the government that the defendants should have received longer sentences for their leadership roles in the conspiracy. I. History The defendants in this case, Andreas and Wilson, were executives at Archer Daniels Midland Co., the Decatur, Illinois-based agriculture processing company. Mark E. Whitacre, the third ADM executive named in the indictment, did not join this appeal. 1 ADM, the self-professed “supermarket to the world,” is a behemoth in its industry with global sales of $14 billion in 1999 and 23,000 employees. Its concerns include nearly every farm commodity, such as corn, soybeans and wheat, but also the processing of commodities into such products as fuel ethanol, high-fructose sweeteners, feed additives and various types of seed oils. ADM has a worldwide sales force and a global transportation network involving thousands of rail lines, barges and trucks. The company is publicly held and listed on the New York Stock Exchange. The Andreas family has long controlled ADM. Dwayne Andreas is a director and the former CEO, G. Allen Andreas is the board chairman and president, and various other family members occupy other executive positions. Michael D. Andreas, commonly called “Mick,” was vice chairman of the board of directors and executive vice president of sales and marketing. Wilson was president of the corn processing division and reported directly to Michael An-dreas. A. The Lysine Industry Lysine is an amino acid used to stimulate an animal’s growth. It is produced by a fermentation process in which nutrients, primarily sugar, are fed to microorganisms, which multiply and metabolize. As a *651 product of that process, the microorganisms excrete lysine, which is then harvested and sold to feed manufacturers who add it to animal feed. Feed manufacturers sell the feed to farmers who use it to raise chickens and pigs. The fermentation process tends to be very delicate, and utmost care must be used to keep the fermentation plant sterile. Until 1991, the lysine market had been dominated by a cartel of three companies in Korea and Japan, with American and European subsidiaries. Ajinomoto Co., Inc. of Japan, was the industry leader, accounting for up to half of all world lysine sales. Ajinomoto had 50 percent interests in two subsidiaries, Eurolysine, based in Paris, and Heartland Lysine, based in Chicago. The other two producers of lysine were Miwon Co., Ltd. (later renamed Se-won Co., Ltd.) of South Korea, and Kyowa Hakko, Ltd. of Japan. Miwon ran a New Jersey-based subsidiary called Sewon America, and Kyowa owned the American subsidiary Biokyowa, Inc., which is based in Missouri. Lysine is a highly fungible commodity and sold almost entirely on the basis of price. Pricing depended largely on two variables: the price of organic substitutes, such as soy or fish meal, and the price charged by other lysine producers. Together, the three parent companies produced all of the world’s lysine until the 1990s, presenting an obvious opportunity for collusive behavior. Indeed the Asian cartel periodically agreed to fix prices, which at times reached as high as $3.00 per pound. In 1989, ADM announced that it was budding what would be the world’s largest lysine plant. If goals were met, the Illinois facility could produce two or three times as much lysine as any other plant and could ultimately account for up to half of all the lysine produced globally. Even before the plant became operational, ADM embarked on an ambitious marketing campaign aimed at attracting large American meat companies, such as Tyson Foods, in part by capitalizing on anti-Asia sentiment prevalent at the time. Also around 1990, another South Korean company, Cheil Je-dang Co., began producing lysine. Despite some early difficulties with the fermenting process, the ADM plant began producing lysine in 1991 and immediately became a market heavyweight, possibly even the industry leader. The two new producers created chaos in the market, igniting a price war that drove the price of lysine down, eventually to about 70-cents per pound. The Asian companies understandably were greatly concerned by developments in this once profitable field. B. Start of the Conspiracy Against this background, Kyowa Hakko arranged a meeting with Ajinomoto and ADM in June 1992. Mexico City was chosen as the site in part because the participants did not want to meet within the jurisdiction of American antitrust laws. Ajinomoto was represented by Kanji Mi-moto and Hirokazu Ikeda from the Tokyo headquarters, and Alain Crouy from its Eurolysine subsidiary. Masaru Yamamoto represented Kyowa Hakko, and Wilson and Whitacre attended for ADM. Mimoto, Ikeda, Crouy and Yamamoto testified as government witnesses at trial. At this meeting, the three companies first discussed price agreements and allocating sales volumes among the market participants. Wilson, who was senior to Whit-acre in the corporate hierarchy, led the discussion on behalf of ADM. The price agreements came easily, and all present agreed to raise the price in two stages by the end of 1992. According to internal Ajinomoto documents prepared after the meeting, the cartel’s goal was to raise the price to $1.05 per pound in North America and Europe by October 1992 and up to $1.20 per pound by December, with other price hikes for other regions. The companies agreed to that price schedule and presumed that Ajinomoto and Kyowa would convince Sewon and Cheil to agree as well. *652 The sales volume allocation, in which the cartel (now including ADM) would decide how much each company would sell, was a matter of strong disagreement. In ADM’s view, ADM should have onethird of the market, Ajinomoto and its subsidiaries should have one-third and Kyowa and the Koreans should have the remaining third. Ajinomoto — the historical industry leader — disagreed vehemently and thought ADM did not deserve an equal portion of the market and could not produce that much lysine in any case. Wilson also suggested each company pick an auditor to whom sales volumes could be reported so that the cartel could keep track of each other’s business. The meeting ended without a sales volume allocation agreement, but two months later, at the recommendation of Whitacre, the cartel raised prices anyway, and prices rose from $.70 to $1.05 per pound. Still, the cartel considered a price agreement without allocating sales volume to be an imperfect scheme because each company would have an incentive to cheat on the price to get more sales, so long as its competitors continued to sell at the agreed price. With cheating, the price ultimately would drop, and the agreement would falter. An effort had to be made to get the parties to agree to a volume agreement, and to that end, Whitacre invited Ajinomo-to officials to visit ADM’s Decatur lysine facility to prove that it could produce the volume ADM claimed. Mimoto, Ikeda and other Ajinomoto officials, including an engineer named Fujiwara, visited the plant in September 1992. At a meeting before the tour, Whitacre and Mimoto confirmed the price schedule to which the parties had agreed in Mexico City. The cartel met again in October 1992, this time in Paris. All five major lysine producers attended, along with representatives of their subsidiaries. Wilson and Whitacre again represented ADM. To disguise the purpose of the meeting, the parties created a fake agenda, and later a fictitious lysine producers trade association, so they could meet and share information without raising the suspicions of customers or law enforcement agencies. According to the agenda, the group was to discuss such topics as animal rights and the environment. In reality, they discussed something much dearer to their hearts — the price of lysine. According to internal Ajinomoto documents, the “purpose of the meeting” was to “confirm present price level and reaction of the market, and 2, future price schedule.” Shortly after this meeting, under circumstances explained below, Whitacre began cooperating with the FBI in an undercover sting operation aimed at busting the price-fixing conspiracy. As a result, most of the meetings and telephone conversations involving Whitacre and other conspirators after October 1992 were audiotaped or videotaped. Despite the cartel’s efforts to raise prices, the price of lysine dropped in 1993. According to executives of the companies who testified at trial, without a sales volume agreement, each company had an incentive to underbid the agreed price, and consequently each company had to match the lower bids or lose sales to its underbidding competitors. This resulted in the price of lysine falling in the spring of 1993. The group, calling itself “G-5” or “the club,” met in Vancouver, Canada, in June 1993 to deal with the disintegrating price agreement. Wilson and Whitacre again represented ADM. At this meeting, the Asian companies presented a sales volume allocation that limited each company to a certain tonnage of lysine per year. ADM, through Wilson, rejected the suggested tonnage assignment because it granted ADM less than one-third of the market. Ajinomoto still considered ADM’s demands too high. That summer’s strong commodities market permitted frequent increases in the lysine price, to which each of the companies agreed, despite the absence of a volume allocation. The cartel’s continued strong interest in a volume allocation to *653 support the price agreement led to another meeting in Paris in October 1993. The failure to reach a volume schedule in Paris finally led to a call for a meeting between the top management at Ajinomoto and ADM: Kazutoshi Yamada and Mick An-dreas. In October 1993, Andreas and Whitacre met with Yamada and Ikeda in Irvine, California. With Whitacre’s assistance, the meeting was secretly videotaped and audiotaped. Andreas threatened Yamada that ADM would flood the market unless a sales volume allocation agreement was reached that would allow ADM to sell more than it had the previous year. The four discussed the dangers of competing in a free market and hammered out a deal on volume allocations, with Andreas accepting less than a one-third share of the market in exchange for a large portion of the market’s growth. Specific prices were not discussed, but Andreas acknowledged the price deal that had already been negotiated. Yamada agreed to present ADM’s proposal to the other three Asian producers. A central concern to Andreas was the difficulty he expected the Asian producers to encounter in maintaining their agreed price level. As Andreas explained at some length, the Asian companies had a more decentralized sales system that depended on agents making deals with customers. ADM featured a very centralized system in which agents played a small role in overall sales and had no discretion over price. In such an environment, maintaining control over price was easy; for the Japanese, Andreas feared it would be difficult and suggested that Ajinomoto move to a more ADM-like centralized pricing system. Andreas also expressed concern that customers could “cheat” the producers by bargaining down the price, apparently by claiming to have received lower bids from competing producers. Ikeda and Yamada agreed that customer cheating was a problem, and the four briefly discussed a quick-response system that would allow the producers to verify with each other the prices offered to particular customers. After the Irvine meeting, the cartel met in Tokyo to work out the details of the Andreas-Yamada arrangement. All the companies except for Cheil now agreed to both tonnage máximums and percentage market shares. The group excluded Cheil from this discussion because it considered Cheil’s volume demand unreasonable. The cartel, expecting the lysine market to grow in 1994, thought it wise to agree on percentages of the market that each company could have since it was possible that all five producers could sell more than their allotted tonnage. With a total expected market of 245,000 tons for 1994, Ajinomoto was to sell 84,000 tons, ADM would sell 67,000 tons, Kyowa would sell 46,000 tons, Miwon would sell 34,000 tons and Cheil, if it eventually accepted the deal, would get 14,000 tons, according to the deal hammered out by Yamada and Andreas in Irvine. As they had before the Andreas-Yama-da meeting, Wilson and Whitacre attended these Tokyo meetings for ADM. In Tokyo, Wilson suggested, and the members agreed, that each producer report their monthly sales figures by telephone to Mi-moto throughout the year, and if one producer exceeded its allocation, it would compensate the others by buying enough from the shorted members to even out the allocation. The producers also agreed on a new price of $1.20 for the United States market. The agreement to buy each other’s unsold allocation cemented the deal by eliminating any incentive for a company to underbid the sales price. According to Mimoto: “[Sjince there is an agreement on the quantity allocation, our sales quantity is guaranteed by other manufacturers of the lysine. So by matching the price, to us, lowering the price is very silly. We can just keep the price.” With the agreement on prices and quantities in place, the lysine price remained at the agreed level for January and February 1994. *654 On March 10, 1994, the cartel met in Hawaii. At this meeting, attended by Wilson and Whitacre on behalf of ADM, the producers discussed the progress of the volume allocation agreement, reported their sales figures and agreed on prices. They also considered letting Cheil into the allocation agreement and agreed to grant the company a market share of 17,000 tons. Cheil accepted this arrangement at a meeting later that day, at which Wilson explained that the conspiracy would operate almost identically to the scheme used to fix prices in the citric-acid market. The cartel further agreed on prices for Europe, South America, Asia and the rest of the world, and discussed how the global allocations would work on a regional basis. According to the figures reported to Mimoto through May 1994, prices were maintained, and both ADM and Ajinomoto were on track to meet their sales volume limits. In the summer of 1994, the producers met in Sapporo, Japan, for a routine cartel meeting. Whitacre represented ADM by himself. At this meeting, Sewon demanded a larger share of the market for 1995. This created a problem for the cartel, which necessitated another meeting between Andreas and Yamada. In October 1994, while on a separate business trip to the United States, Yamada met with An-dreas in a private dining room at the Four Seasons Hotel in Chicago. Whitacre, Wilson and Mimoto also attended along with their bosses. The cartel met in Atlanta in January 1995, using a major poultry exposition as camouflage for the producers being in the same place at the same time. The cartel, without the presence of Sewon, decided to cut Sewon out of the agreement for 1995 because of its unrealistic volume demand. Sewon then joined the meeting and agreed to abide by the set price, if not the volume. The group discussed the year-end sales figures for 1994, comparing them to each company’s allocated volume, and discussed the new allotment for 1995. According to the 1994 numbers, each company finished fairly close to its allotted volume. The cartel met once more in Hong Kong before the FBI raided the offices of ADM in Decatur and Heartland Lysine in Chicago. These raids ended the cartel. Heartland Lysine immediately notified its home office in Japan of the search, and Ajinomoto began destroying evidence of the cartel housed in its Tokyo office. Mimoto overlooked documents stored at his home and later turned these over to the FBI. Included in these saved documents were copies of internal Ajinomoto reports of the Mexico and Paris meetings. C. The Investigation Mark E. Whitacre joined ADM in 1989 as president of its bioproducts division. That year, ADM announced that it would enter the lysine market dominated by Asian producers. Whitacre, who held a Ph.D. in biochemistry from Cornell University and degrees in agricultural science, answered directly to Mick Andreas. Just 32 years old when he joined the company, Whitacre’s star clearly was rising fast at ADM, and some industry analysts thought he could be the next president of ADM. In 1992, Whitacre began working with Wilson, and the two attended the first meetings of the lysine producers in Mexico City. Also in 1992, Whitacre began embezzling large sums of money from ADM and eventually stole at least $9 million from the company by submitting to ADM phony invoices for work done by outside companies, who would then funnel the money to Whitacre’s personal offshore and Swiss bank accounts. To cover up the embezzlement, Whitacre hatched a scheme in the summer of 1992 to accuse Ajinomoto of planting a saboteur in ADM’s Decatur plant. Whitacre would accuse the saboteur of contaminating the delicate bacterial environment needed for the production of lysine, a story made believable because of the many early difficulties the ADM lysine plant encountered. In accordance with the plot, Whitacre told Mick Andreas that an engineer at *655 Ajinomoto named Fujiwara had contacted him at his home and offered to sell ADM the name of the saboteur in exchange for $10 million. The story was a lie. However, Dwayne Andreas believed it and feared it could jeopardize relations between the United States and Japan. He called the CIA, but the CIA, considering the matter one of federal law enforcement rather than national security, directed the call to the FBI, which sent agents out to ADM to interview Whitacre and other officials about the extortion. Whitacre apparently had not expected this and realized quickly that his lie would be discovered by the FBI, particularly after Special Agent Brian Shepard asked Whitacre if he could tap Whitacre’s home telephone to record the next extortion demand. Whitacre knew that when the extortionist failed to call, Shepard would know Whitacre had invented the story. Whitacre confessed the scheme to Shepard, but to save himself, he agreed to become an undercover informant to help the FBI investigate price fixing at ADM. He did not come totally clean with the FBI, however; he failed to mention the millions he embezzled and in fact continued to embezzle after he began working for the government. For the next two- and-a-half years, Whitacre acted as an undercover cooperating witness — legally a government agent — and secretly taped hundreds of hours of conversations and meetings with Wilson, Mick Andreas and the other conspirators. In addition, the FBI secretly videotaped meetings of the lysine producers. Whitacre made between 120 and 130 tapes for the FBI during the investigation, beginning with a November 9, 1992, conversation with Yamamoto, by using recording equipment, tapes and instruction provided by the government. FBI agents met with Whitacre more than 150 times during the investigation. The tapes were collected and reviewed usually within a day or two of the FBI receiving them, and Department of Justice (DOJ) attorneys regularly participated in reviewing the tapes and monitoring the supervision of Whitacre. However, the FBI’s supervision of Whitacre was not flawless. Whit-acre was, to say the least, a difficult cooperating witness to handle. Whitacre lied to the FBI during the probe, failed polygraph tests, bragged to his gardener about his role as an FBI mole, all while continuing to embezzle millions of dollars from the company. He even envisioned himself ascending to the ADM presidency as a hero once Andreas, Wilson and Randall 2 were taken down in the FBI sting. In short, he was out of control, and the FBI struggled to keep him on track. Nonetheless, the FBI and the DOJ considered him the best opportunity to stop a massive price-fixing scheme. Whitacre exercised much discretion in deciding which conversations to record. He was given a tape recorder that could be hidden in his coat breast pocket and another that could be stowed in his briefcase. Agent Shepard showed him how to use the devices and sometimes affixed a recording device to Whitacre’s body. Another recording device was used to tap one of Whitacre’s home telephones, but not his cellular telephone. All recordings were done with Whitacre’s express, signed consent, and all but one were done after Whitacre confessed that his story about a saboteur was a hoax and he began cooperating. Whitacre was told to record conversations relevant to the conspiracy, but not to record anything about ADM’s legitimate business. In direct contravention of the FBI’s recording policy, Whitacre did not record many conversations he had with the alleged conspirators. The record shows Whitacre telephoned Ajinomoto and Kyo-wa 114 times, but 80 were never recorded or documented by the FBI as required. In addition, many conversations with co-defendants Wilson and Andreas were never recorded or documented. *656 Whitacre once claimed that Shepard ordered him to destroy tapes bearing exculpatory conversations, but Shepard denied this charge and Whitacre later recanted it in a sworn affidavit. Both Whitacre and a friend he entrusted with some of the tapes testified that no tapes were destroyed at Shepard’s command. A tape expert testified for the government that none of the tapes exhibited evidence of splicing or alteration and that only a few showed evidence of “bulk erasure” or over-recording. Although that meant that some recordings may have been taped over, the expert expressed an opinion that none of the final recordings had been altered. Andreas and Wilson moved to suppress the inculpatory tapes before trial and to allow them to introduce evidence that exculpatory tapes had been destroyed. For reasons explained below, the motion was denied although the trial court found that the FBI’s supervision of Whitacre and its blatant inability to follow its own internal policies “border on gross negligence.” D. Barrie Cox As part of its investigation into lysine and citric-acid price fixing by ADM, the government sought to interview Barrie R. Cox, a British national and president of ADM’s food additives division in Europe. Cox, who reported directly to Wilson from 1991 through June 1995, was believed to have information regarding a conspiracy to fix prices in the citric-acid market. Prosecutors thought he could help them better gauge the value of ADM’s cooperation, which was a factor in determining how high the fine should be when ADM eventually pleaded guilty, a plea which was expected to follow within a week. To avoid extradition problems from Great Britain and to procure Cox’s cooperation, the San Francisco antitrust office of the DOJ sent Cox a letter dated October 11, 1996, guaranteeing use-immunity for any information provided by Cox during the interview. The letter stated in part: This is to confirm, as set forth in my letter to Mr. William W. Taylor, III, ... that in connection with the interview of Archer Daniels Midland Company’s (“ADM”) employee, Mr. Barrie R. Cox, the United States acknowledges that statements made by Mr. Cox and information provided by Mr. Cox during the interview are covered by Federal Rule of Criminal Procedure 11(e)(6) and also may not be used directly or indirectly against ADM or any of its employees, subsidiaries or affiliates in any criminal prosecution. When the letter was sent and Cox was interviewed, the government was in the final stages of negotiating ADM’s guilty plea agreement. Rule 11(e)(6) of the Federal Rules of Criminal Procedure prohibits the government from using the following against a defendant who made a plea or participated in plea discussions: (C) any statement made in the course of any proceedings under this rule regarding either [a guilty plea that was later withdrawn or a plea of nolo contendere]; or (D) any statement made in the course of plea discussions with an attorney for the government which do not result in a plea of guilty or which result in a plea of guilty later withdrawn. Based on this guarantee, Cox submitted to the interview. In the interview and later at trial, Cox provided details of the citric-acid conspiracy that showed it to be closely similar in design and function to the lysine conspiracy. Andreas and Wilson moved to suppress Cox’s testimony and argued that the government, by its letter to Cox, intended to immunize them as ADM employees, despite the fact that they had already been notified that the government would seek indictments against them. The district court found this argument unpersuasive and denied the motion to immunize Andreas and Wilson or suppress the testimony. Cox testified that ADM fixed prices and participated in volume allocations in the *657 citricacid market for at least four years, from 1991 to 1995. Wilson, Cox’s superior, was actively involved in the schemes in which citric-acid producers representing about two-thirds of the global market would meet on a regular basis to set prices and agree to sales quotas for each company. Cox testified that before he joined ADM, 3 Andreas asked him if it was possible to arrange a meeting of the competitors in the citric-acid market. Later, Wilson and Cox arranged meetings with the major competitors, who agreed to fix prices and establish volume quotas. The quotas were considered necessary to discourage any cartel member from cutting prices. As in the lysine conspiracy, the allocations were determined by each company’s historical sales performance. If any company sold too much, it would be required to buy the following year from the company that sold too little. To monitor the progress of the conspiracy, each company reported its sales monthly to a designated cartel member. Additionally, a trade association was formed to help cover up the cartel’s actions. Wilson participated in several of the cartel’s meetings. E. Closing Arguments In closing argument at the end of the two-month trial, then-Assistant U.S. Attorney Scott Lassar gave his opinion of the sufficiency of the evidence: I think that you’re going to see — and you probably suspect this already — that the case that has been presented here by the government is one of the most compelling and powerful that has ever been presented in an American courtroom. Why do I make a statement like that? Well, the most powerful evidence you could ever have would be a videotape of the defendant committing the crime. You can’t get better evidence than that. You’ve got it as to defendant Andreas and defendant Wilson. Defense counsel objected to what they considered Lassar’s impermissible vouching for the strength of the government’s case when he called it “one of the most compelling and powerful that has ever been presented in an American courtroom.” The court agreed and gave a limiting instruction to the jury to disregard Lassar’s personal opinion. Lassar also remarked on defendants’ responses to the FBI questioning at the time of the raids on ADM in June 1995. At that time, the FBI briefly questioned both Andreas and Wilson. After denying that they committed a crime, both men refused to answer questions without the presence of counsel. At trial, Wilson and Andreas exercised their right not to testify. Lassar characterized the defendants’ initial responses by saying, “they lied and lied and lied.” He then continued with his closing: When the defense attorneys address you, they’re going to come up with all kinds of different defenses all over the place. But when you’re hearing all those defenses, ask yourselves why didn’t we hear those defenses from Mr. Wilson and Mr. Andreas on June 27, 1995? That was their opportunity if they had a defense. They were confronted. That was their opportunity to give all these defenses. You’re not going to hear those lies from the attorneys because the attorneys have an advantage over their clients. The attorneys have heard all the evidence the government has. They knew before trial about all those tapes, and so they constructed new defenses for your benefit that they’re going to argue to you, not the ones their clients came up with, and that’s evidence to you that the defenses you’re going to hear are not true because if they were true, you would have heard them given to the FBI by Mr. Wilson and Mr. Andreas in June 1995. The three defendants argued that Las-sar sought to introduce indirectly the de *658 fendants’ choice not to testify. Judge Manning strongly rebuked Lassar, but declined to declare a mistrial. Instead, the court instructed the jury to disregard Las-sar’s impermissible comments. F. Sentencing The jury convicted the three defendants on the single-count conspiracy indictment. On July 9, 1999, the court sentenced the defendants. United States Sentencing Guidelines § 2R1.1 mandated a base-offense level of ten and a seven-level increase because the volume of commerce affected was more than $100 million. With criminal histories in category I, the applicable range under the Guidelines for an offense level of seventeen was twenty-four to thirty months. The Presentence Investigation Reports (PSR) recommended a four-level increase for Andreas and three-level increase for Wilson based on their leadership roles in the conspiracy, pursuant to U.S.S.G. § 3B1.1. The court rejected the leadership role enhancements because it found that Wilson and Andreas were no more culpable than their co-conspirators. The court then sentenced each defendant to twenty-four months in prison. II. Analysis On appeal, Andreas and Wilson raise ten issues including, among others, challenges to evidentiary rulings, the sufficiency of the evidence and the calculation of their sentences under the Sentencing Guidelines. The government appeals only one ruling, the denial of an upward adjustment for the defendants’ leadership roles in the crime. A The Tape-Recorded Evidence 1. Admission of Audiotape Evidence The defendants appeal the district court’s decision to admit the tape recordings made by Whitaere on two grounds. First, they claim they were denied due process because evidence showed that the FBI and Whitaere engaged in “selective taping” and destroyed exculpatory tapes, which rendered the tapes unreliable, misleading and the product of bad faith. Second, they allege that the tapes were made in violation of the federal wiretap statute, 18 U.S.C. § 2511. The district court considered and rejected these arguments, and we review that decision for abuse of discretion. See United States v. Bradley, 145 F.3d 889, 892 (7th Cir.1998). The abuse of discretion standard for evidentiary rulings presents a high hurdle for defendants, allowing reversal “only when no reasonable person could agree” with the trial judge, United States v. Sinclair, 74 F.3d 753, 756-57 (7th Cir.1996), and only if the error was not harmless. See Holmes v. Elgin, Joliet & E. Ry. Co., 18 F.3d 1393, 1397 (7th Cir.1994). a. Due Process The defendants claim the admission of the tapes violated their due process rights because the FBI failed to supervise Whit-acre adequately, badly mismanaged the two-year taping operation and because Whitaere had ulterior motives for acting as a mole, thereby rendering the tapes so unreliable as to make them constitutionally defective. See United States v. Feekes, 879 F.2d 1562, 1564 n. 2 (7th Cir.1989); United States v. Faurote, 749 F.2d 40, 44 (7th Cir.1984). After holding an evidentia-ry hearing, the trial court denied the defendants’ motions to suppress the tape recordings. In Feekes, we expressed in dicta that government conduct in managing an undercover taping investigation could be so outrageous as to “run afoul of the constitutional guarantee of due process.” Feekes, 879 F.2d at 1564 n. 2. As examples, we mentioned selective taping and editing of conversations and deliberate destruction of certain tapes. Id. However, we also noted that credibility determinations regarding an informant belong to the jury, not the court, and that it was equally important to consider the total circumstances of the undercover operation in as *659 sessing the supposed outragepusness' of the government’s conduct. Id. at 1565. In conducting criminal investigations, law enforcement frequently must rely on unsavory characters, such as Whitacre, whose motives are less than pure. As with all due process analyses, the touchstone consideration is whether the proceeding was fundamentally fair, and selective recording without more does not offend the Constitution. See United States v. Chaudhry, 850 F.2d 851, 857 (1st Cir.1988). Whitacre’s behavior while acting as a cooperating witness can be characterized as troublesome and, at times, criminal. That is to say, he lied, cheated, stole and then lied some more. He failed to follow orders and had delusions of grandeur that would make Napoleon blush. Still, this Court cannot fathom how that affected the accuracy of his recording equipment. The tapes themselves reflect complete conversations and are internally consistent and corroborated by other witnesses. While evidence that an informant selectively failed to record exculpatory evidence would raise due process concerns, the defendants produced no such evidence. Rather, they rely merely on an assumption that because Whitacre was dishonest and sought to benefit from having his superiors convicted, then he must have selectively failed to record exculpatory conversations. The defendants contend that the FBI granted Whitacre unfettered discretion to choose what to tape, but this mischaracter-izes the FBI’s instructions to Whitacre. Andreas and Wilson say Whitacre was told to tape incriminating conversations, not conversations regarding legitimate ADM business, and this amounts to an instruction not to tape exculpatory remarks. The FBI’s actual instructions were to tape all conversations regarding the conspiracy, which would include inculpatory and exculpatory statements, but to omit conversations about other ADM business. Had the subjects of the investigation had a conversation related to the conspiracy that was exculpatory, Whitacre was under orders to record it. His discretion was not. unfettered, nor was he told to do anything improper. In Faurote, we reaffirmed the principle that the party seeking to introduce taped evidence bears the burden of establishing its truth, accuracy and authenticity, and that the trial judge has broad discretion in deciding whether this standard has been met. 749 F.2d at 43. Defendants cannot mount a serious challenge under this standard. The government established the accuracy of the recordings through witnesses who attended the meetings, and defense counsel took full advantage of the opportunity to voir dire and cross-examine these witnesses on the- truth, accuracy and meaning of the tapes. A tape expert testified that although some of the tapes had been reused, none of the conversations on the tapes had been altered or edited in any way. We see no “extraordinary circumstances” (in fact, no circumstances whatsoever) that would cause us to reverse the trial court’s decision to admit the tapes. Finally, the defendants contend that the FBI ordered Whitacre to destroy exculpatory tapes, which would undoubtedly violate due process if true. See California v. Trombetta, 467 U.S. 479, 488-89, 104 S.Ct. 2528, 81 L.Ed.2d 413 (1984); United States v. Watts, 29 F.3d 287, 290 (7th Cir.1994). To establish such, a violation, the defendants must show that (1) the government acted in bad faith by not preserving evidence, (2) the exculpatory nature of the evidence was apparent before its destruction and (3) the defendant cannot obtain the same evidence elsewhere. See Trombetta, 467 U.S. at 488-89, 104 S.Ct. 2528; Watts, 29 F.3d at 290. The defendants produced no credible evidence that any evidence was actually destroyed. Whitacre never claimed he destroyed tapes; rather, he offered but then recanted an allegation that a friend to whom he sent some tapes destroyed them after the FBI told Whitacre to get rid of the tapes. That friend, David Hoech, denied destroying any tapes. It follows that because no *660 evidence was destroyed, its exculpatory nature could not have been apparent before its destruction. Furthermore, because Whitacre recanted his allegation that the FBI ordered him to destroy tapes — an allegation that was far from credible even when made — no evidence indicates bad faith by the government. b. Federal Wiretap Laws The defendants further contend that the tape recordings violated federal wiretap laws, and therefore must be excluded from trial based on 18 U.S.C. § 2515, which prohibits the evidentiary use of any illegally obtained tape recording. Two exceptions to § 2515 potentially apply. First, § 2511(2)(c) allows the use of tape recordings made by a participant to the conversation who was “acting under color of law.” 18 U.S.C. § 2511(2)(c). Second, § 2511(2)(d) allows the use of recordings made by participants in a conversation unless that party had a “criminal or tortious” purpose in making the recording. 18 U.S.C. § 2511(2)(d). Because we find that Whitacre acted under color of law, we do not need to reach the second possibility. The government asserts that Whitacre was acting as a cooperating witness, and therefore under color of law, from November 1992 through the end of the conspiracy. See Obron Atlantic Corp. v. Barr, 990 F.2d 861, 864 (6th Cir.1993) (allowing use of tape recordings made by corporate executive in price-fixing investigation); United States v. Haimowitz, 725 F.2d 1561, 1582 (11th Cir.1984) (holding that cooperating witness under direction of FBI was acting under color of law); United States v. Horton, 601 F.2d 319, 322 (7th Cir.1979) (holding that tapes made by FBI informant were admissible under § 2511(2)(e)-(d)); United States v. Craig, 573 F.2d 455, 476 (7th Cir.1977) (holding that informant acted under color of law when FBI supervised recording). Andreas and Wilson counter that the FBI’s supervision of Whitacre was so lax as to strip him of this status. In Craig, we noted several factors in the government’s supervision of an informant that indicated the government directed the recording. 573 F.2d at 476. In that case, such factors included whether the government supervised every aspect of the recording, selected the conversations to -be recorded, supplied and operated the equipment, and recovered the tapes and equipment after each session. Id. We did not suggest that these factors were necessary to a finding that the witness acted under color of law, only that they were sufficient. Id. Therefore, their absence in the instant case, while probative, is not dispositive. Defendants cite dicta in Thomas v. Pearl, 998 F.2d 447, 451 (7th Cir.1993), for the proposition that because police officers “who secretly taped conversations without a warrant or the approval of their superiors” would not be acting under color of law, then a fortiori, a private citizen acting without a warrant or the approval of superiors cannot be. In Thomas, we were comparing the “color of law” provision from the wiretap statute with the way the term has been interpreted in cases arising under 42 U.S.C. § 1983. In civil rights cases, we have interpreted the term very broadly, equating it with state action. In Thomas, we held that such a broad reading of “color of law” in the wiretap statute would be nonsensical because it would permit every government employee to tape with impunity, regardless of their purpose. 998 F.2d at 451. We used the example of police officers acting in violation of the Fourth Amendment to make the point that government employment by itself does not mean acting under color of law for purposes of the wiretap statute. Id. Here, the government does not contend that Whit-acre was acting under color of law because he was a government employee. Thomas, then, is of only marginal relevance. Rather, when assessing whether someone acted under “color of law” for the wiretap statute, the question is whether the witness was acting under the government’s direction when making the record *661 ing. See Craig, 573 F.2d at 476; see also Obron Atlantic, 990 F.2d at 864; Haimow-itz, 725 F.2d at 1582; United States v. Shields, 675 F.2d 1152, 1156-57 (11th Cir.1982); United States v. Tousant, 619 F.2d 810, 813 (9th Cir.1980). No cases demand that the government’s supervision of its cooperating witnesses and informants need be flawless. In fact, the investigation in Obron Atlantic suffered many of the same defects as the ADM investigation. 990 F.2d at 863. The mole in Obron Atlantic used his own equipment, decided which calls to tape, failed to maintain a log of his recordings and sometimes held on to tapes for weeks or months before turning them over. Id. The court found that the witness’s “continuous, albeit irregular, contact [with] DOJ attorneys, following their explicit request that he assist them in this very way and their instructions on how to conduct the calls, outweighs the lack of direct DOJ supervision over the recording process and [his] failure to comply with certain directives.” Id. at 865. What we find essential is that the government requested or authorized the taping with the intent of using it in an investigation and that they monitored the progress of the covert surveillance activities. To be sure, the FBI’s supervision of Whitacre’s surreptitious taping activities will likely never make it into the textbooks. The defendants make use of the technical errors in the supervision to paint a picture of a rogue witness, completely out of control, acting alone, throwing away tapes and manipulating evidence with callous indifference. Many conversations between Whitacre and one or more conspirators that should have been recorded were not, and the FBI frequently did not file the necessary reports or provide explanations for these missed conversations. Many of the tapes Whitacre made were not collected as promptly as they should have been, and the catalogue of tapes given to and collected from Whitacre was not meticulously maintained. The FBI did not seem to follow its own internal guidelines on supervising taping activities, but this does not provide a basis for constitutional challenge. See United States v. Caceres, 440 U.S. 741, 752, 99 S.Ct. 1465, 59 L.Ed.2d 733 (1979) (holding that a breach of administrative guidelines does not establish a constitutional violation automatically). Still, these technical deficiencies do not show Whitacre acting independently of the FBI. FBI agents requested Whitacre begin taping his eoconspirators, instructed him on what type of conversation to record, supplied him with taping equipment and tapes, instructed him on the proper use of the equipment and met with him regularly to discuss developments in the conspiracy and collect the tapes. When possible, the FBI itself monitored the conversations by setting up remote-controlled video recorders to tape the face-to-face meetings of the conspirators and having FBI agents act as hotel staff to infiltrate the meetings. As in Craig, this evidence was sufficient to prove that Whitacre acted at the direction of the FBI in gathering the tapes, and therefore acted under color of law. 2. Evidence of Exculpatory Audiotapes Wilson and Andreas next contend that the trial court’s decision to exclude the testimony of Special Agent Athena Var-ounis denied them the use of potentially exculpatory evidence. The defendants believe that Varounis would have testified about her investigation of claims by Whit-acre and his wife that the FBI instructed Whitacre to destroy exculpatory tapes. On April 16, 1997, after he learned he would be indicted, Whitacre and his wife, Ginger Whitacre, met with Varounis in Chicago and alleged that Agent Shepard told him to destroy tapes. Whitacre later recanted the allegation, but Wilson and Andreas sought to introduce it as hearsay pursuant to Rule 804(b)(3) of the Federal Rules of Evidence as a statement against penal interest. Whitacre exercised his Fifth Amendment right not to testify at trial, making him unavailable to testify, so *662 defendants sought to have Varounis recount Whitacre’s statements to her regarding the FBI’s alleged order to destroy evidence. The trial court refused to allow the testimony because the statements were not, on balance, against Whitacre’s penal interest when made and were not adequately corroborated. To be admissible under Rule 804(b)(3), a statement must have been against the declarant’s penal or pecuniary interest at the time it was made, must be corroborated to ensure its trustworthiness and the declarant must be unavailable to testify. See United States v. Garcia, 897 F.2d 1413, 1420 (7th Cir.1990); see also Williamson v. United States, 512 U.S. 594, 114 S.Ct. 2431, 129 L.Ed.2d 476 (1994). Courts must look to the totality of circumstances to determine whether the declarant truly exposed himself to criminal liability by making the statements. See United States v. Butler, 71 F.3d 243, 253 (7th Cir.1995). The trial court found that Whit-acre’s statements were not credible when made and were contradicted by other evidence. Hoech, the friend to whom Whit-acre supposedly sent the tapes, testified that he did not destroy any tapes, and other evidence showed Whitacre’s story to be a poorly constructed hoax. For instance, Whitacre claimed the order to destroy evidence came during a meeting in Illinois on a day when records show Whit-acre was out of the state. Varounis found no evidence that any tapes had been destroyed. Whitacre himself recanted the allegation in a sworn affidavit before being sentenced for embezzlement. Whitacre’s propensity to lie cannot be doubted, and the court chose not to accept his (by then recanted) story over contradictory statements of other witnesses. Andreas and Wilson contend that Whit-acre’s statements to Varounis indicate Whitacre obstructed justice and were therefore against his penal interest, but it is unclear how this could be true. Whit-acre, who was about to be charged with conspiring to violate the antitrust law, and Whitacre’s wife said only that the FBI instructed him to destroy tapes, and he denied that he ever actually destroyed evidence. Furthermore, because Whitacre was acting as a government agent since November 1992, none of the tapes could have been inculpatory as to him. Therefore, by claiming the FBI ordered tapes destroyed, he did not damage his own defense against the antitrust conspiracy charge at all, but he delivered a potentially crippling blow to the FBI agents’ credibility at trial. Since Whitacre’s antitrust conviction would be based largely on FBI and co-conspirator testimony regarding the pre-November 1992 events, this tactic could have been a major boon to him in fighting his own conspiracy charge. Whit-acre may also have preferred conviction on the less serious charge of obstructing justice rather than face a longer prison term for criminal conspiracy. Judge Manning correctly found that, on balance, the Whit-acres’ allegations of evidence tampering were not against Whitacre’s penal interest. The trial court did not abuse its discretion in barring Agent Varounis’ testimony. B. Barrie Cox 1. The Immunity Agreement The government and Cox entered into a use immunity agreement to facilitate Cox’s interview with the FBI and the DOJ in preparation for ADM’s impending plea agreement, which would settle all charges against the corporation. At all times, the government was preparing to prosecute Wilson and Andreas criminally, which makes the defendants’ request that this Court interpret the Cox immunity agreement (the “agreement” or “letters”) to immunize them truly remarkable. They contend that this absurd result follows from a logical chain beginning with the government’s intent to immunize Andreas and Wilson, even though Andreas and Wilson were the prime individual targets of the government’s three-year investigation. *663 The defendants contend they are third-party beneficiaries of the agreement and that because the government cannot present an entirely independent source for Cox’s testimony, the indictment must be dismissed, or at the very least, Cox’s testimony regarding the citric-acid conspiracy should have been suppressed. We decline to take the first step down this too clever road. Without deciding whether third parties can ever be immunized by another’s compelled testimony, 4 we agree with the district court that Wilson and Andreas do not have standing to enforce the terms of the Cox agreement. Immunity agreements, like plea bargains, are interpreted as ordinary contracts in light of the parties’ reasonable expectations at the time of contracting. See Wilson v. Washington, 138 F.3d 647, 652 (7th Cir.1998); United States v. Fields, 766 F.2d 1161, 1168 (7th Cir.1985). Individuals who are not parties to a contract may enforce its terms only when the original parties intended the contract to directly benefit them as third parties. See Restatement (Second) of Contracts § 304 (1979); Holbrook v. Pitt, 643 F.2d 1261, 1270 (7th Cir.1981) (“Under settled principles of federal common law, a third party may have enforceable rights under a contract if the contract was made for his direct benefit.”); see also Carson Pirie Scott & Co. v. Parrett, 346 Ill. 252, 178 N.E. 498, 501 (1931). 5 A contract creates a right in a third-party beneficiary if recognition of that right effectuates the intent of the parties and the “circumstances indicate that the promisee intends to give the beneficiary the benefit of the promised performance.” Restatement (Second) of Contracts § 304; Holbrook, 643 F.2d at 1271 n. 17 (adopting the Second Restatement definition); see generally Cahill v. Eastern Benefit Sys., Inc., 236 Ill.App.3d 517, 177 Ill.Dec. 718, 603 N.E.2d 788, 792-93 (1992) (“The critical inquiry centers on the intention of the parties, which is to be gleaned from the language of the contract and the circumstances surrounding the parties at the time of its execution.”) (citing People ex rel. Resnik v. Curtis & Davis, Architects & Planners, Inc., 78 Ill.2d 381, 36 Ill.Dec. 338, 400 N.E.2d 918, 919 (1980)). In this ease, the circumstances conclusively establish that neither the promisee (Cox) nor the promisor (the government) intended to give Andreas and Wilson any benefit of the promise since both knew Andreas and Wilson specifically would be excluded from the plea deal. In October 1996, the government was in the final stages of negotiating a plea agreement with ADM that would end the investigations into the corporation’s responsibility for antitrust violations in the lysine and citric-acid industries. The plea agreement included a statement that “the United States agrees: (a) not to bring charges against any current director, officer or employee of the defendant or any of the defendant’s subsidiaries or affiliates (other than Michael D. Andreas and Terrance Wilson).” In exchange for the plea, ADM agreed to pay a $100 million fine and cooperate (and allow its employees to cooperate) with the government. In the October 11 letter to Aubrey M. Daniel, attorney for ADM, the DOJ expressly conditioned the plea on “the cooperation of ADM’s employ *664 ees with the investigation and resulting prosecutions.’’ (Emphasis added.) The DOJ sought Cox’s testimony in advance of the plea hearing to help it “assess the value of ADM’s proffered cooperation.” The government had agreed that if ADM’s cooperation was especially helpful, it would not seek a higher fíne under the Sentencing Guidelines. Both letters expressly referenced Rule 11(e)(6) of the Federal Rules of Criminal Procedure, placing the letters squarely in the context of the impending plea agreement, which expressly excluded Andreas and Wilson. The letter to ADM’s attorney (the “Daniel letter”) incorporated the letter to Cox’s attorney, Taylor (the “Taylor letter”). The Taylor letter specifically referenced the proposed plea agreement of ADM and expressed the understanding of the United States that “the interview is being conducted in the course of our plea discussions with your clients’ employer, ADM.” The Daniel letter, like the Taylor letter, further refers to the Federal Rules of Criminal Procedure. The references to the plea negotiations and the plea agreement express the intent of the parties to execute an immunity agreement to protect Cox, ADM and all ADM employees except for Andreas and Wilson, from prosecution based on Cox’s testimony. The text of the letters and the circumstances surrounding them do not evince an intent to vest third-party rights in Andreas and Wilson. To the contrary, the evidence demonstrates an intent to exclude Andreas and Wilson from any benefit of the agreement. Because they are not parties or third-party beneficiaries, we hold that Wilson and Andreas do not have standing to enforce the terms of the immunity agreement. 6 2. Citric-Acid Conspiracy Evidence Defendant Andreas objected to the admission of Cox’s testimony regarding the citric-acid conspiracy as unduly prejudicial. Andreas contends that no evidence showed he had been involved in the citric-acid conspiracy, and therefore it could not be admitted against him under Rule 404(b) of the Federal Rules of Evidence, which allows evidence of other crimes or bad acts to be used to show a defendant’s motive, plan or intent in the instant crime. Rule 404(b) strictly prohibits the evidence of other crimes or bad acts to support the inference that the defendant has a propensity to commit that type of crime, but we do not believe that happened here. First, Andreas contends vigorously that the evidence of the citric-acid conspiracy fails to implicate him in any crime, including the citric-acid conspiracy, so it follows that the potential for an impermissible inference regarding his character must be nil. However, we find an alternative basis for allowing Cox’s testimony. Rule 404(b) guards against the impermissible inference that because a defendant committed Crime A at some time in the past, he is more likely to have committed Crime B, the crime charged in the present. The risk that the jury may improperly comprehend and weigh evidence of prior bad acts looms so large that courts in this country have long forbidden the government from invoking it. See Victor J. Gold, Federal Rule of Evidence UOS: Observations on the Nature of Unfairly Prejudicial Evidence, 58 Wash. L.Rev. 497, 524-30 (1983). Yet we have carved out two important categories of cases where the rule does not apply. The first, and most common, is expressly stated in the rule itself, and that allows the use of other crimes evidence for purposes other than to show a propensity to commit the crime, such as to show the defendant’s motive, plan or intent. See Fed.R.Evid. 404(b) (“Evidence of other crimes, wrongs, or acts ... may, however, be admissible for other purposes, such as proof of mo *665 tive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident... The second exception, which applies here, covers acts that are so intricately interwoven with the facts of the charged crime that to omit the evidence relating to it would lead to confusion or leave an unexplainable gap in the narrative of the crime. See United States v. Akinrinade, 61 F.3d 1279, 1285-86 (7th Cir.1995). While not an express exception to Rule 404(b), this type of evidence is permitted by virtue of not being included within the province of the rule. “Other crimes or acts” does not include those acts that are part and parcel of the charged crime itself; they simply are not “other.” To omit the evidence would leave unanswered some questions regarding the charged offense. Such evidence includes acts that although not charged as crimes, “are directly related to the charged offense.” United States v. Adames, 56 F.3d 737, 742 (7th Cir.1995). “[T]he question is whether the evidence is properly admitted to provide the jury with a complete story of the crime.... ” United States v. Ramirez, 45 F.3d 1096, 1102 (7th Cir.1995) (internal quotation omitted). Andreas’ situation mirrors Adames. That case involved a drug conspiracy in which one of the defendants, Adames, had been caught in a drug sting operation in Texas (the “Texas sting”) unrelated to his co-defendants in the charged offense. Adames, 56 F.3d at 741. ' However, the Texas sting prevented Adames from delivering the promised amount of marijuana and caused other changes in the conspirators’ plan. The codefendants moved to exclude evidence of the Texas sting on the ground that it was a separate, extraneous conspiracy that did not implicate them at all. Like Andreas, .they also moved to exclude on the basis that even if allowable under Rule 404(b), it would be unduly prejudicial and should be barred by Rule 403. The trial court found, and we agreed, that the Texas sting was sufficiently linked to the charged offense to be admitted notwithstanding Rule 404(b). Id. at 742. The Texas sting provided direct evidence of the crime charged and therefore could not be considered “other crimes” evidence. Furthermore, the Texas sting was not so shocking, repulsive or emotionally charged that its probative value was outweighed by its prejudicial effect. We noted that probative evidence is always prejudicial, but the question remains whether it is unfairly prejudicial. Id. The evidence of the citric-acid conspiracy answered at least three relevant questions. First, the jurors heard the conspirators in tape-recorded meetings discussing the citric-acid conspiracy, and they heard Wilson explaining that certain aspects of the lysine conspiracy, such as the bogus trade association, would operate in the same way. The evidence of the citric-acid conspiracy was relevant to explain these references in the conspirators’ conversations. Second, testimony at trial showed that in the halls of ADM’s Decatur headquarters, the lysine and citric-acid conspiracies were closely related parts of a master plan to control prices and product supply through collusion with competitors. The citric-acid conspiracy, of which Andreas was aware, provided the blueprint for and motivating force behind the nascent lysine scheme. Many of the lysine cartel’s meetings revolved around the need to allocate sales volume, a lesson dictated by the experience in the citric-acid conspiracy. Finally, omitting the citric-acid evidence would leave Wilson’s participation in the lysine conspiracy unexplained. Wilson— head of the corn division — was called in to work on the bioproducts project solely because he had experience with cartels that he gained from the citric-acid conspiracy. Wilson was to tutor Whitacre in running a citric-acid type conspiracy. The inference cannot be missed that since Wilson reported directly to Andreas, Andreas must have known why his corn processing chief was working so closely and traveling so much *666 with the bioproducts chief. Because Wilson’s entire reason for getting involved in lysine was to share his criminal experience with Whitaere, it takes little imagination to see how evidence of the citric-acid conspiracy implicated Andreas. To omit this evidence would, as in Adames, leave an unexplained gap in the narrative of the crime. We find the evidence of the citric-acid conspiracy was relevant to Andreas’ guilt and not unfairly prejudicial. C. Per Se Violations The grand jury indictment charged the defendants with engaging in a “conspiracy to suppress and eliminate competition by fixing the price and allocating the sales volumes of lysine ... the substantial terms of [the conspiracy] were: (a) to agree to fix and maintain prices ... and (b) to agree to allocate the sales volumes of lysine among the corporate conspirators.” The government’s theory of the case held that the conspirators sought to raise prices by two independent but related means — price fixing and volume agreements — either one of which would accomplish the ultimate goal of the conspiracy. The court instructed the jury that it could convict the defendants of violating § 1 of the Sherman Antitrust Act if it found the defendants entered into an agreement either to fix prices or to “divide sales of a product among the various competitors.” The defendants moved for acquittal on the sales volume portion of the indictment, arguing that it could not be considered a per se antitrust violation. The court denied the motion and a subsequent renewed motion for acquittal following the conviction. We review de novo a denial of motion for acquittal, but view the evidence in the light most favorable to the government. See United States v. Hack, 162 F.3d 937, 942 (7th Cir.1998). On appeal, Wilson and Andre-as contend that the jury instruction impermissibly allowed the jury to convict them for allocating sales volumes without requiring the government to prove with economic evidence that such an allocation unreasonably restrained trade. Violations of § 1 require evidence proving that the charged practice had the effect of unreasonably restraining trade under the “rule of reason,” except in the limited cases referred to as per se violations. See White Motor Co. v. United States, 372 U.S. 253, 261-62, 83 S.Ct. 696, 9 L.Ed.2d 738 (1963); see also Broadcast Music, Inc. v. CBS, Inc., 441 U.S. 1, 7-8, 99 S.Ct. 1551, 60 L.Ed.2d 1 (1979). Per se violations are ones that “always or almost always tend to restrict competition and decrease output” such that the court may dispense with the requirement of economic evidence. Id. at 19-20, 99 S.Ct. 1551. Per se violations are “naked restraints of trade with no purpose except stifling of competition,” White Motor, 372 U.S. at 263, 83 S.Ct. 696, and have been characterized as so “plainly anti-competitive” and lacking “any redeeming virtue” that they are presumed illegal under § 1. See Broadcast Music, 441 U.S. at 8, 99 S.Ct. 1551 (internal quotations and citations omitted). Courts apply per se treatment only after “considerable experience” with a particular business practice has inevitably resulted in a finding of anticom-petitive effects. United States v. Topco Assocs., Inc., 405 U.S. 596, 607, 92 S.Ct. 1126, 31 L.Ed.2d 515 (1972); Bunker Ramo Corp. v. United Business Forms, Inc., 713 F.2d 1272, 1284 (7th Cir.1983). The defendants do not contend that price fixing is not a per se violation, only that the agreement to allocate sales volumes, which according to the indictment and jury charge was a separate and independent goal of the conspiracy, should be subject to rule of reason analysis. We will reverse jury verdicts in multiple-goal conspiracies when the potential exists that the jury convicted the defendant on an improper ground. See United States v. McKinney, 954 F.2d 471, 475 (7th Cir.1992). The issue then is whether the agreement to divide the market among the five lysine producers constituted a per se violation of the Sherman Act. The defendants’ argu *667 ment relies heavily on the fact that neither the words “sales volume allocation” nor any practices precisely identical to their scheme appear in the case law as a per se violation. The agreement did feature some clever characteristics that the conspirators hoped would help them avoid detection, but these small differences are not sufficient to distinguish their plot from more common per se prohibited practices. For instance, a conventional illegal agreement to allocate particular customers raises a strong chance that the customers themselves would become suspicious when the customers found that they could not buy the product from certain companies. See, e.g., United States v. Socony-Vacuum Oil Co., 310 U.S. 150, 60 S.Ct. 811, 84 L.Ed. 1129 (1940); United States v. Cooperative Theatres of Ohio, Inc., 845 F.2d 1367 (6th Cir.1988). The lysine cartel’s plan avoided this risk by allowing the customer to choose from whom to buy. Because the product was entirely fungible and priced equivalently, the source of the product did not matter to either consumers or suppliers, so the customers’ choices mattered little until the end of the year. Other types of market divisions, such as those based on geography, see, e.g., Palmer v. BRG of Georgia, Inc., 498 U.S. 46, 111 S.Ct. 401, 112 L.Ed.2d 349 (1990), or product lines, made little sense and were unnecessary for this particular industry. Similarly, a conventional illegal agreement to limit industry output, see, e.g., Westinghouse Elec. Corp. v. Gulf Oil Corp., 588 F.2d 221, 226 (7th Cir.1978), would be less desirable since the conspirators believed market demand was growing. So long as the lysine price remained high, it served the conspirators’ best interests to allow for market growth, and the agreement adequately accounted for divvying up that growth. Yet the fact that the lysine producers’ scheme did not fit precisely the characterization of a prototypical per se practice does not remove it from per se treatment. At bottom, the lysine cartel’s agreement was a conspiracy to limit the producers’ output and thereby raise prices. Functionally, an agreement to restrict output works in most cases to raises prices above a competitive level, see General Leaseways, Inc. v. National Truck Leasing Ass’n, 744 F.2d 588, 594 (7th Cir.1984), and for this reason, output restrictions have long been treated as per se violations. See Federal Trade Comm’n v. Superior Court Trial Lawyers Ass’n, 493 U.S. 411, 110 S.Ct. 768, 107 L.Ed.2d 851 (1990); National Collegiate Athletic Ass’n v. Board of Regents, 468 U.S. 85, 100, 104 S.Ct. 2948, 82 L.Ed.2d 70 (1984); Socony-Vacuum, 310 U.S. 150, 223, 60 S.Ct. 811, 84 L.Ed. 1129. A prototypical output restriction raises prices by reducing supply below demand. Here, the volume division among the lysine competitors restricted competition over those sales that would lower the commodity price. Putting aside for a moment the provision for market growth, the sales volume allocation divided the market’s expected demand among the five companies on an annual basis. Each agreed not to sell more than their allotment. If after eleven months of a given year, a producer had reached its allocation, the agreement would require it to turn down any additional sales, thereby limiting its output. If it did not stop sales, the agreement required the over-limit producer to purchase an amount equal to its excess from a producer who had fallen short. This would erase the effect of the surplus sales, returning the producer to a state as if it had limited its output. The agreement allowing for market growth did not change the essential nature of the sales volume allocation as a volume limitation; it merely allowed for per-producer volume limits in a growing market. An output limitation in a static market might give each producer a specific tonnage that it could sell. In a growing market, an output limitation could achieve the same end by giving each producer a specific tonnage plus a proportionate share of *668 the growth. Although no one could know exactly how much the market would grow until the final numbers were in, fairly good estimates could be made, and any errors could be corrected at the year-end accounting. This meant that, as in the static market scenario, a producer that reached its expected limit by the start of the eleventh month would be prohibited from making any additional sales. The volume agreement, then, limited competition over those sales that would lower the price, and as we said in General Leaseways, 744 F.2d at 594, such an agreement can be treated as a per se offense. The conspirators began discussing the volume limits at their first meeting in Mexico City when Wilson proposed the idea and explained its vital importance to the overall scheme to control the industry. Ajinomoto, ADM and the others began haggling over how much each would be allowed to produce. This argument continued until Andreas and Yamada met in Irvine, and Andreas threatened to flood the market unless Ajinomoto agreed to the volume limits. The conspirators left this meeting with an agreement that Ajinomoto would sell 84,000 tons of lysine and ADM would sell 67,000 tons, with adjustments for expected growth in the market. This agreement constituted an output limitation, which long has been condemned as a per se violation of the Sherman Act. Therefore, the jury instruction correctly advised the jurors of the required elements of a § 1 violation. Although output limitations have been treated under the per se rule, the Supreme Court has recognized special circumstances when horizontal agreements on production could be pro-competitive and therefore treated under rule of reason analysis. See NCAA, 468 U.S. at 117, 104 S.Ct. 2948; Broadcast Music, 441 U.S. at 19, 99 S.Ct. 1551. In these case, output limitations have been shown to be potentially pro-competitive because of the unique nature of the product involved, and therefore the cases merited rule of reason treatment. In NCAA, the output restriction addressed declining fan attendance caused by widespread television coverage of the athletic contests. Without some restriction on television coverage, the schools feared they would lose too much ticket-based revenue to continue holding games at all. Here, the district court found nothing in the record that rose to the level of the special circumstances in NCAA and Broadcast Music to warrant departure from per se treatment. Nothing suggests that a market allocation was necessary to maintain a competitive industry. In contrast to NCAA, where each school’s athletic program relied on the continued existence of competing schools to stage intercollegiate games, each lysine competitor could have continued selling its product without the others. While market demand might not support the full production of five companies at a profitable price, this fact does not distinguish lysine from many other markets. ADM’s entrance into the market may have resulted in oversupply and lower prices for consumers, but this does not grant a license to violate the antitrust laws. D. Intent Requirement Andreas and Wilson next appeal the district court’s refusal to give a requested instruction highlighting their defense theory on intent. The defendants argued at trial that whenever they seemed to be agreeing and conspiring with their competitors to violate the antitrust laws, they were actually playing a clever game of deception. By pretending to agree, they sought to put the Asian companies at a disadvantage so that they would share information and fall into a false sense of security, while ADM aggressively pursued new customers. Their proposed intent instruction would have advised the jury that an agreement does not exist if “one party did not intend to abide by the agreement.” We review de novo a district court’s deci *669 sion to give or not to give a jury instruction, see United States v. Brack, 188 F.3d 748, 761 (7th Cir.1999), but review the language of an instruction with great deference, upholding instructions that “are accurate statements of the law and which are supported by the record.” United States v. Vang, 128 F.3d 1065, 1069 (7th Cir.1997) (quoting Doe v. Johnson, 52 F.3d 1448, 1456 (7th Cir.1995)). We agree that a defendant’s subjective intent is a required element of a criminal antitrust violation, see United States v. United States Gypsum Co., 438 U.S. 422, 434-36, 98 S.Ct. 2864, 57 L.Ed.2d 854 (1978), and that a defendant who pretended to agree but did not intend to honor the agreement could not be convicted of a crime. See United States v. Bestway Disposal Corp., 724 F.Supp. 62, 67 (S.D.N.Y.1988). However, we reject the defendants’ claim of error for two reasons. First, the defendants’ theory was not supported by any evidence in the record. A defense jury instruction must be given only if “the instruction reflects a theory that is supported by the evidence.” United States v. Fawley, 137 F.3d 458, 468 (7th Cir.1998) (citation omitted). Andreas and Wilson presented no evidence, nor did any emerge during the government’s case in chief, that they never intended to abide by the agreements. In fact, all evidence showed they fully intended to abide by the agreement. Some of the witnesses testified to distrust among the conspirators, but the evidence showed a lack of trust in their co-conspirators to abide by the agreement, not a lack of intent that they themselves would abide by it. The conspirators actually instituted verification measures to force each other to abide by the terms of their agreement and eliminate the potential incentive for themselves and each other to cheat. ADM, through Wilson and Whitacre, proposed these verification measures, belying any reasonable possibility that they intended to cheat. Second, the jury instructions as given adequately covered this possible defense theory. A defense jury instruction must be given only if “the instruction reflects a theory which is not already part of the charge.” Id. The district court instructed the jury: [Y]ou must determine whether the evidence shows beyond a reasonable doubt that the defendant knowingly and intentionally became a member of the charged conspiracy to fix prices and allocate sales volumes. “Knowingly” means that the defendant realized what he was doing and was aware of the nature of his conduct and did not act through ignorance, mistake, or accident. In order to find that the defendant acted knowingly, you must find that he voluntarily and intentionally became a member of the conspiracy charged in the indictment, knowing of its goal and intending to help accomplish it. A supposed conspirator who only pretended to agree to abide by an agreement would not “know[ ] of its goal and intend [ ] to help accomplish it.” If the jury had a reasonable doubt whether Wilson, Whit-acre and Andreas intended to abide by the agreement, this instruction would prevent the jury from convicting them. The defendants sought an instruction that explained their theory in much more argumentative detail, but the court was under no obligation to render it. See Brack, 188 F.3d at 761; United States v. Given, 164 F.3d 389, 394 (7th Cir.1999). U.S. Gypsum requires reversal when the instruction allows conviction on an incorrect theory of the law. 438 U.S. at 446, 98 S.Ct. 2864. For example, the district court in U.S. Gypsum gave an instruction that allowed the jury to convict the defendant entirely on an anticompetitive “effects” theory, which did not require a finding of criminal intent at all. Id. at 434-36, 98 S.Ct. 2864. The Supreme Court reversed because the “effects” instruction did not adequately reflect the statute and held that criminal intent required both an *670 intent to enter the agreement and an intent to effectuate the goal of the conspiracy. Id. In contrast, the district court’s instruction in this case that the defendants must have intended to “help accomplish” the known goal of the conspiracy is entirely consistent with the reasoning and holding of U.S. Gypsum. E. Sufficiency of the Evidence Andreas next asks us to overturn the jury’s verdict because there was insufficient evidence to support it. We will overturn a jury verdict “only if the record contains no evidence, regardless of how it is weighed, from which the jury could find guilt beyond a reasonable doubt.” United States v. Agostino, 132 F.3d 1183, 1192 (7th Cir.1997). We view “the evidence in the light most favorable to the prosecution,” and decide whether “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Agostino, 132 F.3d at 1192 (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)). Andreas attended three meetings of the conspirators and served a vital role in the successful efforts to reach an agreement to implement the price-fixing and volume deals. The jury viewed videotape recordings of Andreas’ meetings with the admitted co-conspirators and heard Andre-as threaten to flood the market if they did not agree. Evidence at trial indicated that the details of the plan were arranged by upper management, but that all sides recognized that their corporate superiors remained in control of the deal and would be called in to settle any unresolved disputes. This in fact happened when the conspirators could not reach an agreement on output; Andreas and Yamada were called in as the deal closers, and they succeeded in that role. At the Irvine meeting, Andreas expressed his concerns about the management of the Asian firms in regard to whether they would be able to carry out their part of the price-fixing scheme. A jury rationally could understand Andreas’ words at this meeting only to indicate his knowledge of, participation in and control of the entire plot. Furthermore, Andreas directly supervised Wilson and Whitacre. They reported the results of the meetings to him, and he on more than one occasion coached them on what to say at an upcoming meeting. Evidence showed Andreas knew that the conspirators were working on a price deal and a volume deal and gave Whitacre orders on how to set up the volume agreement. In an April 1993 conversation heard by the jury, Andreas called Whit-acre into his office before a meeting of the cartel and told Whitacre to pretend he was Yamada. Andreas then rehearsed for Whitacre what he would say to Yamada: “We go over there and say to 'em like we’ve thought it over carefully. Uhm, we know that you feel that we shouldn’t be at the same size as you at this stage ... we’ve decided that the best thing for the industry would be that you and I decide that we will stay the same size.” The FBI also caught Andreas on tape threatening the Asian companies and insisting on how he thought the volume production should be divided. It would require a great leap of imagination to believe that Andreas knew nothing of the illegal deals on price and output carried out by his direct subordinates, yet happened to play a key role in Irvine and at subsequent meetings to facilitate those deals. The jury apparently, and reasonably, considered insincere and facetious Andreas’ occasional statements that ADM would not do anything illegal at a time when he was actively playing a vital role in achieving a criminal purpose. In fact, the jury heard the conspirators laughing when Wilson reported Andreas’ “we don’t make deals” statement. None of the conspirators believed this, and the jury certainly was not required to believe it either. Based on the overwhelming evidence presented at trial, we cannot conclude that the jury acted irrationally in convicting Andre-as of conspiring to restrain trade. *671 F. Closing Arguments The government’s closing argument twice prompted objections related to improper comments, requiring the trial court to assess the damage done to the fairness of the proceedings. After a thorough analysis, the court refused to declare a mistrial, admonished the government and instructed the jury appropriately. The defendants appeal the denial of a mistrial on two grounds. 1. Vouching The defendants contend that lead prosecutor Scott Lassar impermissibly vouched for the strength of the government’s case. In closing argument, Lassar characterized the case against the three defendants as “one of the most compelling and powerful that has ever been presented in an American courtroom.” The trial court agreed with the defense, but declined to declare a mistrial after finding the comment to be harmless. We review for abuse of discretion a trial court’s refusal to grant a mistrial. See United States v. Morgan, 113 F.3d 85, 89 (7th Cir.1997). In cases of prosecutorial misconduct during argument, we determine first whether the prosecutor’s comment considered by itself was improper and then examine the entire record to see if the improper comment deprived the defendants of a fair trial. See United States v. Severson, 3 F.3d 1005, 1014 (7th Cir.1993). As the Supreme Court has repeatedly said, “it is not enough that the prosecutors’ remarks were undesirable or even universally condemned ... The relevant question is whether the prosecutors’ comments ‘so infected the trial with unfairness as to make the resulting conviction a denial of due process.’ ” Darden v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (internal citations omitted). Vouching occurs when the prosecutor interjects his personal opinion about the credibility of a witness or the strength of the evidence as a whole. Rodriguez v. Scillia, 193 F.3d 913, 919 (7th Cir.1999); United States v. Alexander, 163 F.3d 426, 429 (7th Cir.1998). In such a situation, vouching introduces credibility evidence that would have been inadmissible during trial. However, a prosecutor may draw reasonable inferences from the evidence adduced at trial, even going so far as to call a defendant a liar if the record supports that accusation. See United States v. Goodapple, 958 F.2d 1402, 1409-10 (7th Cir.1992); see also Morgan, 113 F.3d at 89 (holding that a prosecutor calling a witness an “honest citizen” was a fair inference from the record). Looking at the comment in isolation, two reasonable interpretations of Lassar’s comments emerge. 7 The “most compelling and powerful” case remark came amid Lassar’s discussion of the type of evidence used in the case, evidence that arguably caught the defendants red-handed. Most criminal cases do not feature the defendants committing the crime on camera, so the prominent use of that type of evidence could be considered the “most compelling and powerful” type of evidence used in a court in America. In fact, Lassar told the jury “the most powerful evidence you could ever have would be a videotape of the defendant committing the crime. You can’t get better evidence than that.” Lassar’s comment that this was among the “most compelling” cases, could fairly have been interpreted as meaning the case featured among the “most compelling” types of evidence. *672 Alternatively, a jury could interpret Lassar’s remarks as expressing his personal opinion about the strength of the evidence compared to the many other cases prosecuted in America, the vast majority of which result in convictions. The influence of his opinion could not help but be bolstered by his status as a seasoned prosecutor and the newly appointed United States Attorney for the Northern District of Illinois. By this comment, Lassar did not merely suggest to the jury what he thought they might find when examining the evidence, a type of comment that we have approved although it steps close to the line of impermissible argument. See Whitaker, 127 F.3d at 606-07. He introduced a comparison that invited the jury to rely on his experience as a prosecutor while preventing any real response from the defense. Where there are two reasonable interpretations of a prosecutor’s conduct—one proper and one improper—we cannot say that the trial court abused its discretion in finding it to be improper. See United States v. Cheska, 202 F.3d 947, 950 (7th Cir.2000) (holding that discretion is abused only when no reasonable person could agree with the trial court’s assessment) (citations omitted). Here, the trial court’s judgment that Lassar improperly vouchéd for the government’s case was reasonable and therefore not an abuse of discretion. We next look to see whether the remark deprived the defendants of a fair proceeding when considered in the context of the whole trial. See Alexander, 163 F.3d at 429-30; United States v. Reed, 2 F.3d 1441, 1450 (7th Cir.1993). To guide us in this decision, we consider five factors: (1) the nature and seriousness of the statement; (2) whether defense counsel invited it; (3) whether the district court sufficiently instructed the jury to disregard it; (4) whether defense counsel had the opportunity to respond to the improper statement; and (5) whether the weight of the evidence was against the defendant. See Rodriguez v. Peters, 63 F.3d 546, 558 (7th Cir.1995); United States v. Johnson-Dix, 54 F.3d 1295, 1304 (7th Cir.1995). First, we consider the prosecution’s comment on the weight of the evidence to be less damaging than other forms of impermissible argument. Typically, in vouching situations, the prosecution has attempted to bolster a witness’s credibility by introducing facts that were not in evidence. See Cheska, 202 F.3d at 950-52 (holding that a prosecutor’s comment that a witness’s cooperation had “convicted 23 other people” impermissibly bolstered witness’s credibility through evidence outside the record); Johnson-Dix, 54 F.3d at 1304 (finding improper but harmless the prosecutor’s comment that a federal agent would risk his career by committing perjury). Lassar’s comment did not serve to bolster anyone’s credibility and so did not invade the province of the jury to assess credibility or determine facts. Essentially, the prosecution appealed to the jury’s supposed belief that the government only prosecutes strong eases and this was, in Lassar’s opinion, one of the strongest. Although improper, this generalized comment cannot be considered nearly as damaging as introducing a fact that bolsters a particular witness’s credibility. Cf. Johnson-Dix, 54 F.3d at 1304 (holding that prosecutor’s remark vouching for credibility of government agent was “certainly improper”). Furthermore, the prosecution made the comment only once, which considering the length of the trial and the closing argument, could not have weighed that heavily in the minds of the jury. See Alexander, 163 F.3d at 429 (considering frequency of improper statements as an element of its seriousness). Defense counsel could not have invited Lassar’s comment and could not counter it directly during their own closings, so those two factors weigh in favor of reversal. However, the two remaining factors strongly support the district court’s decision. The court instructed the jury before the completion of closing arguments with the following: *673 During the course of Mr. Lassar’s closing argument he made reference to the strength of the evidence in this case as compared to other cases. Such references to other cases are totally irrelevant. So I would instruct you that you should absolutely disregard any statements or references comparing this case to any other case, and you should decide this case solely on the evidence presented in this case without regard to any comparison to any other case. We presume juries can and do follow curative instructions. See United States v. Mazzone, 782 F.2d 757, 764 (7th Cir.1986) (presuming jury followed curative instruction given after prosecutor’s improper statements in closing). Considering the largely irrelevant implication of Lassar’s comparison, we believe a jury could easily follow this instruction. Finally, the Court has reviewed all of the evidence against Andreas and Wilson and can fairly characterize it as overwhelming. Cf United States v. Owens, 145 F.3d 923, 928 (7th Cir.1998); Johnson-Dix, 54 F.3d at 1305 (holding that weight of the evidence indicates that jury verdict cannot be attributed solely to prosecutor’s closing comment that FBI agent would not risk his career through perjury). In Owens, 145 F.3d at 928, the prosecutor told the jury that he, the prosecutor, told the witness “if you lie to me, your deal is off.” Without deciding whether the comment in isolation was improper, we held that “in light of the overwhelming evidence against” the defendant, the remark did not deprive him of a fair trial. The evidence at trial included the defendant “caught on both audio and video tape” in a drug transaction that officers surveilled. Id. at 925. The taping had been accomplished because a man arrested on a drug charge had agreed to cooperate as an undercover informant and wear a wire during the sting operation. Three officers and the informant testified at trial against the defendant. In our view, this amounted to “overwhelming evidence,” which combined with a curative instruction, rendered the trial fair despite the improper vouching. Id. at 928. After reviewing the entire record, including several videotapes and audiotapes, we find the evidence against Wilson and Andreas to be much stronger than that proffered in Owens. Lassar’s missteps came at the end of a two-month trial in which the jury heard directly from cocon-spirators, heard the defendants’ voices and saw their faces on video making illegal deals. It would challenge credibility to say that a prosecutor’s rather nugatory comment assessing the evidence at trial rendered the trial fundamentally unfair. Therefore, we cannot say that Judge Manning abused her discretion in denying the motion for mistrial. 2. Fifth Amendment During closing, Lassar also discussed the defendants’ interviews with the FBI in June 1995 at which they denied any knowledge of price fixing or sales volume allocation agreements. At the time of those interviews, the defendants did not know of the extensive tape-recorded evidence of their conversations detailing both agreements. That evidence severely undercut a “no knowledge” defense, and at trial, the defendants did not deny knowledge. Rather, defense counsel argued that the agreements were pro-competitive or that they were part of a clever deception. These theories were directly inconsistent with the denials Andreas and Wilson offered in June 1995. Lassar suggested to the jury that they “ask [themselves] why didn’t we hear those defenses from Mr. Wilson and Mr. Andreas on June 27,1995? That was their opportunity if they had a defense. They were confronted. That was their opportunity to give all these defenses.” He then implied that defense counsel would fabricate new explanations for their clients’ behavior that their clients did not offer a year earlier and that the new explanations were lies. The defense objected on the *674 ground that Lassar’s statements punished the defendants for invoking their Fifth Amendment right not to testify. The district court agreed, finding Lassar’s closing to be improper under the standard announced in United States v. Cotnam, 88 F.3d 487, 497 (7th Cir.1996). Judge Manning strongly rebuked the government for this error, but ultimately found the remarks to be harmless. Cf. id. at 499-500 (applying harmless error review); Rodriguez v. Peters, 63 F.3d at 562 (holding that defendant suffered “no prejudice” from allegedly improper comment on defendant’s refusal to testify). She instructed the jury to disregard the improper portions of Las-sar’s closing and not to penalize the defendants for remaining silent. The government contends that Lassar referred only to the “lies” that Andreas and Wilson told when questioned by the FBI in June 1995, and in fact he prefaced this section of his argument by saying, “There’s one more event to talk about, and that event occurred on June [27], 8 1995.” The district court, however, rejected this explanation. In Judge Manning’s view, Lassar’s comments were not narrowly confined to an attack on defendants’ inconsistent statements, but reached well into their refusal to testify. The right against self-incrimination is violated when (1) the prosecutors manifestly intended to refer to the defendant’s silence, or' (2) the remark was of such a character that the jury would “naturally and necessarily” take it to be a comment on the defendant’s silence. Rodriguez v. Peters, 63 F.3d at 561 (citations omitted.) Once we determine that a violation occurred, we apply harmless error review to decide whether the remark prejudiced the defendant’s case. See id. As an initial point, the defense emphasizes the distinction between error that is “harmless” and error that is “harmless beyond a reasonable doubt.” The defense believes Judge Manning applied a lower standard of harmless error review to the purported Fifth Amendment violation, and because she found the error to be “just barely” harmless, it follows that under the higher standard, the error could not be harmless. As we acknowledged in Cotnam, 88 F.3d at 498 n. 11, this Court has not always clearly articulated the different analyses to be applied to prosecutorial misconduct under the Fifth Amendment compared to that applied under a general due process claim. Rodriguez v. Peters, for example, seemed to apply both the five-factor due process test to a Fifth Amendment violation, 63 F.3d at 557, as well as the two-part Fifth Amendment test. 63 F.3d at 561. Ultimately, we found “no prejudice” stemming from the Fifth Amendment error in Rodriguez v. Peters, 63 F.3d at 562, a holding that does not reveal whether in that case we considered the appropriate standard to be harmless or harmless beyond a reasonable doubt, since “no prejudice” would be harmless under either standard. Judge Manning addressed the improper prosecutorial comment claims together, see United States v. Andreas, 23 F.Supp.2d 855, 862 (N.D.Ill.1998), rather than separately. As such, she applied the five-factor test we use for due process challenges to both types of claims. See id. While this may not have been technically correct, Judge Manning did apply the highest standard of review — “harmless beyond a reasonable doubt” — to both sets of claims. See Andreas, 23 F.Supp.2d at 862 (citing Cotnam, 88 F.3d at 498) (“[T]he government bears the burden of proving beyond a reasonable doubt that the defendants would have been convicted absent the unconstitutional remarks.”). The district court conflated the tests for the two types of cases, but much more importantly, the court reviewed both the due process and Fifth Amendment- challenges under the “harmless beyond a reasonable doubt” standard. If this constituted error, it served only to overprotect the defendants’ *675 rights, not to underprotect them. 9 As such, we do not find that Judge Manning applied the wrong standard for harmless error and review her denial of a mistrial for abuse of discretion. As a first step in addressing the Fifth Amendment claim in this case, we do not believe that the government intended to draw attention to Andreas’ and Wilson’s silence at trial. We credit the government’s explanation, bolstered by the context of the remark, that it meant to point out the inconsistency between the statements made by Wilson and Andreas in June 1995 with the defense theories at trial. That leaves open the possibility that a jury would “naturally and necessarily” take the remarks to be a comment on the defendants’ silence at trial. While part of the comments innocently referred to the “lies” told in June 1995, the government stepped over the line when it directed the jury to “ask [yourselves] why didn’t we hear those defenses from Mr. Wilson and Mr. Andreas on June 27, 1995. That was their opportunity if they had a defense ... That was their opportunity to give all these defenses.” While unintended, these sentences “naturally and necessarily” imply guilt from the defendants’ silences; they indicate a requirement that innocent people must supply defenses, and in that way, the remarks violated the Fifth Amendment. Once a constitutional violation has been found, “the government can only prevail if it sustains the burden of proving beyond a reasonable doubt that the defendant would have been convicted absent the prosecutor’s unconstitutional remarks.” Cotnam, 88 F.3d at 500 (quoting United States ex rel. Burke v. Greer, 756 F.2d 1295, 1302 (7th Cir.1985)). Considering the overwhelming nature of the evidence, we agree with the district court that the error was entirely harmless. See, e.g., Chapman v. California, 386 U.S. 18, 22-24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967) (holding that trial court must determine whether Fifth Amendment violation was harmless beyond a reasonable doubt); Cotnam, 88 F.3d at 499-500; Rodriguez v. Peters, 63 F.3d at 562; United States v. Hubbard, 61 F.3d 1261, 1269 (7th Cir.1995); Williams v. Lane, 826 F.2d 654, 667 (7th Cir.1987) (applying harmless beyond a reasonable doubt standard to Fifth Amendment violation); United States v. Buege, 578 F.2d 187, 189 (7th Cir.1978) (same). To determine the extent of the harm from an improper remark, we must consider the context in which it was offered. See Hubbard, 61 F.3d at 1268. In Hubbard, the government objected to the introduction of a hearsay statement by saying, “That is hearsay ... Let Hubbard [the defendant] tell us.” Id. We found that comment to be less damaging than if it were made in a closing argument, but in viewing the context of the remark, we credited the government’s explanation that it meant only to refer to the hearsay problem, not to the defendant’s refusal to testify. Id. Considering the context of the remark, we found it to be harmless. Here also, the context shows the government sought to point out the inconsistency between the defendants’ prior statements and the current defense theories. The remarks immediately followed a discussion of the June 1995 raids and the defendants’ voluntary statements at that time. The jury may have drawn no more than that from Lassar’s remarks. Judge Manning properly instructed the jury to disregard any inference that the defendants should have testified at trial, and we presume juries follow proper instructions. See Rodriguez v. Peters, 63 F.3d at 562. This curative instruction undercuts the potential that the statements caused the jury to convict the defendants. *676 Finally, the evidence as a whole included statements from co-conspirators and tape-recorded conversations of both Andreas and Wilson that clearly showed they knew of and participated in the conspiracy to fix prices and restrain trade. There simply could be no doubt in the jurors’ minds after hearing overwhelming evidence of the defendants’ meetings with the cartel that they knowingly violated the Sherman Act. Assuming that the prosecution indirectly—although impermissibly—called to the jury’s attention the lack of a defense justification for their actions, these comments amounted to a few brief words in the midst of a two-month trial. To say that these brief comments resulted in the convictions would ignore the far more plausible conclusion that the overwhelming evidence of guilt led to the jury verdict. In that context, we find the error to be harmless. G. Sentencing The defendants and the government each appeal one issue related to sentencing. The first, whether “volume of commerce” includes all sales or some subset of all sales affected by the conspiracy, is a question of law, which we review de novo. See United States v. McClanahan, 136 F.3d 1146, 1149 (7th Cir.1998). However, once we determine the correct legal principle, we review deferentially the lower court’s findings of fact regarding the volume of commerce affected. See United States v. Hammick, 36 F.3d 594, 597-98 (7th Cir.1994) (holding that factual findings in sentencing context are reviewed for clear error). The second issue is whether the district court correctly denied a sentencing enhancement based on the defendants’ leadership roles in the conspiracy, a factual finding which we also review for clear error. See id. 1. Volume of Commerce Enhancement The district court enhanced An-dreas’ and Wilson’s sentences based on a volume of commerce affected by the conspiracy greater than $100 million. See U.S. Sentencing Guidelines Manual § 2R1.1(b)(2)(G). After an evidentiary hearing, at which both sides presented evidence and argument regarding the amount of sales affected by the conspiracy, the court accepted the report of the U.S. Probation Office that the volume of commerce amounted to $168 million. The court, relying in part on the Sixth Circuit’s opinion in United States v. Hayter Oil Co., 51 F.3d 1265 (6th Cir.1995), rejected the defendants’ argument that “affected commerce” means only that quantity sold at the targeted price and determined that “affected commerce” includes all sales made within the scope of the conspiracy, which amounted conservatively to $168 million. Wilson and Andreas contend that “affected commerce” means only sales that reflect a successful price agreement, meaning sales at or above the target price. This is clearly wrong. When construing the Guidelines, we look first to the plain language, and where that is unambiguous we need look no further. This is one of those cases. Section 2R1.1 directs the court to increase the base offense level by seven if the “volume of commerce attributable to the defendant” was more than $100 million. It then explains that “the volume of commerce attributable to an individual participant in a conspiracy is the volume of commerce done by him or his principal in goods or services that were affected by the violation.” U.S.S.G. § 2R1.1. The plain language of this section makes clear that the volume of commerce includes only those sales “affected by the violation,” rather than all sales. However, “affected” is a very broad term whose breadth does not support the unduly constricted meaning given to it by the defendants, ie., only those sales made at the price set by the conspirators. In this view, had the price been 70-cents per pound and the conspirators agreed to raise it to $1.05, none of the subsequent sales between $.70 and $1.04 would be affected by the conspiracy. This *677 interpretation is ridiculous. To support this view, the defendants cite a district court case from New York. See United States v. SEW Metals & Alloys, 4 F.Supp.2d 166, 172 (W.D.N.Y.1997). The Second Circuit, agreeing that this argument is plainly wrong, reversed SEW Metals after Andreas and Wilson filed their initial briefs. See United States v. SKW Metals & Alloys, Inc., 195 F.3d 83, 91 (2d Cir.1999) (“SKW Metals II”). In their reply, the defendants now argue that, consistent with SEW Metals II, no sales were affected by the conspiracy because the conspiracy was entirely, or almost entirely, ineffective. In Hayter Oil, the court held that “affected” meant all sales “during the period of the conspiracy, without regard to whether individual sales were made at the target price.” 51 F.3d at 1273. Hayter Oil involved a simple conspiracy by gasoline station owners in a Tennessee town to set prices at a certain above-market level. Because of competition from non-conspirators and cheating by conspirators, the price did not always hold at the agreed level, and frequent meetings of the conspirators were required to reestablish the price. The district court sentenced the defendants based on sales only at the agreed level and not on all sales affected by the conspiracy. See id. at 1272. The Sixth Circuit reversed and held that the plain language of the Guidelines allowed for a much broader definition of “affected,” including “all commerce that was influenced, directly or indirectly, by the price-fixing conspiracy.” Id. at 1273. That would include sales made above the market price, even though below the target price. Ultimately, the court held that standard may have encompassed all sales of gasoline, assuming that all sales were a penny or more above the market price. To that extent, we would agree with the outcome of Hayter Oil to include all sales during the time period of the conspiracy, but would disagree to the extent that it forecloses the possibility that some sales might have been unaffected even though occurring during the conspiracy. The Sixth Circuit reasoned that a broad definition of affected would encompass “even sales lost due to, in accordance with the normal economic principles of supply and demand, the decreased demand that accompanies higher prices.” Id. We agree in principle with this focus on sales broadly affected by the changed dynamics of a market influenced by illegal restraints. Economic decisions, such as pricing and production, depend on the interplay of a host of variables, none of which can act “independently” in any meaningful sense of that word. In most cases, an agreement to raise prices necessarily affects demand, which will affect output, and the burden to show that some sales were “unaffected” is a difficult one. However, like the Second Circuit, we disagree with the Hayter Oil holding in so far as it implies that all sales during the time period of the price-fixing conspiracy should be counted for purposes of § 2R1.1 simply because they occurred during the period of the conspiracy. While Hayter Oil reflects a possible and not unreasonable reading of the Guidelines, it is not the most natural one. Section 2R1.1 counts “the volume of commerce done by him or his principal in goods or services that were affected by the violation.” Recognizing that many companies have multiple product lines that compete in separate markets, this language may simply instruct the court to count only the commerce in the product line that was the subject of the illegal agreement. “Affected” might mean all sales of lysine, which was a product line within the scope of the agreement, but not corn oil, which was not. That reading would permit counting all lysine sales during the time period of the conspiracy and even those sales at or below the market price. Although a permissible reading, we do not adopt Hayter Oil because the purpose of the § 2R1.1 enhancement is to gauge the harm inflicted by the illegal agree *678 ment. See U.S.S.G. § 2R1.1 background para. 4 (“Tying the offense level to the scale or scope of the offense is important in order to ensure that the sanction is in fact punitive ... [but] damages are difficult and time consuming to establish. The volume of commerce is an acceptable and more readily measurable substitute [for determining the scale of the offense].”). Theoretically, sales that were entirely unaffected did not harm consumers and therefore should not be counted for sentencing because they would not reflect the scale or scope of the offense. In SKW Metals II, the Second Circuit agreed with Hayter Oil in reversing the trial court’s judgment that affected sales meant only sales at or above the target price in a price-fixing conspiracy. See 195 F.3d at 90. The court also adopted a broad reading of “affected” in line with the realities of the economic marketplace in which few things are ever truly “unaffected” by other market forces. See id. The court reasoned that “[s]ales can be ‘affected’ by a conspiracy when the conspiracy merely acts upon or influences negotiations, sale prices, the volume of goods sold, or other transactional terms. While a price-fixing conspiracy is operating ... it is reasonable to conclude that all sales made by defendants during that period are ‘affected.’ ” Id. The court refused to adopt the government’s categorical position that all sales be counted regardless of whether they were “affected” by the conspiracy. Id. at 91-92. An action may affect commerce in many ways other than achieving a predetermined price level, and we will not frustrate the goal of this provision by grafting some narrow meaning onto the ordinary use of the word “affected.” The Guidelines provision serves to set the punishment based on a measurement of the harm done by the crime, and the drafters chose “volume of commerce” as a proxy for determining that harm. Conspiracies to limit output have broad-ranging effects on all decisions made by the former competitors from the moment of their inception. Decisions to expand production, decrease price, institute promotions or compete for certain customers all are affected by an agreement to limit production. See SKW Metals II, 195 F.3d at 90. An agreement to raise prices, similarly, affects the conspirators’ decisions related to production and consumers’ decisions related to demand. Therefore, the presumption must be that all sales during the period of the conspiracy have been affected by the illegal agreement, since few if any factors in the world of economics can be held in strict isolation. Still, it is conceivable that under a price agreement, sales made before new price schedules are issued or new quotes given to potential customers may be wholly unaffected, or that some subsequent sales might be sold at the actual market price. See, e.g., id. at 93 (Newman, J., concurring) (positing example of “rare instance” where a supplier may quote a bargain price for his brother-in-law without regard to the agreed price). 10 We agree with the Second Circuit that these odd sales completely unaffected by the conspiracy should not be counted for sentencing purposes. See id. at 92. The burden of proof under the Guidelines requires only that the government establish relevant conduct by a preponderance of the evidence, see United States v. Kroledge, 201 F.3d 900, 908-09 (7th Cir.2000), a standard that supports a rebutta-ble presumption that all sales during the conspiracy were affected by the illegal agreement. See SKW Metals II, 195 F.3d at 93-94. (Newman, J., concurring) (requiring defendant prove that one or more sales were not affected by the conspiracy). *679 Courts frequently require defendants to prove affirmative defenses by a preponderance of the evidence, see, e.g., United States v. Hunte, 196 F.3d 687, 693 (7th Cir.1999) (requiring defendant to prove basis for a downward departure by a preponderance of the evidence); United States v. Wicks, 132 F.3d 383, 389 (7th Cir.1997) (holding that a defendant must prove an affirmative defense at sentencing stage by a preponderance of evidence). Evidence of the “rare circumstance” of a completely unaffected transaction “would be peculiarly within the knowledge of the defendant,” SKW Metals II, 195 F.3d at 93, and the defendant should bear the burden of proving that rare circumstance by a preponderance of the evidence. Because horizontal agreements to restrain trade, whether by price or output restrictions, naturally affect all sales during the period that the conspiracy operates, the trial court correctly determined the volume of commerce based on all sales within the scope of the conspiracy. Andre-as and Wilson presented evidence at sentencing that certain sales were not affected, and the district court considered that proof. The lysine conspiracy restrained trade by allocating each market participant’s output and fixing prices. Together these two methods served to raise the price beginning in the summer of 1992 and lasting for nearly three years. The price fluctuated, and cartel members cheated each other when they could, but the evidence soundly supports a volume of commerce influenced by the conspiracy of at least $168 million. Based on the evidence at trial, the court was entitled to find that the conspiracy was indeed successful at affecting more than $100 million in commerce. 2. Leadership Roles The government requested that Andreas’ and Wilson’s sentences be increased based on their leadership roles in the conspiracy. See U.S.S.G. § 3B1.1. The district court denied the enhancement, finding that neither man was more culpable than his co-conspirators. We review for clear error the district court’s application of a sentencing enhancement under § 3B1.1. See United States v. Golden, 954 F.2d 1413, 1418 (7th Cir.1992). Section 3B1.1 enhances a defendant’s sentence based on the defendant’s role in the offense. An organizer or leader of a criminal activity that “involved five or more participants or was otherwise extensive” receives a four-level increase, while a manager or supervisor earns a three-level increase. See U.S.S.G. § 3Bl.l(a), (b). Section 3B1.1 requires that the district court find that the “defendant organized or supervised a criminal activity involving four other participants.” United States v. Kamoga, 177 F.3d 617, 621 (7th Cir.1999). The district court found that the conspiracy satisfied the size requirements of § 3B1.1, but that Andreas and Wilson did not control the requisite number of participants to merit the increase. See United States v. Mustread, 42 F.3d 1097, 1103 (7th Cir.1994). After reviewing the record, we hold that the district court erred in making this finding of fact. Evidence submitted at trial and during the sentencing phase indicated that at least three sales executives — Marty Allison, Alfred Jansen and John Ashley — in addition to Andreas, Wilson and Whitacre, helped to implement the pricing and volume allocation schemes. Even discounting Whitacre, who was a government agent during part of the conspiracy and therefore cannot be counted as a participant for that part, see U.S.S.G. § 3B1.1 application note 1, the crime still involved the requisite number of participants for an enhancement. Furthermore, the court should have considered Andreas’ control over the foreign co-conspirators at the Irvine meeting as counting toward the minimum number of participants needed for the § 3B1.1 enhancement. A co-conspirator who used his power to guide or direct other eonspir- *680 ators qualifies as an organizer even though his control was not absolute. See Kamoga, 177 F.3d at 621. The need to negotiate some details of the conspiracy with the cartel members also does not strip a defendant of the organizer role. See United States v. Evans, 92 F.3d 540, 545 (7th Cir.1996) (recognizing possibility of collective leadership fulfilling § 3B1.1); United States v. Barnes, 993 F.2d 680, 685 (9th Cir.1993). The district court erred in focusing on the conspiracy as a union of equals, which it was only in part. Neither the Guidelines nor our cases require the “participants” to be mere drones working for their queen. In Evans, 92 F.3d at 545, we recognized the “concept of collective leadership,” which is the case here. Evidence from the Irvine meeting showed that An-dreas used coercive power to force the foreign competitors to accept ADM’s leadership role in the cartel, demonstrating his control over the cartel and its participants. When the cartel had internal squabbles and disputes, Andreas was called in to resolve them. ADM’s market power gave Andreas the ability to coerce the other cartel members into submission, and the evidence is clear that he used that power to lead the conspiracy. The fact that control over co-conspirators was not absolute and that he had to negotiate does not negate the conclusion that Andreas was the ultimate leader of the price-fixing cabal. The evidence at trial conclusively showed that Wilson engaged in the conspiracy by running the meetings and speaking for ADM. He appears on countless tapes proposing ways to run the cartel and ways to make it more efficient. His entire purpose in attending lysine meetings as the head of the corn processing division was to bring his management skills to the cartel. Neither he nor Andre-as can claim in any meaningful way to be merely equally culpable with the other conspirators since it was ADM that suggested the scheme, planned it and carried it out. Therefore, we find the district court’s decision to deny the four- and three-level enhancements for Andreas and Wilson, respectively, to be clearly erroneous. III. CONCLUSION For the reasons stated above, the convictions of Andreas and Wilson are Affirmed and the cases are Remanded to the district court for resentencing in accordance with this opinion. Footnotes [1] At his insistence, Whitacre was tried in ab-sentia from the prison where he is serving a 108-month sentence for embezzlement. He was represented vigorously by counsel at trial and aided his defense through telephone communication with his lawyer. Kazutoshi Ya-ntada, an employee of Ajinomoto Co. of Japan, was the fourth defendant named in the indictment. He has not been tried and remains a fugitive. [2] Randall was not indicted. [3] Until 1990, Cox worked for a company that produced citric acid. In 1990, ADM bought the citric-acid operation, and Cox joined ADM at that time. [4] Kastigar v. United States, 406 U.S. 441, 92 S.Ct. 1653, 32 L.Ed.2d 212 (1972), and its progeny, including United States v. Palumbo, 897 F.2d 245 (7th Cir.1990), deal with the use of evidence against defendants obtained from those defendants pursuant to an immunity agreement. Here, the defendants who seek to benefit from the immunity agreement have not testified nor have they ever entered into any agreement. They cannot claim to have been induced into testifying against themselves and can point to no violation of the Fifth Amendment, as in Kastigar and Palum-bo. [5] Federal courts look to general principles of contract law to interpret a plea or immunity agreement. See United States v. Given, 164 F.3d 389, 395-96 (7th Cir.1999). The parties focus on Illinois law, which fairly typifies the general law of contracts and is persuasive in this instance. [6] The analysis and resolution of this issue overlaps with the question of whether, assuming standing, the terms of the agreement actually immunized Andreas and Wilson. We also would answer that question in the negative. [7] The government’s argument that the prefatory “I think that you're going to see” saves an otherwise impermissible statement is unavailing. This court has allowed a prosecutor to begin with phrases such as "I believe that you will find” because it only suggests what the government thinks the evidence adduced at trial means. See United States v. Whitaker, 127 F.3d 595, 606-07 (7th Cir.1997). "I believe” and "I think” are but patterns of speech that can be innocuous. Such phrases, however, do not automatically immunize any statement that follows. [8] Lassar misspoke in closing and used the wrong date. [9] Similarly, in misstating the two-part test for a Fifth Amendment violation as a conjunctive rather than disjunctive, the district court again overprotected the defendants' rights, which by definition cannot prejudice the defendant. [10] We acknowledge this example as one of the rare instances when a price fixer would forgo anticompetitive profits, but it also illustrates how rare the occasion when a price fixer able to charge higher prices would act in an economically irrational way and sell below the inflated market price.