Full opinion text
COFFEY, Circuit Judge. This case presents the consolidated appeals of eight Defendants who were charged with conspiracy to distribute cocaine and marijuana and were convicted of a variety of federal narcotics offenses. Defendants on appeal raise challenges to their convictions and sentences. We affirm. I. Factual Background The conspiracy to distribute cocaine and marijuana centered around Defendant-Appellant Mukglis Toma (Toma), who was a wholesaler of cocaine and marijuana in the Chicago area. Toma purchased quantities of cocaine and marijuana from suppliers, and resold it to street dealers, who in turn sold it to their clients. Toma’s cocaine suppliers included Defendants-Appellants Ramiro Magana (Magana), Santiago Rabón (Rabón), Jose Pinto (Pinto), Raul Aguilera (Aguilera), and Wilson Iturralde (Iturralde). Toma was also supplied cocaine by Ramon Valencia (Valencia), who worked with Magana but was not named in the superseding indictment, and Rodolfo Garcia (Garcia), who was indicted, but ultimately agreed to testify for the government in exchange for entering a plea of guilty to reduced charges. Garcia supplied Toma with marijuana as well. A number of individuals assisted Toma or were supervised by him in the furtherance of the drug distribution scheme. All of these individuals-George Ishu (Ishu), Doris Ress (Ress), Ammanuel Youkhanna (Youkhanna), and Wesam Youmaran (Youmaran)—were named in either the original or superseding indictment, but they were not listed as Defendants in the instant case. Toma resold the cocaine and marijuana to Defendants-Appellants Robert Ameneiro (Ameneiro) and Ismael Rosa (Rosa). Toma also sold cocaine and marijuana to Miguel Rivera (Rivera), Janice King (King), Ishu, Youkhanna, and Herman “Yum” Matthews (Matthews). These latter five individuals were indicted, but were not named in the instant case. Finally, Toma sold cocaine to Stuart Glaser (Glaser), who, for reasons we will discuss, was not ultimately indicted in this case. On July 21, 1993, after purchasing a quarter-kilogram of cocaine from Toma at Toma’s mother’s residence on the northwest side of Chicago, Glaser departed from the residence in his Jeep. Unbeknownst to Glaser, the residence was under surveillance by officers of the Chicago Police Department assigned to work on a special FBI narcotics task force. As Glaser left the house in his Jeep, the officers kept him under surveillance, until Glaser sped away down an alley, where the officers followed and observed Glaser throwing out his recent cocaine purchase. The officers in pursuit retrieved the cocaine, and apprehended Glaser later that day. After his arrest, Glaser agreed to assist the government and began recording the phone calls he made to Toma. During these taped conversations Glaser stated that he would continue to purchase cocaine from Toma. At the suggestion of FBI agents, Glaser also supplied Toma with a cellular phone furnished by the FBI. Glaser represented to Toma that, because the phone was “digital,” it was untraceable and Toma would not have to pay for the calls he made. In fact, all of Toma’s phone calls from this phone were subject to a “pen register.” During this period, Glaser and Toma both spoke over the phone several times concerning cocaine transactions, and met in person on numerous occasions. Each time they met in person, Glaser was equipped with a recording device. In addition to the taped conversations between Toma and Glaser, and conversations between Toma and the other members of the conspiracy, the government obtained wiretap authorization for the telephones of Aguilera and Valencia. The roughly 650 conversations intercepted yielded evidence of eighteen separate narcotics transactions over the five-month period from January through May 1994. In January 1995, a Grand Jury returned a 66-count superseding indictment against a total of sixteen individuals for various narcotics crimes arising from the conspiracy. The eight Defendants-Appellants here were tried jointly, and following a five-week jury trial, commencing February 22, 1995, all eight were found guilty on April 4, 1995, of conspiracy to distribute cocaine and marijuana. At Defendants’ trial, 428 of the approximate 650 conversations which had been taped were introduced and received into evidence. In addition to the conspiracy charge, the jury found each Defendant guilty of at least one other count in the indictment. Defendants have individually and jointly challenged their convictions and sentences. II.Issues on Appeal I. Whether the district court’s rulings denying Defendants’ motions for a mistrial and for a voir dire of the jury were proper; A. Defendants’ motion for mistrial; B. Defendants’ motion for voir dire of the jury; II. Whether the district court properly denied Defendants’ motions for severance; A. Defendants’ motion for severance based on alleged variance between indictment and proof at trial; B. Whether the indictment was duplicitous; C. Pinto’s motion for severance based on alleged exculpatory testimony; III. Whether the district court erred in denying Defendants’ motions for mistrial based on alleged prosecutorial misconduct; A. Alleged “coaching” of witness Youmaran; B. Alleged “coaching” and subornation of perjury by Ishu; C. Alleged subornation of perjury by witness Ress; D. Questioning concerning arson at a building owned by Aguilera and Iturralde; IV. Whether sufficient evidence supported the convictions of various Defendants; A. Rosa; B. Rabón; C. Pinto; V. Whether the district court’s enhancement of Toma’s sentence under § 3Bl.l(a) of the Sentencing Guidelines was proper; VI. Whether the district court’s attribution of certain drug quantities to Toma for sentencing purposes was proper; VII. Whether the trial court properly declined to grant additional peremptory challenges to Defendants; VIII. Whether the district judge’s ruling admitting tape recordings based on the identification of the voices of Aguilera and Iturralde was proper; IX. Whether the trial judge erred in declining to give Ameneiro’s proposed instruction concerning the reliability of voice identification; X. Whether the mandatory minimum sentence Rabón received is constitutional; and XI. Whether the district court’s refusal to permit Rosa to collaterally challenge a prior conviction used to enhance his sentence was proper? I. Whether the district court’s rulings denying Defendants’ motions for a mistrial and for a voir dire of the jury were proper. On appeal, Defendants initially argue that the judge erred in denying their motion for a mistrial, and in refusing to conduct a voir dire of the jury, based on the presence in the jury room of transcripts of certain tapes which had been admitted in evidence but never played at trial. A. Defendants’ motion for mistrial During her testimony, government witness Ress authenticated a number of the tapes the government introduced in evidence. She testified that she was familiar with the voices of Defendants (except Aguilera and Iturralde), and further that she had reviewed the transcripts. She testified that the transcripts accurately reflected the conversations on the tapes (except the Spanish tapes, as Ress did not speak Spanish) and also properly identified the speakers on the tapes. During the trial, the government played only 428 of the roughly 650 tapes received in evidence, leaving more than 200 unplayed. The tapes played were of conversations in either English, Spanish, or Assyrian. The jury was provided a binder during trial which contained transcriptions of all of the roughly 650 recorded conversations, and which they were referred to and examined while tapes were being played. Four days prior to closing arguments, the trial judge discussed with the lawyers out of the jury’s presence which exhibits would be given to the jury for consideration during deliberations. Some of Defendants’ lawyers sought to bar the jury from receiving transcripts of the English-language tapes, but the trial judge overruled their objections, ruling that, since there had been so many tapes played throughout the course of the trial, all of the transcripts, whether they were of English or foreign-language conversations, would be made available to the jury during their deliberations. At that time, the judge also directed the respective attorneys to place the tapes and transcripts on a table, in order that they would be available to all of them for inspection prior to their submission to the jury. The trial judge specifically informed all of the attorneys for both sides that he expected them to review the exhibits prior to them being given to the jury and stated, “[s]o if there is any question, it can be raised before the marshall takes the material to the jury room.” Four days later, on the day scheduled for closing arguments, the judge met with the lawyers to review the proposed instructions and hear and rule on any final objections. At that time, counsel for Iturralde and counsel for Rabón objected to eight specific tapes and transcripts being given to the jury on the ground that the tapes were not played during trial. The government responded that, since all of the tapes and transcripts had previously been admitted in evidence, they should be available for the jury. The court agreed with the defense lawyers and sustained the objections to the eight tapes. While acknowledging that all tapes and transcripts had been admitted in evidence, the judge nonetheless stated: “if [the government] never presented [the unplayed tapes and corresponding transcripts] to them, why should they listen to them, or why should they be sent back to them?” The judge ordered the government to remove those eight transcripts from the books, and the government complied with the judge’s order. Immediately thereafter, counsel for Magana observed that there were a number of other tapes which, though admitted in evidence, had not been played, and for which the jury had not reviewed the corresponding transcripts. The following colloquy between Judge Hart and counsel for Magana then occurred: [COUNSEL FOR MAGANA]: It seems, your Honor, that there are a number of tapes and transcripts in there that if they didn’t play the tape, then they ought to remove them all. THE COURT: Well, you tell us which ones they are. I know you have been following the case with great care, as well. [COUNSEL FOR MAGANA]: I have, your Honor. I am just saying there are quite a few. Those that apply to other people, I haven’t, but the government knows. THE COURT: I tried to keep track of them. I am sure you did, as well. So let me know if there is a problem. (Tr. at 2832-33.) No further discussion was had about the tapes and transcripts prior to the commencement of the jury deliberations. On the second full day of deliberations, the jury sent a note to the judge, asking: “Is it correct that all transcripts and notebooks are in evidence even though the related tape is not in the jury room?” At that time, the court learned that, except for the eight tapes and transcripts which he had specifically ordered removed, the transcripts for the approximately 200-plus unplayed tapes that had been received in evidence had not been removed from the binders which had been sent back to the jury room. However, the unplayed tapes themselves were not made available to the jurors. At this time, the judge questioned the government’s lawyers, who explained that they interpreted the court’s prior order as requiring them to only remove the eight specific tapes and transcripts objected to by counsel for Rabón and Iturralde. The lawyers for the government reiterated that the tapes and transcripts at issue had been admitted in evidence prior to trial. The prosecutors further acknowledged that they were aware that the judge did not want transcripts of unplayed tapes sent to the jury, however they did not believe they had enough time to go through all of the jury’s binders and remove the 200-plus transcripts prior to the commencement of deliberations. The district court stated that the fact that it was “administratively inconvenient” was “no excuse” for the government’s failure to remove the transcripts. Defendants all moved for a mistrial based on the presence of the transcripts in the jury room. Despite his displeasure with the actions of the government lawyers, the district judge denied Defendants’ motion for a mistrial. In his ruling, he agreed with the government and noted that the transcripts at issue had all been admitted in evidence, and that based upon this, there would have been no question had the government played the tapes that the jury would have had all of the transcripts for review. He also observed that none of Defendants had specifically moved for the exclusion of the transcripts of the unplayed tapes, though he commented that he would probably have granted such a motion had it been made in a proper and timely manner. Defense counsel for Magana asserted that the court’s response to his prior objection placed the responsibility on the government to remove all transcripts of unplayed tapes. In response, the judge stated: I gave you [defense counsel] that responsibility. I said it on the record. Check those [binders] yourselves. Be sure that what goes back is correct. That is your responsibility as attorneys to do that. You can’t cast that entirely on the government. The fault lies both on the government and the defense counsel. (Tr. at 3315.) Judge Hart then ruled that the jury would be sent home for the day, and at that time he ordered the marshall to retrieve all binders from the jury room and instructed the attorneys (both government and defense counsel) to remove all transcripts from the binders which referred to tapes that had not been played during trial. When the trial reconvened after the transcripts in question had been removed, the judge responded to the jury’s question by giving this curative instruction: You have all the English-language tapes that are in evidence. Some transcripts were inadvertently provided to you for tapes that were never played. During the weekend, all of those transcripts were removed from your transcript notebooks. If, during deliberations, you read a transcript for which there was no tape, you must disregard what was in that transcript. It may not be considered in reaching your verdict. (Tr. at 3339.) When Defendants renewed their motions for a mistrial, the judge once again made clear that he would not declare a mistrial. He agreed with Defendants that the transcripts of unplayed tapes should not have been sent back to the jury room; however, he reiterated that the transcripts contained information which the government could have placed before the jury had the tapes been played. He also concluded that the government’s decision not to play the tapes spared the jury from hearing “cumulative” material, and he suggested that the fact that the jury alertly picked up on the absence of certain tapes meant that they were following instructions by listening to the tapes, and not referring to the transcripts alone. Finally, he reiterated his belief that the defense lawyers shared the responsibility for the episode, since he had specifically directed them to review all the evidence that was being given to the jury prior to its submission. Judge Hart also declined, in response to the defense lawyers’ requests, to conduct a voir dire of the jurors concerning whether they had looked at the transcripts and what, if any, effect those transcripts had on their deliberations. Defendants argue that the judge should have granted their motion for a mistrial based on the presence of the transcripts of admitted but unplayed tapes in the jury room. We review the denial of a motion for mistrial under the abuse of discretion standard. United States v. Best, 939 F.2d 425, 431 (7th Cir.1991) (en banc). Under the abuse of discretion standard, “the proper inquiry is not how the reviewing court would have ruled if it had been considering the case in the first place, but rather whether any reasonable person could agree with the district court.” Id. at 429 (internal quotation marks omitted). Throughout their briefs and at oral argument, Defendants have repeatedly suggested that the government’s actions in failing to remove the transcripts of unplayed tapes from the binders sent back to the jury room amounted to deliberate prosecutorial misconduct. We see no need to discuss this allegation. Even if a defendant alleges that improper material was before the jury as a result of prosecutorial misconduct, he must still show “that there was some prejudice or substantial right affected by the presence” of the transcripts in the jury room. Best, 939 F.2d at 431. As discussed below, Defendants in this ease have failed to demonstrate that they were prejudiced in any way by the presence of the transcripts of the unplayed tapes in the jury room. As an initial matter, we observe that Defendants failed during trial to make a timely and specific motion requesting that all the tapes which had been admitted in evidence but not played not be presented to the jury for deliberation, and that the corresponding transcripts of those tapes be removed from the binders and not be displayed to the jury. Counsel for Magana did not object nor did he argue until the day scheduled for closing arguments, nearly five weeks after the commencement of the trial, that there were “a number” of tapes that had not been played and should be removed, and the judge responded that, if counsel sought to have any tapes in particular removed, he was directed to bring those particular tapes to the court’s attention prior to their submission to the jury. Thereafter, with the exception of the eight specific tapes and transcripts objected to by counsel for Rabón and Iturralde, which were removed by the government, neither counsel for Magana, nor any of the other defense lawyers, explicitly requested that the judge remove any other unplayed tapes and corresponding transcripts. Second, as Judge Hart noted, he specifically instructed the lawyers for both sides when he conferred with them concerning the final jury instructions, four days prior to the date of closing argument, to place all of the exhibits introduced on a table in the court, and directed them to review the exhibits prior to their submission to the jury so that they could examine the material and object if such was proper. It appears that counsel for Iturralde and Rabón were attentive to which tapes had not been played, as they objected to eight specific tapes and transcripts prior to closing arguments, and as a result those tapes and transcripts were removed. It also appears, however, that none of the other defense lawyers examined the exhibits to discover and identify the numerous transcripts of unplayed tapes which should have been excluded. Given that over 200 tapes were not played at trial, even a cursory examination of the transcript binders at some point over the four-day period would certainly have revealed the presence of the transcripts of unplayed tapes. In this regard, we observe, as we have in the past, that “it is not the responsibility of the prosecutor or the judge to do the work of the defense counsel.” United States v. Zambrana, 841 F.2d 1320, 1328 (7th Cir.1988). Further, as the trial judge observed, the transcripts and tapes had been properly admitted in evidence. We have observed in the past that “ ‘[ejourts possess wide discretion in determining whether to permit the jury to use written transcripts as aids in listening to tape recordings.’ ” Id. at 1335 (quoting United States v. Keck, 773 F.2d 759, 766 (7th Cir.1985)). Indeed, we have specifically approved of the practice of sending transcripts back to the jury room. See United States v. Crowder, 36 F.3d 691, 697 (7th Cir.1994) (“The decision to allow the transcripts to be used during deliberations is committed to the sound discretion of the district court.”). Therefore, had the government opted (as it could have done) to play all 650 of the tapes during trial, there would have been no question but that the transcripts could have gone to the jury without any further discussion. Thus, this situation presents a far less compelling case for a finding of prejudice than prior cases before this court, in which material extraneous to the admitted evidence was placed before the jury. For example, in United States v. Sababu, 891 F.2d 1308 (7th Cir.1989), we held that it was not an abuse of discretion for the trial judge to refuse to declare a mistrial where a transcript of a taped conversation which had been excluded from evidence was inadvertently sent back to the jury room. 891 F.2d at 1333-34. As we stated in Best: “If exposure to such improper evidence did not warrant a new trial in ... [eases where the jury was exposed to improper evidence], the jury’s exposure in this case to copies of documents properly admitted in evidence in a binder that the jury had used for the length of the trial cannot warrant a new trial.” 939 F.2d at 431 (emphasis in original) (citing, inter alia, Sababu). Defendants have made no effort to delineate anything in these transcripts which contained material prejudicial to them. Finally, even assuming that the transcripts were improperly before the jury, the trial court gave a curative instruction specifically informing the jurors that the transcripts for tapes which had not been played had been removed, and if they had read any such transcripts prior to their removal, “you must disregard what was in that transcript. It may not be considered in reaching your verdict.” Thus, the instruction specifically directed the jury not to consider any of those transcripts in reaching their verdicts. As a jury is presumed to follow the court’s instructions, see Evans v. Young, 854 F.2d 1081, 1084 (7th Cir.1988), and since Defendants have failed at any time (including on appeal) to offer any evidence that any of the material contained within the transcripts was prejudicial, we refuse to conclude that Defendants suffered any prejudice as a result of the presence of the transcripts in the jury room. B. Defendants’ motion for voir dire of the jury We likewise disagree with Defendants’ contention that the trial judge erred in refusing to conduct an individual voir dire of the jurors to determine the potential prejudicial impact of the transcripts. Trial judges are vested with wide latitude with respect to remedying the potential prejudicial influence that may arise when jurors are exposed to improper information, and the district court’s decision not to conduct a voir dire will only be reversed for an abuse of discretion. Sababu, 891 F.2d at 1334; see United States v. Carson, 9 F.3d 576, 589 (7th Cir.1993). When refusing to conduct a voir dire of the jury, the experienced trial judge noted that the defendants had failed to delineate any specific examples of prejudicial material in those transcripts. This was particularly noteworthy since defense counsel had an opportunity at the time the tapes and transcripts were admitted to argue that they contained irrelevant or prejudicial information, and were specifically told four days prior to the start of closing arguments to inspect the exhibits that were being sent back to the jury. Furthermore, the trial judge observed that conducting a voir dire of the jury during deliberations can be “fraught with problems,” since it could cause the jurors to focus disproportionately on the removed material. This court has noted its agreement with this observation in the past. In Sababu, we observed that such a voir dire could conceivably jeopardize an accused’s rights, because it is possible that polling jurors individually could cause ‘“the jurors polled to attach undue significance to the incident.’ ” 891 F.2d at 1334 (quoting United States v. Williams, 822 F.2d 1174, 1189-90 (D.C.Cir.1987)). As in Sababu, in this ease we conclude that the trial court did not commit error in refusing to conduct a voir dire and deciding instead to give a curative limiting instruction. II. Whether the district court properly denied Defendants’ motions for severance A. Defendants’ motion for severance based on alleged variance between indictment and proof at trial During the time period the FBI was investigating Toma, the Drug Enforcement Administration (DEA) was investigating Aguilera and Iturralde. Pursuant to the DEA’s investigation, Jorge Tutuianu (Tutuianu), a former narcotics dealer working for the government, obtained a position at the Alamedas Casino, a nightclub owned by Aguilera and Iturralde. Tutuianu introduced Aguilera to DEA agents Juan Perez (Perez) and Frank Guerra (Guerra), who were posing as major suppliers of narcotics, for the purpose of setting up a potential 100-kilogram shipment of cocaine. The government agents were posing as sellers, rather than buyers, of narcotics, and this was referred to at trial by the government’s witnesses Perez and Guerra as a “reverse buy.” On appeal, Defendants argue that this specific proposed transaction was a separate conspiracy as distinguished from the general conspiracy among Defendants to distribute cocaine and marijuana. Defendants claim that, since the proof at trial demonstrated the existence of separate conspiracies while the indictment charged only one overarching conspiracy, there was a “variance” between the indictment and the proof presented at trial. We disagree. We observe as an initial matter that, except for Pinto, Ameneiro, and Rosa, none of Defendants properly preserved the severance issue for appeal; thus we review this issue with respect to all other Defendants under the “plain error” standard. United States v. Balzano, 916 F.2d 1273, 1279-80 (7th Cir.1990). To prevail under this standard, a defendant must demonstrate that the error is obvious, prejudicial, and seriously affected the fairness, integrity, or public reputation of the judicial proceedings. United States v. Olano, 507 U.S. 725, 732, 736, 113 S.Ct. 1770, 1777, 1779, 123 L.Ed.2d 508 (1993). “A variance arises when the facts proved by the government at trial differ from those alleged in the indictment.” United States v. Townsend, 924 F.2d 1385, 1389 n. 1 (7th Cir.1991). “A defendant asserting a claim of variance will succeed in obtaining reversal of his conviction only if he establishes that (1) the evidence presented at trial was insufficient to support the jury’s finding of a single conspiracy, and (2) he was prejudiced by the variance.” United States v. Curtis, 37 F.3d 301, 305 (7th Cir.1994). “The Seventh Circuit defines a conspiracy as a combination or confederation of two or more persons formed for the purpose of committing, by their joint efforts, a criminal act.” United States v. Rodriguez, 53 F.3d 1439, 1444 (7th Cir.1995) (internal quotation marks omitted). In United States v. Briscoe, 896 F.2d 1476 (7th Cir.1990), this court reviewed what is necessary to establish a single conspiracy: “Various people knowingly joining together in furtherance of a common design or purpose constitute a single conspiracy. While the conspiracy may have a small number of co-conspirators, other parties who knowingly participate with these co-conspirators and others to achieve a common goal may be members of an overall conspiracy. In essence, the question is what is the nature of the agreement. If there is one overall agreement among the various parties to perform different functions in order to carry out the objectives of the conspiracy, the agreement among all the parties constitutes a single conspiracy.” 896 F.2d at 1505 (quoting United States v. Varelli, 407 F.2d 735, 742 (7th Cir.1969)). We went on to observe in Briscoe: It is well settled that a single conspiracy may consist of a small core of people with whom other conspirators knowingly participate to achieve the common purpose of the conspiracy. It is equally well established that the parties involved in a single conspiracy need not know one another or participate in every aspect of the conspiracy____ In any ease, as long as the evidence demonstrates that the eoconspirators ... knowingly embraced a common criminal objective, this is sufficient to establish the existence of a single overall conspiracy among the eoeonspirators. 896 F.2d at 1507 (citations and internal quotation marks omitted) (emphasis added). Finally, in United States v. Gonzalez, 933 F.2d 417 (7th Cir.1991), we addressed the manner in which this court reviews an argument alleging a variance between the indictment and the proof at trial: “In performing a variance review we do not comb the evidence de novo, as the appellants might like. Our review is second-hand. The jury gets first crack at deciding ‘whether there is one conspiracy or several when the possibility of a variance appears.’ United States v. Percival, 756 F.2d 600, 609 (7th Cir.1985). This is so because a question of variance is a question of fact, which is something especially within the jury’s realm of expertise ---- At this stage the question for us simply is whether the evidence is sufficient to support the jury’s determination. We must view the proof at trial in the light most favorable to the prosecution, and we must uphold the jury’s single conspiracy determination if any rational trier of fact could have found beyond a reasonable doubt the one conspiracy. ‘We give deference to the jury’s weighing of the evidence and its drawing of reasonable inferences. ” [United States v. Sababu, 891 F.2d 1308, 1322 (7th Cir.1989) ]. This deference is significant: Given the nature of conspiracies, juries often must infer their existence and scope from circumstantial evidence and ‘the reasonable inferences drawn therefrom.’ ” 933 F.2d at 438 (quoting United States v. Paiz, 905 F.2d 1014, 1019 (7th Cir.1990)) (emphasis in original). Whether to grant a motion to sever the trials of joint defendants alleged to have participated in a single conspiracy is a matter within the sound discretion of the trial judge, and we will reverse a decision denying severance only when such denial amounts to an abuse of that discretion. Sababu, 891 F.2d at 1330-31. To succeed on appeal, Defendants bear the heavy burden of demonstrating that they were in fact prejudiced by the denial. Id. In this context, “prejudice” does not mean that their odds of acquittal would have been increased; rather, Defendants must demonstrate that, absent the severance, they were unable to obtain a fair trial. Id. When reviewing the decision of the trial court denying a motion for severance, we keep in mind, particularly in conspiracy cases, that there is a strong interest in trying defendants who have been jointly indicted in a single trial. Id. As we explained in Briscoe, those interests include: (1) reducing expenditure of judicial and prosecutorial time; (2) preventing the increased demand on witnesses’ time that would result from multiple trials; (3) reducing the chance that each defendant will try to create reasonable doubt by blaming an absent colleague. 896 F.2d at 1516-17 (citing United States v. Buljubasic, 808 F.2d 1260, 1263 (7th Cir.1987)). The taped conversations which evidenced the transactions comprising the conspiracy reflect that the co-conspirators did not specifically refer to cocaine as such; rather, they referred to the narcotics transactions in code language. During trial, Agents Guerra and Perez, as well as Defendant Pinto, testified concerning the content of the code used by Defendants. In United States v. Vega, 860 F.2d 779 (7th Cir.1988), we had occasion to discuss the use of such “drug code” in the narcotics trade and how it may be considered at trial: Conversations regarding drug transactions are rarely clear. A fact-finder must always draw inferences from veiled allusions and code words. In this case the jury was confronted with conversations which contained “code words” that, when considered in isolation, might seem unclear, veiled and almost nonsensical, but when analyzed properly, in the context of the totality of the evidence, can be clearly seen to be “code words” for drugs. See generally United States v. Abascal, 564 F.2d 821, 827 (9th Cir.1977) (“The conversing conspirators frequently discuss non-nareotic-related matters at the beginning of conversations, and often resorted to jargon and code words, a frequent practice in narcotics dealings”); United States v. Chavez, 533 F.2d 491, 494 (9th Cir.1976) (“Jargon and code words are commonly used by those dealing in illicit drugs and were employed here”) (citation omitted)____ Not only are code words always used by drug conspirators when they realize, as they do in today’s drug culture, that their telephone conversations are frequently intercepted, such terms were obviously used by the conspirators in this case. 860 F.2d at 795 (internal quotation marks omitted). We have also observed that “ ‘[jjudges in the federal system, whether they are in the trial or appellate system, do not operate in a vacuum, shielded from knowledge of drug operations in the real world.’” United States v. Nobles, 69 F.3d 172, 191 (7th Cir.1995) (quoting United States v. Hatchett, 31 F.3d 1411, 1420 (7th Cir.1994)). After review of the record, we are of the opinion that the government presented more than sufficient evidence of a single conspiracy. With respect to Aguilera, Iturralde, Rabón, and Magana, who served as Toma’s suppliers, Toma engaged in frequent conversations with each concerning the specifics of a variety of proposed and past drug transactions. Toma also dealt in “fronted” narcotics with them, reflecting a sense of interdependence among the various stages of the conspiracy network, and establishing more than a mere “buyer-seller” relationship. See United States v. Lechuga, 994 F.2d 346, 349-50 (7th Cir.1993) (fronting of narcotics is evidence of more than a simple buyer-seller relationship). Toma’s load cars were used to transport narcotics, and the suppliers would in fact deal directly with Toma’s customers on occasion. As to Rosa, his frequent transactions with Toma not only took the form of both buyer and seller, they extended beyond that as well. Toma on occasion while actively participating in the conspiracy counted drug money at Rosa’s house, and also “cut,” i.e., diluted for resale, quantities of cocaine there. Rosa also spoke with Magana and Matthews, as reflected in taped conversations, on occasion concerning narcotics transactions. Finally, Ameneiro received fronted drugs from Toma, spoke with Ress and Ishu concerning narcotics transactions on occasion, and in one instance dealt directly with Ishu, when Ishu, acting on Toma’s instruction, visited Ameneiro to pick up drugs which Toma had previously fronted to Ameneiro and which Ameneiro was returning because of their poor quality. Further, review of the specifics of the “reverse buy” transaction falls short of convincing us that it constituted a wholly separate conspiracy from the overall conspiracy charged in the indictment. On May 6, Perez spoke with Aguilera, who indicated that he needed “100 women.” According to Perez, “100 women” was an example of the code language employed as a reference to “100 kilos” of cocaine. Afterwards, Aguilera spoke with Pinto, and Pinto and Aguilera arranged to meet and did in fact meet at a park on the north side of Chicago. On May 9, Aguilera called Perez back, and stated that they could come up with “half.” On May 10, Aguilera called Pinto and told him that “I’m waiting for them to call ... I think he has a concert ready.” Pinto, when he testified, admitted that he was aware that “concert” was code for a cocaine transaction. Immediately after Aguilera called Pinto, Perez spoke with Aguilera and told him that “the man is on his way.” Aguilera assured Perez that he had things “under control,” and that he could move those “100 ladies” in “one month maximum.” Immediately thereafter, Aguilera called Pinto and arranged to meet at a park in Chicago, and Pinto later admitted under oath that he attended that meeting. After the meeting, Aguilera called Toma and informed him that he had “good news” and they arranged to meet. The next day, Guerra met with Tutuianu, Aguilera and Iturralde at a bar, where they agreed, pursuant to their earlier discussion, that Guerra would deliver the cocaine, but Guerra insisted on getting $200,000 up front (about half of the purchase price). They also agreed on the use of a load car, i.e., a ear with a secret compartment specifically designed for transporting the drugs. On May 12, Aguilera called Toma, who had a number of “load cars,” and told him that he needed to use Toma’s “car.” Toma later called Matthews and told Matthews that he was going to see “the tickets,” and was going to lend his car to his supplier. Toma also requested that Matthews bring him some money to show Guerra. Later, Aguilera, Iturralde and Tutuianu arrived at the same park where Aguilera had met with Pinto two days earlier. Toma arrived driving one of his “load cars.” Ultimately, no deal was consummated at that time, as Toma did not have the $200,000 available for display. The meeting broke up, and Defendants were arrested the next day, on May 13. A variance occurs only when the “evidence offered at trial proves facts materially different from those alleged in the indictment.” United States v. Johnson, 26 F.3d 669, 686 (7th Cir.1994). “Whether a single conspiracy exists is a question of fact; consequently the jury gets first crack at deciding whether there is one conspiracy or several when the possibility of a variance appears. This is because the jury’s verdict must be interpreted as a finding that the government presented sufficient evidence to prove its indictment beyond a reasonable doubt, and that is all that we require of the prosecution.” Townsend, 924 F.2d at 1389 (citations and internal quotation marks omitted). In this case, the evidence revealed a series of interrelated drug credit transactions between Toma, his suppliers and his customers, over a period spanning the early months of 1994. It also revealed that the network of suppliers and dealers were aware of each other’s existence, dealt with each other not just through Toma, but also on occasion with each other directly, employed a similar drug code, and used the same meeting places, and modes of transportation at times to further their transactions. Further, with respect to the “reverse buy” transaction, it in no way appears to be out of the ordinary for the conspiracy. One of Toma’s suppliers (Aguilera) sought to acquire cocaine to deliver to Toma, who was in the process of making arrangements to deliver the cocaine to one of his suppliers (Matthews). Based on the foregoing review of the record, we conclude that the evidence supported the jury’s conclusion that a single conspiracy existed among Toma and the other coconspirators, and Defendants were not prejudiced by the district judge’s refusal to grant severances based on any alleged variance. Furthermore, the trial judge, in instructing the jury on the law of conspiracy, gave explicit and thorough limiting instructions as follows: Although the defendants are being tried jointly, you must give separate consideration to each defendant. In doing so, you must analyze what the evidence in the case shows with respect to each defendant, leaving out of consideration any evidence admitted solely against some other defendant or defendants. Each defendant is entitled to have his case decided on the evidence and the law applicable to him. Mere association with the conspirators is not sufficient to establish a defendant’s participation or membership in a conspiracy. Presence at the scene of a crime and/or knowledge that a crime is being committed are not sufficient to establish a defendant’s guilt. In Count 1 the government has charged a single conspiracy. You are instructed that proof of several separate conspiracies is not proof of the single overall conspiracy alleged in Count 1, unless one of the several conspiracies which is proved is the single conspiracy which Count 1 of the indictment charges. What you must do is determine whether the single conspiracy charged in the indictment existed between two or more conspirators. If you find that no such conspiracy existed, then you must acquit the defendants as to that charge. However, if you are satisfied that such a conspiracy existed, you must determine who were the members of that conspiracy. If you find that a particular defendant is a member of another conspiracy and is not also a member of the conspiracy charged in the indictment, then you must acquit that defendant. In other words, to find a defendant guilty, you must find that he was a member of the conspiracy charged in the indictment, whether or not he was a member of some other separate conspiracy- (Tr. at 3167, 3171-72.) As in United States v. Collins, 966 F.2d 1214 (7th Cir.1992), a case in which a similarly thorough limiting instruction was given, the instruction here “adequately informed the jury that it must find each defendant guilty of the conspiracy charged, a single conspiracy ... in order to convict that defendant.” 966 F.2d at 1221. It is evident that the jury was careful in its consideration of the evidence with respect to the individual counts and Defendants, since, while finding Defendants guilty of a number of counts in the indictment, it also found a number of Defendants not guilty on various charges. For example, Toma was acquitted of one count of cocaine distribution (Count 3), and another count of attempted cocaine distribution (Count 53). With respect to Count 53, the jury found other Defendants guilty. The jury also found Magana not guilty of one count of cocaine distribution (Count 21), and found all Defendants charged not guilty of Count 66, alleging use of firearms. For the reasons discussed, we conclude that no prejudice resulted to Defendants from any alleged variance. B. Whether the indictment was duplicitous Defendants further argue that, because the indictment did not set out the “reverse buy” transaction in a separate conspiracy count from the main conspiracy alleged, the indictment was “duplicitous.” “ ‘Duplicity’ is the joining of two or more offenses in a single count.” United States v. Marshall, 75 F.3d 1097, 1111 (7th Cir.1996) (citation omitted). We initially observe in response that none of Defendants raised the question of duplicity before trial, and thus they “waived this argument by failing to raise it prior to trial.” United States v. Hammen, 977 F.2d 379, 382 (7th Cir.1992). While we may review waived arguments for “plain error,” we are not obligated to do so. See United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 1778, 123 L.Ed.2d 508 (1993). Under this standard, defendants must establish “ ‘that there was error, that the error was plain, that the error affected [their] substantial rights, and that the error seriously affected the fairness, integrity or public reputation of the judicial proceedings.’ ” United States v. Bursey, 85 F.3d 293, 296 (7th Cir.1996) (quoting United States v. Penny, 60 F.3d 1257, 1264 (7th Cir.1995), cert. denied, — U.S. -, 116 S.Ct. 931, 133 L.Ed.2d 858 (1996)). Review of Defendants’ argument concerning the alleged “duplicity” makes clear that it is little more than a rehash of their variance argument—that the evidence at trial showed that the “reverse buy” was a separate conspiracy. Indeed, even the case law cited by Defendants actually deals with the question of variance. For example, Defendants in their brief cite United States v. Zemek, 634 F.2d 1159 (9th Cir.1980), as setting forth factors a court should consider “[i]n determining whether a single conspiracy charge is duplicitous.” (Joint Br. of Defendants at 48.) In fact, the Ninth Circuit specifically stated in Zemek that the factors it was setting forth were in response to the defendants’ variance argument. 634 F.2d at 1167 (“Appellants assert that, while count 1 alleged but a single conspiracy, the evidence adduced at trial established two separate conspiracies resulting in a variance affecting their substantial rights.” (emphasis added)). In United States v. Simone, 931 F.2d 1186 (7th Cir.1991), this court was faced with a situation similar to the present case. Defendants were charged with and convicted of a single count of conspiracy, and they argued on appeal that the evidence at trial showed that more than one conspiracy existed. In reviewing the indictment, we concluded that it “described a single ongoing drug distribution conspiracy ... involving core members who bought from and sold to various suppliers and dealers.... This circuit has treated such schemes as single conspiracies rather than a series of smaller separate conspiracies.” 931 F.2d at 1192 n. 6. Here, the indictment likewise described a single set of participants who engaged in repeated transactions from April 1993 through May 1994. We have previously determined, supra, that the evidence at trial was sufficient to establish that the “reverse buy” transaction was part of the single, overarching conspiracy charged in the indictment, because the evidence showed that it was but another example of the many transactions which made up the single conspiracy. Thus, it was clearly proper for the indictment to charge but one conspiracy, since only one existed, and Defendants have failed to demonstrate plain error with respect to their argument that the indictment was duplicitous. C. Pinto’s motion for severance based on alleged exculpatory testimony Several weeks prior to trial, Pinto made a motion for severance and it was denied. Approximately two weeks into the trial, he renewed his motion, this time accompanied by an affidavit from one of the Co-Defendants, Aguilera. In the affidavit, Aguilera stated that: I would be willing to testify if Mr. Pinto has a separate trial, since I have knowledge of facts which would show that Jose Pinto is not guilty of the charges in this ease. Mr. Pinto has never supplied me with any cocaine. I have never received any cocaine from Mr. Pinto at any time. (R.545.) Judge Hart denied the motion, and Pinto argues that the denial of his motion prejudiced his right to a fair trial. When a defendant requests a severance based upon an allegation that a co-defendant will offer exculpatory testimony, the district court considers: “(1) whether the co-defendant’s testimony would be exculpatory; (2) whether the codefendant would in fact testify; and (3) whether the testimony would bear on defendant’s case.” Granada v. United States, 51 F.3d 82, 84 (7th Cir.1995) (quoting United States v. Chrismon, 965 F.2d 1465, 1476 (7th Cir.1992)), cert. denied, — U.S. -, 116 S.Ct. 970, 133 L.Ed.2d 890 (1996). We review the trial judge’s denial of a motion for severance for an abuse of discretion, see United States v. Boykins, 9 F.3d 1278, 1289 (7th Cir.1993), cert. denied, - U.S. -, 117 S.Ct. 1271, 137 L.Ed.2d 348 (1997), keeping in mind the strong interest in joint trials in conspiracy cases. Granada, 51 F.3d at 84; Briscoe, 896 F.2d at 1516-17; see supra 1186. In our opinion, the trial judge did not abuse his discretion in denying Pinto’s motion for severance, since Aguilera’s affidavit fads to satisfy even the first prong of the above test. The fact that Aguilera claimed that Pinto never delivered cocaine to him simply does not exculpate Pinto of the charges set forth against him in the indictment. Pinto was charged not with actual delivery of cocaine, but with attempted distribution of cocaine, as well as being a member of the conspiracy to distribute cocaine. Furthermore, the evidence against Pinto was not based on actual observance of delivery of narcotics, but rather on his phone conversations that were recorded in which narcotics deals were discussed. As the trial court noted in denying Pinto’s motion: the problem ... with your motion [for severance] is that ... Mr. Pinto, is charged with conspiracy. He is charged with attempt. And he is charged, as well, with telephone charges which could conceivably be proven without actually establishing a distribution____ Mr. Aguilera’s testimony, although it might he helpful to him, would not be exculpatory or operate to exonerate him. Indeed, all Aguilera’s affidavit stated was that “Mr. Pinto has never supplied me with any cocaine. I have never received any cocaine from Mr. Pinto at any time.” This would not be inconsistent with participation by Pinto in a narcotics conspiracy, an attempted (though not actual) delivery of drugs by Pinto, or even with a theory that Pinto actively supplied cocaine to people other than Aguilera in furtherance of the conspiracy. A similar issue was presented to us in Gonzalez, 933 F.2d 417. In that ease, a defendant had been charged with making a trip to Chicago in furtherance of a narcotics conspiracy. He requested a severance on the basis of affidavits from his alleged co-conspirators stating that, during the time of the conspiracy, the defendant had traveled to Chicago for legitimate business reasons. We held that since “neither of the affidavits contained statements that excluded the possibility that [defendant] also traveled to Chicago on drug-related business,” they did not exculpate the defendant. 933 F.2d at 425 (emphasis added). Likewise, in the present case, Aguilera’s affidavit did not exculpate Pinto, since it did not contain testimony inconsistent with the charges Pinto faced. Thus, since it is not truly exculpatory, the affidavit simply fails to provide a basis sufficient for concluding that Judge Hart abused his discretion in denying Pinto’s renewed motion for severance. III. Whether the district court erred in denying Defendants’ motions for mistrial based on alleged prosecutorial misconduct Defendants also claim that they were entitled to be granted a mistrial based upon several instances of alleged “prosecutorial misconduct.” In particular, they claim that the prosecution: coached witness Youmaran into making a false and perjurious in-court identification of Defendant Ameneiro; coached witness Ishu into making a false identification of Ameneiro and suborned perjury with respect to Ishu’s testimony concerning a meeting with Ameneiro; knowingly presented false testimony by witness Ress; and improperly questioned a witness concerning arson at a building owned by Aguilera and Iturralde. We address each in turn. In United States v. Saadeh, 61 F.3d 510 (7th Cir.1995), we addressed the quantum of proof a defendant must establish to succeed when making a claim that he was entitled to receive a new trial on the basis that the government knowingly used perjured testimony: In order to receive a new trial on the basis of the government’s use of allegedly perjured testimony, the defendant must establish that: (1) the prosecution’s case included perjured testimony; (2) the prosecution knew, or should have known, of the perjury; and (3) there is a likelihood that the false testimony affected the judgment of the jury. We have repeatedly held, however, that mere inconsistencies in testimony by government witnesses do not establish the government’s knowing use of false testimony. Rather, the alleged perjured testimony must bear a direct relationship to the defendant’s guilt or innocence. Finally, when a defendant alleges that the prosecution used perjured testimony, we must inquire into whether the defendant had adequate opportunity to expose the alleged perjury on cross-examination. 61 F.3d at 523 (citations and internal quotation marks omitted). A. Alleged “coaching” of witness Youmaran Youmaran testified that he accompanied Toma on two occasions in March or April 1994 to Ameneiro’s tanning salon for the purpose of attempting to obtain payment from Ameneiro for cocaine previously delivered by Toma, but that Ameneiro refused to pay on either occasion. Youmaran testified that he knew Ameneiro, and he identified him in court. During the cross-examination of Youmaran, Ameneiro’s lawyer suggested that the government had “coached” Youmaran’s testimony by displaying a photo of Ameneiro two days prior to trial and telling him to identify Ameneiro when asked. Defendants argue that, since Youmaran was shown a photo of Ameneiro prior to trial, his in-court identification of Ameneiro was “coached” and was inaccurate. This argument, however, is based on a self-serving and selective view of the record. During re-direct examination, Youmaran made clear that he had been shown an array of photos, not just Ameneiro’s, and he also denied that his identification had been “coached” by the government. [THE GOVERNMENT] How many photographs did you see? [YOUMARAN] A few. [THE GOVERNMENT] A few? [YOUMARAN] Quite a few, yes. [THE GOVERNMENT] Not just a photograph of Mr. Ameneiro? [YOUMARAN] No. [THE GOVERNMENT] Now, let me ask you this, did I tell you what to say this morning? [YOUMARAN] No, sir. [THE GOVERNMENT] Did any agent of the United States government, FBI agent or U.S. Attorney’s office ever tell you what to say? [YOUMARAN] No. [THE GOVERNMENT] What did I tell you you had to say today? [YOUMARAN] The truth. [THE GOVERNMENT] What did you understand will happen to you under your plea agreement if you don’t tell the truth? [YOUMARAN] I will be facing the maximum sentence. (Tr. at 830-31.) As the foregoing demonstrates, Youmaran made clear that the government instructed him to tell the truth during his testimony. Counsel for Ameneiro had ample opportunity during cross-examination to suggest that Youmaran’s testimony was “coached,” and he further had the opportunity, and took advantage of this opportunity, to present his arguments concerning “coaching” directly to the jury. He recited to the jury directly from his cross-examination of Youmaran, and suggested to them that the coaching of Youmaran “creates more than reasonable doubt.” Thus, the issue of the veracity of Youmaran’s identification was fully and vigorously argued before the jury, which was able to make its determination in light of these extensive arguments. As stated, for a defendant to receive a new trial on the basis of allegedly perjured testimony, he must first show that the testimony was in fact false. Saadeh, 61 F.3d at 523; see also United States v. Ferguson, 35 F.3d 327, 332 (7th Cir.1994). Since Defendants have “failed to provide any evidence that [Youmaran] committed perjury, much less that the government knew or should have known” of any alleged perjury, Saadeh, 61 F.3d at 523, there is no basis for us to conclude that any prosecutorial misconduct occurred. B. Alleged “coaching” and subornation of perjury by Ishu Ishu testified that, at Toma’s direction, he met with Ameneiro early in 1994 for the purpose of retrieving cocaine Toma had previously fronted to Ameneiro. Ameneiro was returning the cocaine because, in his opinion, the cocaine was not of high quality. Initially Ishu testified that the date of the meeting between himself and Ameneiro was March 1994. When the government attorney, in an attempt to refresh Ishu’s recollection, showed Ishu a transcript dated January 1994, from a phone call he placed to Ameneiro immediately prior to his meeting with Ameneiro, Ishu corrected himself and stated that the meeting occurred in January. Ishu also identified Ameneiro in open court. During Ishu’s cross-examination, Ameneiro’s lawyer attempted to confuse Ishu into thinking and testifying that the meeting between himself and Ameneiro had in fact occurred in March 1994. He also insinuated that the government had coached Ishu into thinking the meeting occurred in January 1994. Ameneiro’s counsel further elicited self-contradictory statements from Ishu concerning how he disposed of the cocaine he obtained from Ameneiro at their January 1994 meeting. Ishu testified on direct examination that the cocaine he received from Ameneiro was eighteen grams short of the amount Toma had instructed him to obtain. On cross-examination, Ishu at first denied that he had taken the eighteen grams for himself, but later he admitted that he and some friends had snorted the eighteen grams of cocaine. Defendants argue that, taken together, the alleged “coaching” of Ishu by the government concerning the date of his meeting with Ameneiro, along with Ishu’s correction of his testimony regarding missing cocaine, amounted to subornation of perjury by Ishu. For a defendant to obtain a new trial on the basis of the government’s use of perjured testimony, “the perjured testimony must be directly related to the defendant’s guilt or innocence and must relate to material facts rather than collateral issues.” Ferguson, 35 F.3d at 332. Further, “ ‘[m]ere inconsistencies in testimony by government witnesses do not establish the government’s knowing use of false testimony.’ ” United States v. Adcox, 19 F.3d 290, 295 (7th Cir. 1994) (quoting United States v. Griley, 814 F.2d 967, 971 (4th Cir.1987)). The inconsistency in Ishu’s testimony concerning the date of his meeting with Ameneiro, which he corrected upon having his memory refreshed through seeing the phone logs, is in our opinion simply too minor to have borne directly on the issue of Defendants’ guilt. Cf. Adcox, 19 F.3d at 295 (“ ‘the complained of discrepancies went to immaterial and collateral issues’ ”) (quoting United States v. Douglas, 874 F.2d 1145, 1160 (7th Cir.1989)). The issues of whether Ishu properly recalled the date of his meeting with Ameneiro, and whether he took eighteen grams of the cocaine he received for himself may well have borne on his credibility as a witness, but falls far short of rising to the level of perjury, much less demonstrating the government’s knowing use of perjured testimony. Like Youmaran, Ishu testified that he had been told to tell the truth at all times. [THE GOVERNMENT] Mr. Ishu, there were a lot of questions from [counsel for Ameneiro] about people telling you what to say, telling you what to do. What was the one thing the government asked you to do today? [ISHU] To say the truth. Further, like the defendant in Saadeh, the defense lawyers in this ease “had an ample opportunity, of which [they] took advantage, to cross-examine [Ishu] during the trial, discredit him, and expose any alleged perjury.” 61 F.3d at 523. During closing arguments, counsel for Ameneiro, as he had with Youmaran, argued that Ishu’s testimony was false, and read extensive portions of the transcript of his cross-examination of Ishu in an attempt to buttress his point. Ishu, like Youmaran, testified that he had been instructed by the prosecutors to testify truthfully and was in fact testifying truthfully, and the jury had the opportunity to evaluate Ishu’s credibility in light of the totality of the testimony as well as the arguments made by the defense lawyers concerning these allegations. Thus, since they had ample opportunity to expose any alleged perjury by Ishu, and they have not demonstrated on appeal that his testimony was false, we conclude that Defendants have failed to demonstrate grounds for reversal in Ishu’s testimony. C. Alleged subornation of perjury by witness Ress Ress testified that, prior to trial, she had reviewed a number of tapes and transcripts of conversations between and among the co-conspirators and authenticated that the transcripts accurately reflected the conversations at the time in question and corresponded with the voices on the tapes. She testified that she was familiar with the voices of all of Defendants (except for Aguilera and Iturralde). Several of the tapes included Ameneiro’s voice. While the jury was in deliberations, counsel for Ameneiro filed a motion for a mistrial. The motion, which was not accompanied by an affidavit from Ress and was based solely on the attorney’s account of a meeting he allegedly had with Ress after all the evidence had been presented, claimed that Ress had told Ameneiro’s counsel the following: a. She advised [counsel for