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Full opinion text

RIPPLE, Circuit Judge. The defendants have been convicted of violating various provisions of 21 U.S.C. §§ 841, 843 and 846, for their respective roles in a narcotics conspiracy. They have timely appealed their convictions on various grounds. For the reasons set forth in this opinion, we affirm the judgment of the district court. However, for certain defendants, we order limited remands for resentencing. I BACKGROUND On September 7, 2004, a grand jury indicted the defendants and many other individuals for various narcotics and firearm offenses. The indictment described the’ participation in a sprawling narcotics-distribution network on the west side of Chicago, Illinois, that had been in existence since 1998. A large part of the network consisted of a street gang called the “Mafia Insane Vice Lords” or the “Mafia Insanes.” That gang was organized hierarchically and employed violence to control “drug spots” where narcotics were sold. Individual sellers paid a fee to the gang’s leadership (a “street tax”) in return for supply of narcotics, protection and the ability to sell at the drug spots. Troy Martin was the founder and “king” of the Mafia Insanes. Eddie Bell and Donnell Simmons were high-ranking members of the Mafia Insanes’ leadership who supplied narcotics to the sellers and collected street taxes from the drug spots. Jerome Terrell was a member of another gang called the “Cicero Insane Vice Lords” and also supplied narcotics to Mr. Simmons. Mario Taylor was a member of another street gang called the “Four Corner Hustler” gang; Mr. Taylor coordinated the supply of narcotics to Mr. Simmons and Mr. Terrell. John Braboy assisted Mr. Taylor with packaging and transporting narcotics to Mr. Simmons. Many of the defendants pleaded guilty. The remaining defendants proceeded to trial. In August 2006, Messrs. Martin, Bell and two others were tried and convicted. In April 2007, Messrs. Taylor and Braboy were tried and convicted. In July 2007, Mr. Terrell was tried alone and convicted. At each trial, the Government’s evidence consisted primarily of wiretap recordings that the Government had obtained during its investigation into the conspiracy, as well as the testimony of police officers, federal agents and cooperating witnesses. Additional facts shall be provided on an issue-by-issue basis. II ANALYSIS A. Challenge to the Admissibility of the Wiretap Recordings 1. In December 2002, the Government began utilizing the procedures described in Title III of the Omnibus Crime Control and Safe Streets Act of 1968, see 18 U.S.C. §§ 2510-22, for intercepting wire communications of suspected members of the conspiracy. Several suspects’ phones were targeted during the Government’s investigation. We are concerned primarily with the Government’s wiretaps on the phones of Messrs. Martin and Simmons. Each time the Government desired to intercept communications on a particular phone, it sought authorization from the Chief Judge of the United States District Court for the Northern District of Illinois. Included with the Government’s wiretap applications were probable cause affidavits that identified the phone to be targeted and a description of the subject matter of the communication that the Government expected to intercept. The affidavits also described the bases for the Government’s belief that criminal matters would be discussed. The Chief Judge issued orders authorizing the interception of communications on the phones for thirty days at a time. If the Government desired to continue a phone intercept for longer than thirty days, the Government would submit to the Chief Judge a renewal application, including updated probable cause affidavits. The Government recorded the wiretap intercepts on magneto-optical (“MO”) disks. MO disks cannot be edited. At the completion of each thirty-day intercept period for a particular phone, irrespective of whether the Government had obtained an extension to continue its wiretap on that phone, the Government sealed, in the Chief Judge’s presence, the original MO disks. The Government kept the sealed MO discs in a DEA evidence vault. The Government made duplicate recordings of each MO disc for its own use in its pending investigation. Also, police officers created, in real time, line-sheets describing the substance of the intercepted communications. These line-sheets were disseminated to officers and used extensively in the Government’s pending investigation. The Government employed these procedures for wire communications on the suspects’ phones from approximately December 2002 until October 2003. With respect to the phones relevant on this appeal, the Chief Judge authorized the Government to wiretap Messrs. Martin’s and Simmons’s phones for the following periods: Mr. Martin’s target phone 2 from February 2003 to September 9, 2003, and Mr. Simmons’s target phone 4 from August 2003 to September 17, 2003. See Tr. at 55-58, 61-62, Mar. 3, 2006. In October 2003, the Government’s investigation was nearing an end, and the Government planned to arrest many of the suspects. The Government intended to play the wiretap recordings for the arrestees to facilitate the interrogations. However, on October 10, 2003, the Government discovered that some of its working copies of the communications on Messrs. Martin’s and Simmons’s phones were incomplete. On the same day, the Government informed the Chief Judge and sought permission to unseal the MO disks that had been stored in the DEA vault. On October 14, 2003, the first business day after the Columbus Day holiday, the court authorized unsealing. On that same day, the Government unsealed the recordings in its vault and discovered that portions of certain sealed MO discs were blank (hereinafter referred to as “the blank-sealed recordings”). Later, that same day, after receiving the Chief Judge’s permission to do so, the Government sealed reconstituted MO discs of the blank-sealed recordings, which the Government had created by duplicating its working copies; however, certain working copies of the blank-sealed recordings had been lost and, for those portions of intercepted communications, no reconstituted MO discs could be sealed. The takedown was delayed because of the problem with the tapes; the Government continued its investigation without using the blank-sealed recordings. For instance, the Government developed probable cause applications for wiretaps on additional suspects’ phones without reference to the contents of the blank-sealed recordings. According to one Government agent, the Government essentially “set [the blank-sealed recordings] aside and decided not to use them in any further enforcement action or investigation.” Tr. at 61, Mar. 3, 2006. Eventually the takedown occurred, and Mr. Martin was arrested. 2. During pretrial proceedings, Mr. Martin filed a motion to suppress, contending that the Government had violated the immediate sealing requirement of 18 U.S.C. § 2518(8)(a). R.626 at 1. In his view, the statute had been violated because the reconstituted copies had not been sealed immediately after the conclusion of the wiretaps. He requested an evidentiary hearing “to determine whether evidence resulting from the illegally intercepted conversations should be suppressed.” Id. at 2. The Government opposed the motion and Mr. Martin’s request for a hearing. R.882. The Government conceded that it had sealed MO discs that it believed to have contained recordings, but which were actually blank or partially blank. Id. at 1. However, the Government volunteered not to use any of the blank-sealed recordings as evidence at trial. Id. at 7. With respect to evidence derived from those recordings, the Government contended that the derivative evidence should be admissible for two reasons. First, the Government contended that, even though it would not use the blank-sealed recordings at trial, they were admissible in any event because the Government had a “satisfactory explanation” for the non-sealing: “DEA technician error.” Id. at 9-10. Second, the Government contended that evidence derived from the blank-sealed recordings, before the sealing obligation arose for those recordings, should be admissible because 18 U.S.C. § 2517(l)-(2) permits the use of recordings for investigatory purposes. Id. at 11-12 (citing United States v. Donlan, 825 F.2d 653, 657 (2d Cir.1987)). Confronting the prohibition in § 2518(8)(a) against the use or disclosure at trial of evidence derived from unsealed recordings, the Government contended that the prohibition should not be applied strictly. The Government urged the district court to adopt the United States Court of Appeals for the Second Circuit’s broad construction of the statute, as explained in United States v. Donlan, 825 F.2d 653 (2d Cir.1987). In response, Mr. Martin contended that no excuse could justify the major delay in sealing that had occurred in his case. R.927. He refuted the Government’s proposed excuse — operator error — as unsupported by the record because the Jasevicius affidavit stated that the DEA “was unable to conclude why the error occurred.” Id. at 3. Furthermore, Mr. Martin contended that the Supreme Court of the United States has not endorsed “mistaken belief’ as a satisfactory explanation for a sealing error. Id. at 3-4 (citing United States v. Ojeda Rios, 495 U.S. 257, 110 S.Ct. 1845, 109 L.Ed.2d 224 (1990)). Nor was lack of proof of alteration sufficient to excuse the sealing error because, according to the Supreme Court, “ ‘[t]o hold that proof of nontampering is a substitute for a satisfactory explanation is foreclosed by the plain words of the sealing provision.’ ” Id. at 3 (quoting Ojeda Rios, 495 U.S. at 264, 110 S.Ct. 1845). Finally, Mr. Martin contended that no derivative evidence should be admitted because Donlan and its broad construction of § 2518(8)(a) misunderstood “the context of the entire statute.” Id. at 4. The district court held an evidentiary hearing on the motion to suppress. The district court stated that, because the Government had volunteered not to use the actual tapes, the district court understood Mr. Martin’s motion only to apply to “any information that’s derivative of the tapes.” Tr. at 3, Feb. 17, 2006. The district court wanted to know “exactly what information we are talking about.” Id. In response, the Government explained that it had planned to use the blank-sealed recordings in draft affidavits and complaints to secure arrest warrants in October 2003. Id. at 11-12. Then, when the sealing problem was discovered in mid-October, the Government scrapped those drafts and decided simply to exclude the problematic calls from its investigation from that point forward. Id. However, the Government conceded that it had used information obtained from the blank-sealed recordings in order to prepare officers while the wiretaps were still active — ie., during the investigation. Id. at 11. The Government raised its two arguments for why the derivative evidence — any derivative evidence — was admissible: the satisfactory excuse for non-sealing and the broad interpretation of § 2518(8)(a). At the evidentiary hearing, Mr. Martin contended that the Government had the burden to show what evidence was derived from the blank-sealed recordings. Id. at 14, 22, 36, 39. He contended that the Government had failed to meet its burden, but, in any event, he posited that the derivative evidence was extensive because “during each one of these tapings [the Government] ha[d] agents monitoring these calls,” “making line sheets and making summaries of the calls,” and “making transcripts of the calls.” Id. at 14; see also id. at 37. Mr. Martin contended that the line-sheets, summaries and transcripts were used throughout the Government’s investigation, which “mushroom[ed] out from the wiretaps.” Id. at 14-16; see also id. at 20 (“There is no way we can now go back and sort out and say, ‘Well, they didn’t use that[,] ... they erased the knowledge that they obtained.’ ”). Mr. Martin suggested that if the Government could not establish what derivative use was made of the blank-sealed recordings, the proper sanction would be to dismiss the indictment. Id. at 21-22. He also reiterated his opposition to the Government’s two arguments for the admissibility of the derivative evidence. The district court suggested that this case was sui generis because the Government made a mistake in recording, not in sealing. Id. at 30-31. The district court stated, “I am really uncomfortable with the idea that we ought to somehow say that everything during the taped period is off the — is somehow tainted in a way that requires dismissal of the indictment.... It seems to be a sledgehammer of relief when what we really need is much more of a precision tool.” Id. at 33. Instead, the district court requested more information about how the Government had used its copies of the blank-sealed recordings and clarification on what exactly was derived from them. Id. at 34. Another hearing was held, and Mr. Martin cross-examined DEA special agent Jeffrey Konvalinka, who had managed the investigation and the wiretap operation. Mr. Martin’s counsel asked Agent Konvalinka about when and how the blank-sealed recordings were used. See generally Tr. at 70, Mar. 3, 2006 (describing how summaries and line-sheets were prepared as calls were recorded); id. at 71-72, 74-75 (describing how information derived from the blank-sealed calls was routed to officers to assist their surveillance efforts). Mr. Martin argued to the district court that the Government used the blank-sealed recordings to secure additional wiretap authorizations and, thus, that the sealing problem was so pervasive that the indictment must be dismissed. See id. at 104. The district court declined to rule, despite the Government’s request that the court do so, on the Government’s first argument for admissibility: that the Government had a satisfactory explanation for the sealing error. The district court considered that issue to be “moot,” because the court found that the blank-sealed recordings “were not used in connection with any ongoing arrests,” “weren’t presented to the grand jury,” “weren’t used in any affidavits for purposes of search warrants,” “weren’t used to draft any complaints,” and “weren’t used in connection with obtaining an indictment.” Id. at 99, 101. The district court stated, “I haven’t heard about what specific improper use of any of this evidence has happened.” Id. at 100. Nevertheless, the district court seems to have concluded that at least some evidence was derived from the blank-sealed recordings. The district court noted that the Government stopped using the blank-sealed recordings as soon as the sealing error was discovered and did not intend to use them as evidence at trial. Thus, the district court ruled that “the motion is effectively granted without objection.” Id. at 99. Mr. Martin proceeded to trial, during which 160 incriminating recordings of calls from the wiretapped phones and transcripts of the calls were admitted into evidence. See generally Trial Tr. at 85-86, 95-96, 103, 107, Aug. 30, 2006. Neither the blank-sealed recordings nor any transcripts of those recordings were admitted. Mr. Martin was convicted and sentenced to life in prison. Mr. Martin appealed his conviction to this court, contending that the district court had erred by refusing to dismiss the indictment. After hearing oral arguments and considering the parties’ submissions, we maintained jurisdiction over the case and granted a limited remand to the district court to rule on whether the Government had a satisfactory explanation for the sealing error, the issue it had pretermitted earlier. See App. R.112 (No. 07-2272). The district court considered the issue and ruled that “the government’s explanation for its failure to seal is satisfactory.” R.2374 at 3. The district court noted that the Government never has stated definitively the cause for the sealing error, but believed it was caused by operator error. The district court applied the framework articulated in United States v. Coney, 407 F.3d 871, 875 (7th Cir.2005), and concluded that the Government’s explanation was satisfactory. The district court noted that the Government’s explanation was believable because all of the Government’s actions had been consistent with its reasonable belief that it had, in fact, properly sealed the blank-sealed recordings. The district court did not find the length of delay in sealing to be “troublesome.” Id. at 4. The district court believed the nature of the crime charged and the relative lack of notoriety of the defendants tended to support the Government’s explanation because nothing about this narcotics conspiracy case was unusual. Finally, the district court considered the importance of the problematic recordings to be minimal because the Government did not use them once it realized that the sealing error had occurred and because they played no part during the trial. 3. The parties’ contentions before this court largely mirror the arguments made during the district court proceedings. Mr. Martin contends that the district court misapplied § 2518(8)(a). He contends that the district court should have found that the Government lacked a satisfactory explanation for the sealing error. He further contends that so much evidence was derived from the blank-sealed recordings that, without a satisfactory explanation for the sealing error, much of the Government’s evidence at trial should have been excluded. He asks that his conviction be reversed. The Government concedes that the reconstituted recordings were not tendered for judicial sealing immediately upon the expiration of the wiretap authorizations. The Government urges us to interpret § 2518(8)(a) broadly so as not to require suppression of the derivative evidence. Alternatively, the Government contends that the operator error and the Government’s good-faith attempt to comply with the sealing requirement constitute satisfactory explanations for its failure to comply with the sealing statute. 4. Title III of the Omnibus Crime Control and Safe Streets Act of 1968 established a comprehensive statutory regime by which the Government may intercept wire, oral or electronic communications. See 18 U.S.C. §§ 2510-22; Clifford S. Fishman & Anne T. McKenna, Wiretapping and Eavesdropping: Sw"veillance in the Internet Age § 1:10 (3d ed.2009) (providing background); Wayne R. LaFave et al., Criminal Procedure §§ 4.5-4.6 (5th ed.2009) (discussing the history of the Act and its amendments). The Act created procedural safeguards to protect individuals’ privacy and to prevent other forms of misuse of wiretapping. See generally 18 U.S.C. § 2518 (establishing wiretap authorization procedures for the Government). One of the safeguards of this statute is a provision where-by wiretap intercepts may be authorized only for thirty days at a time; any extension must comply with the same procedures required to obtain an initial wiretap authorization. See 18 U.S.C. § 2518(5). The Act also strictly regulates how intercepted communication may be used or disclosed during and subsequent to a Government investigation. See generally 18 U.S.C. § 2517. The Act requires that wiretap intercepts “shall, if possible, be recorded ... in such a way as will protect the recording from editing or other alterations.” 18 U.S.C. § 2518(8)(a). “Immediately upon the expiration of the period of the [wiretap authorization] order, or extension thereof, such recordings shall be made available to the judge issuing such order and sealed under his directions.” Id. The purpose of this sealing requirement “is to ensure the reliability and integrity of evidence obtained by means of electronic surveillance.” United States v. Ojeda Rios, 495 U.S. 257, 263, 110 S.Ct. 1845, 109 L.Ed.2d 224 (1990). “[T]he seal is a means of ensuring that subsequent to its placement on a tape, the Government has no opportunity to tamper with, alter, or edit the conversations that have been recorded.” Id. We apply the immediacy requirement strictly. See United States v. Coney, 407 F.3d 871, 873 (7th Cir.2005) (“ ‘The term “[i]mmediately” means that the tapes should be sealed either as soon as practical after the surveillance ends or as soon as practical after the final extension order expires.’ ” (quoting United States v. Williams, 124 F.3d 411, 429 (3d Cir.1997))); see also Fishman & McKenna, supra, § 19:10 (discussing other circuits’ application of the immediacy requirement). The Supreme Court also has stated that “ § 2518(8)(a) applies to a delay in sealing, as well as to a complete failure to seal, tapes.” Ojeda Rios, 495 U.S. at 264, 110 S.Ct. 1845. Similarly, we believe that what occurred in this case, sealing blank recordings, does not comply with the sealing requirement. Cf. id. at 263, 110 S.Ct. 1845 (“The presence or absence of a seal does not in itself establish the integrity of electronic surveillance tapes. Rather, the seal is a means of ensuring that subsequent to its placement on a tape, the Government has no opportunity to tamper with, alter, or edit the conversations that have been recorded.”). Nor is the sealing of line-sheets or call summaries a proper method of compliance. The sealing provision includes its own exclusionary remedy: “The presence of the seal provided for by this subsection, or a satisfactory explanation for the absence thereof, shall be a prerequisite for the use or disclosure of the contents of any wire, oral, or electronic communication or evidence derived therefrom under subsection (3) of section 2517.” 18 U.S.C. § 2518(8)(a). The Supreme Court has noted that the satisfactory explanation prong of § 2518(8)(a) “require[s] that the Government explain not only why a delay occurred but also why it is excusable.” Ojeda Rios, 495 U.S. at 265, 110 S.Ct. 1845. In Ojeda Rios, the Supreme Court concluded that the Government’s “good-faith, objectively reasonable misunderstanding of the statutory term ‘extension’ ” was a satisfactory explanation for the Government’s failure to seal immediately wiretap recordings. Id. at 264-66, 110 S.Ct. 1845. The Supreme Court insisted on a showing of “good cause for the sealing delays” and rejected the Government’s attempt to show merely that no tampering with the recordings had occurred. Id. at 264-65, 110 S.Ct. 1845 (“To hold that proof of nontampering is a substitute for a satisfactory explanation is foreclosed by the plain words of the sealing provision.”). We have noted that “what should be deemed ‘satisfactory’ in the context of a statute aimed at preventing government tampering with electronic evidence” must depend largely on “the statutory objective.” Coney, 407 F.3d at 875. A satisfactory explanation must dispel any reasonable suspicion of tampering, and also must be both accurate and believable. Id. Whether the explanation is satisfactory also may depend on the delay in sealing, unique pressure on the Government to obtain a conviction due to particularly notorious charges or defendants, the importance of the recordings to the Government’s case and whether the Government has established a procedure for complying with its sealing obligations. Id.; cf. United States v. Mora, 821 F.2d 860, 867-69 (1st Cir.1987) (listing additional factors that the court believed contributed to satisfactoriness but stressing “that there is no stock formula by which the adequacy of an explanation can invariably be gauged”). In Coney, we applied these principles and held that “mixed-signals” between Assistant United States Attorneys qualified as a satisfactory explanation for a ten-day delay in sealing. Coney, 407 F.3d at 875. In other cases, we have concluded that a prosecutor’s mistaken belief, caused by recording technicians’ delay, about the time needed to secure a replacement recording device constituted a satisfactory explanation, see United States v. Jackson, 207 F.3d 910, 918 (7th Cir.), judgment vacated on other grounds, 531 U.S. 953, 121 S.Ct. 376, 148 L.Ed.2d 290 (2000), as did a bureaucratically caused delay, see United States v. Plescia, 48 F.3d 1452, 1463 (7th Cir.1995). We review for clear error a district court’s conclusion that the Government’s explanation for failing to seal immediately wiretap recordings is satisfactory. See Coney, 407 F.3d at 874. 5. We begin by noting that evidence was derived from the blank-sealed recordings. Although the district court did not specify the extent of the derivative evidence, it stated that “it is theoretically possible that some information that shows up in the line records or in the transcripts was in the minds of agents when they went out and did their further investigation,” Tr. at 99, Mar. 3, 2006, and the district court recognized that the blank-sealed recordings had been included in the Government’s probable cause affidavits to obtain additional wiretap authorizations, id. at 104; see also supra note 10. We also believe the factual record would support a finding that at least some derivative evidence existed. Our review of the record reveals that portions of the Government’s investigation relied on, at least in part, the contents of the blank-sealed recordings. For example, excerpts of probable cause affidavits show that the Government frequently cited the communication heard on the blank-sealed recordings to secure subsequent wiretap authorizations. See, e.g., R.882-7 at 425; R.882-8 at 253, 255-56, 293; R.882-9 at 341-42. Also, Agent Konvalinka testified that the contents of the blank-sealed recordings were relayed to other officers to assist with the pending investigation. Because the Government voluntarily suppressed the blank-sealed recordings themselves, the derivative evidence properly was the subject of Mr. Martin’s motion to suppress. As we have noted earlier, the district court, applying the factors set forth in Coney, concluded that the derivative evidence need not be excluded because the Government provided a satisfactory explanation for its improper sealing. We agree. The record establishes that operator error most likely caused the blank-sealed recordings to be defective. The district court placed this error in the proper context. The error had more to do with the mechanics of the recording process than with the Government’s established sealing procedures. Throughout the course of its investigation, the Government acted consistent with its sealing obligations and attempted in good faith to rectify its sealing error once it was discovered. The statutory objectives were essentially satisfied: The Government obtained valid judicial authorization for its wiretap intercepts, recorded the communications onto non-editable MO discs and sealed original copies of the MO discs with judicial authorization. The fact that a few of those tapes were defective was unknown until the Government’s investigation nearly was completed, and the sealing error certainly did not interfere with the statutory objectives of ensuring judicial oversight and non-tampering with wiretap recordings. Cf. Ojeda Rios, 495 U.S. at 266-67, 110 S.Ct. 1845 (concluding that the Government’s understanding of the law of extensions was erroneous but, nonetheless, did not interfere with the statutory objectives, and, thus, qualified as an objectively reasonable excuse for the Government’s sealing delay). Mr. Martin has not alleged that the Government obtained a tactical advantage by sealing the blank MO discs, that the Government procrastinated or otherwise acted in bad faith. Indeed, the record is completely devoid of any such evidence. Cf. United States v. Quintero, 38 F.3d 1317, 1328-30 (3d Cir.1994) (rejecting the prosecutor’s heavy workload as a satisfactory explanation for a sealing delay because to do so “would be rendering extraordinary that which is ordinary”); United States v. Carson, 969 F.2d 1480, 1498 (3d Cir.1992) (rejecting the need to enhance the audibility of tapes as a satisfactory explanation for a sealing delay because that need was “readily foreseeable and could just as readily become routine”). We believe the context in which the sealing error occurred in this case supports the Government’s explanation. Although the delay in sealing was significant — approximately thirty-eight days for the reconstituted recordings, and never for the recordings that were lost, see supra note 7 — the Government exhibited substantial compliance with the immediacy requirement by attempting to address the sealing error the same day the Government discovered that it had occurred. We agree with the district court that the delay in sealing is excusable under these circumstances. The charges in this case were unexceptional, and the record does not suggest that the defendants were particularly notorious. The Government had no unique incentive in this case to ignore intentionally its sealing obligations. See Coney, 407 F.3d at 875. The Government had well-established procedures in place to ensure compliance with its sealing obligations, a consideration that contributes to the believability of the Government’s explanation. Cf. id. (noting that the Assistant United States Attorneys had established a procedure for complying with their statutory sealing duties). For example, although the Government was obligated to seal the wiretap recordings only upon the expiration of the final extension period for Messrs. Martin’s and Simmons’s phones, see 18 U.S.C. § 2518(8)(a), the Government sealed the MO discs upon the completion of each thirty-day authorized period, see R.882 at 2. In this regard, the Government followed established Department of Justice protocols. Finally, we agree with the district court’s conclusion that the blank-sealed recordings were of relatively minor importance to the Government’s case. The Government’s voluntary suppression of the recordings themselves indicates how small a role they played in the Government’s case against Mr. Martin. Although our review of the probable cause affidavit excerpts reveals that the contents of the blank-sealed recordings were used to obtain certain wiretap extensions, they were hardly the linchpin of these affidavits. Furthermore, the blank-sealed ■ recordings were a small subset of the wiretap recordings the Government created in this case, most of which were sealed properly. The blank-sealed recordings’ minimal importance contributes to our conclusion that the Government’s explanation is satisfactory. The Government provided a satisfactory explanation in this case and therefore no evidence was excludable under § 2518(8)(a). We therefore affirm the ruling of the district court that the Government’s explanation was satisfactory. B. Sixth Amendment Challenges 1. Messrs. Martin, Bell and Terrell contend that the district court violated their Sixth Amendment rights by limiting then-ability to cross-examine James Rudy Taylor (“Rudy”). Rudy was a member of the Mafia Insanes who worked for Mr. Simmons and managed a drug spot. Rudy was a named defendant in the indictment. He eventually pleaded guilty and entered into a cooperation plea agreement with the Government whereby he agreed to testify against Messrs. Martin, Bell and Terrell, among others, in exchange for a Government recommendation that he receive a reduced sentence. See R.737-38, 764. During the Martin/Bell trial, defense counsel informed the district court that the defense intended to cross-examine Rudy about his involvement in a pending state murder investigation being conducted by the Police Department in Maywood, Illinois. Defense counsel knew that, when Rudy was arrested by federal agents for his role in the Mafia Insanes conspiracy, the Government had made Rudy available to the Maywood Police for questioning. Defense counsel believed that Rudy had given a statement to the Maywood police concerning his involvement in the murder of an individual named Curtis Rios. Defense counsel asked the district court to permit cross-examination of Rudy about whether he expected to receive any benefit in the state murder investigation in return for giving testimony in the Martin/Bell trial. The Government contended that the defense should not be permitted to question Rudy about the pending state murder investigation. The Government said that it had arranged no benefit for Rudy with the Maywood investigators in exchange for his cooperation in the federal case. According to the Government, the federal investigators had “talked with Maywood about working some type of concurrent deal. They were unwilling to do it, so we didn’t do anything with it. That’s it.” Trial Tr. at 1606, Sept. 18, 2006. The Government argued that under Federal Rule of Evidence 609, the Maywood murder investigation was not a proper subject for cross-examination because Rudy had not been convicted; nor was it admissible under Rule 608(b) because the alleged offense “has nothing to do with truth-telling.” Id. at 1607. The Government also informed the defense and the district court that, if asked about the Maywood murder investigation, Rudy intended to invoke his Fifth Amendment right not to incriminate himself. Id. at 1605. The district court stated, “Whether it’s a murder or a traffic offense, if it’s an arrest, it’s not admissible unless there is a benefit given. And I understand, from what everybody tells me, there has not been a benefit given.” Id. at 1606. The district court also noted that the statement given to the Maywood investigators could be used by the defense to impeach Rudy if he testified about the Maywood murder on direct. Id. at 1607. However, the district court did not know whether that contingency would occur. It therefore permitted a voir dire of Rudy to determine whether he intended to testify about the Maywood murder and whether he expected to receive any benefit in that case in exchange for his cooperation in the federal action. Id. at 1607-08. A voir dire was conducted. Defense counsel asked Rudy if he had given a statement concerning the murder of Curtis Rios. Rudy declined to answer, invoking the Fifth Amendment. Id. at 1610. Defense counsel then asked Rudy whether he expected to receive any benefit from the Government in exchange for his cooperation in the federal action. Rudy said that he expected to receive no benefits. Id. at 1610-15. At a sidebar, the district court told defense counsel, If you can establish that [Rudy] has an expectation that he is getting a pass on something out in Maywood as a result of his testimony here, I will then allow you to ask about what it is out in Maywood that he thinks he is getting a pass on. But until that predicate has been laid, there is no basis to inquire into this. And I will just tell you, the 403 balancing goes in favor of the government as well. I’m not — I don’t think it’s appropriate to ask about this, as I understand it, unrelated murder. Id. at 1622. Defense counsel contended that the Maywood murder was related to the drug activity charged in the federal indictment. Id. Defense counsel wanted to clarify whether Rudy intended to invoke the Fifth Amendment if asked about the murder. Id. at 1623. The district court stated, “I don’t think there is any basis, from what I have heard right now, that we ought to even open the door to his taking the Fifth on this. Nor do I think there is any particular benefit to the defendants in letting the jury know that there was a gang-related murder.” Id. at 1627. The district court proposed that defense counsel focus its voir dire questions on whether Rudy expected any deal from the May-wood investigators. Id. Instead, defense counsel asked Rudy about his plea agreement with the Government and what he expected to gain from testifying in the Martin/Bell trial. Id. at 1628. Obviously confused by defense counsel’s questions, Rudy said he expected to receive no benefits at all. Id. The district court interjected and asked Rudy if he understood that, in the written plea agreement with the Government, the Government agreed to recommend a reduced sentence for Rudy in the federal action in return for his cooperation. Id. Rudy confirmed that that was his understanding, and he indicated that he understood that the Government’s favorable recommendation at his sentencing hearing would depend on whether he told the truth during his trial testimony. Id. at 1628-29. The district court asked Rudy, [H]ave you received any other agreement from the government? Have they offered you anything else? ... Has the government offered you any benefits in any other ease? ... Has the government offered to do anything for you in connection with any other charges? ... Is it your expectation or hope that the government is going to do something in some other case for you? Id. at 1629-30. Rudy answered no to each of those questions. Id. Defense counsel then resumed the voir dire questioning and asked Rudy if it was his “understanding that a member of the U.S. Attorney’s Office called the State’s Attorney’s office out in Maywood?” Id. at 1630. Rudy said no. Id. Defense counsel asked, “Did your lawyer talk to you at all about any efforts on the part of the U.S. Attorney to work out your case, your prospective case, in Maywood?” Id. The district court interjected and said, “I want to tell the witness that he has permission not to answer questions about communication with his lawyer.... It doesn’t relate to the Fifth Amendment. It’s an independent privilege.” Id. at 1630-31. Defense counsel then asked Rudy, “Sir, do you expect to be charged out in Maywood?” Id. at 1631. The Government objected and complained that the question “go[es] back to the statement again.” Id. The district court sustained the objection and said, “I think we should bring the jurors in. We are not going to pursue this line of questioning in the jurors’ presence unless the witness’ testimony changes.” Id. Defense counsel sought to clarify the ruling and asked, “Judge, are we precluded from any other questions about benefits when he is on the stand?” Id. at 1632. The district court stated, “No. You are welcome to ask questions about benefits, without reference to this — .” Id. Unsatisfied, defense counsel sought permission to continue the voir dire and ask additional questions about the Maywood murder, which the court allowed. The following colloquy occurred: [DEFENSE COUNSEL]: Are there any outstanding offenses that you are concerned about the Judge knowing about at this point? [THE GOVERNMENT]: Objection, Judge. It’s forcing this witness to take Five on this again. [DEFENSE COUNSEL]: I am not asking him to take Five. I am only asking him whether or not he is concerned about it. [THE GOVERNMENT]: If he says yes, the next question is what offenses? Judge. And then we are back to the statement. [DEFENSE COUNSEL]: That wasn’t going to be my next question, Counsel. [THE GOVERNMENT]: If he says he is concerned, it also is potentially admissible. THE COURT: Look, there are ways that you can ask questions that would elicit this. I have made a 403 decision here that we ought not proceed down this line. So questions that are designed to elicit evidence concerning the episode in Maywood, I am going to sustain those objections, unless there is an indication that the witness has a genuine expectation of a benefit in connection with that. And there has been no such showing. Id. at 1634. Still unsatisfied, defense counsel sought permission to continue the voir dire and ask additional questions about benefits Rudy expected to receive from his cooperation. The district court allowed further questioning. Defense counsel asked Rudy about his plea agreement, and Rudy confirmed that it was his understanding that, in return for his guilty plea and truthful testimony in the federal action, the Government would recommend that he receive a lower sentence. Id. at 1636. The Government asked to clarify the record and asked Rudy, “Sir, if you have cases out in Maywood, or potential eases, do you understand that by cooperating with the government that those will go away?” Id. Rudy answered, “No.” Id. at 1637. Defense counsel then asked, “Do you expect the government to do anything whatsoever to try to help you in that potential case in Maywood?” Id. Rudy responded, “I refuse to answer, your Honor.... I plead the Fifth.” Id. Defense counsel said, “That’s the crux of this, Judge____That’s it.” Id. The district court stated, “It isn’t the crux. The witness has testified about this matter. I don’t think we should pursue it any longer.” Id. The voir dire ended. The trial resumed, and Rudy testified on behalf of the Government, describing his role in Mr. Simmons’s drug operation and, more generally, the involvement of the Mafia Insanes gang. See id. at 1645, 1669-71, 1679-81. Defense counsel did not cross-examine Rudy about the Maywood murder investigation. However, defense counsel attempted to impeach Rudy in other ways. For example, defense counsel asked Rudy about his prior arrests and about aliases that he had given to the police during those arrests. See id. at 1706-08. Defense counsel also asked Rudy about his prior drug abuse. See id. at 1715-17. Defense counsel asked Rudy why he left certain information out of his proffer statement given to the DEA. See id. at 1721-22. Defense counsel also asked Rudy about minor inconsistencies in his testimony. See id. at 1763. Finally, defense counsel asked Rudy about the plea agreement with the Government; Rudy confirmed that, if he testified truthfully, the Government would dismiss certain charges pending against him and recommend that he be sentenced at a level one-third below the low end of his applicable Guidelines range. See id. at 1723-26, 1732-37. The trial continued, and other witnesses offered testimony that further incriminated the defendants. Messrs. Martin and Bell ultimately were convicted and sentenced. 2. Approximately a year after the Martin/Bell trial had concluded, Mr. Terrell was tried separately, and the Government again called Rudy as a cooperating witness. The Government reminded the district court about the substance of Rudy’s testimony in the Martin/Bell trial. The Government asked for the same evidentiary ruling barring cross-examination concerning the Maywood murder investigation. The district court asked defense counsel if she objected, to which she responded, “[T]he only thing I would ask is for another voir dire so we can talk to him and make sure he doesn’t think that this murder that he confessed to is in any way associated with the deal he is getting from the government.” Trial Tr. at 341, Jul. 12, 2007. The district court asked the Government to begin, and the following voir dire occurred: [BY THE GOVERNMENT:] Q. [Rudy], you were questioned by people from the Maywood Police Department about a shooting, weren’t you? A. Yes, sir. Q. You have got a cooperation deal in this case, don’t you? A. Yes, sir. Q. Do you understand that cooperation deal to have taken care of any possible situation you have in Maywood? A. No, sir. Q. Do you know if the United States Attorney’s Office or DEA or anybody reached out to Maywood to, I guess for lack of a better term, make that case go away? A. No, sir. Q. What is your cooperation agreement — what charges do you understand your cooperation agreement to take care of or resolve? A. Contending this case here that I am on. Q. Just this case? A. Yes. Q. Does it take care of any other possible charges? A. No, not to my knowledge. [THE GOVERNMENT:] I don’t have any further questions, your Honor. [THE COURT:] Any cross-examination ... ? [DEFENSE COUNSEL:] Thank you. [BY DEFENSE COUNSEL:] Q. Have you been charged with stuff in Maywood? A. I plead the Fifth on that. Q. Do you know if any charges have been filed against you? A. Yes, sir — yes, ma'am. Q. They have been filed against you? A. The charges that I am up against now. Q. In Maywood, out of that? A. I plead the Fifth on that. [DEFENSE COUNSEL:] Your Hon- or, I think he waived it by answering their questions. And now to invoke it for just this limited part — • [THE GOVERNMENT:] Judge, if I can just step in for a moment. [Rudy’s counsel] was here this morning. I absolutely do not want to get into what [she and Rudy] talked about ... but it would be — I guess I understand that this is not an area where he is going to be willing to answer any questions on. Maybe it makes sense to get [Rudy’s counsel] here if this is going to be something that we need to go into, but my sense is we have covered this ground already. Nothing has changed since then. [THE COURT:] Here is what I want to do. I am going to bring the jury back right now, and what we can do with respect to this issue is get [Rudy’s counsel] over here, see whether that changes anything with respect to whether or not he is willing to answer the question about whether charges have been filed. And if we need to reopen his testimony for some reason, we can do that. Id. at 342-44. Mr. Terrell’s defense counsel did not object to that plan. The trial resumed and Rudy testified about Mr. Terrell’s role in the Mafia Insanes conspiracy. Defense counsel did not cross-examine Rudy about the Maywood murder investigation. However, defense counsel impeached Rudy by asking him about prior inconsistent statements that he had given to police and agents, see id. at 381-83, 386-87, his prior charges, see id. at 387-90, and about his plea agreement with the Government, see id. at 400-02. Rudy’s testimony concluded, and he was excused. Later in the trial, the district court returned to the issue of Rudy’s testimony and summoned Rudy for an additional voir dire. Rudy’s counsel appeared and the following exchange occurred: [BY THE GOVERNMENT:] Q. I just have a few questions for the purpose of follow-up. [Rudy], we talked about your plea agreement previously. Do you understand that cooperation/plea agreement that you have to extinguish or take care of any potential cases that might arise in Maywood, Illinois? A. No, sir. Q. And so do you understand that you received a benefit regarding anything that might have happened in Maywood, Illinois from the United States Attorney’s Officer in connection with your plea agreement? A. No, sir. [THE GOVERNMENT:] No further questions, Your Honor. The Court: Cross-examination? [DEFENSE COUNSEL:] Thank you. [BY DEFENSE COUNSEL:] Q. Now, the case that we’re talking about is a case in Maywood involving a murder, correct? A. Yes, yes, ma'am. Q. And you were questioned about that murder the day you were arrested on this case, right? [RUDY’S COUNSEL:] Your Honor— BY THE WITNESS: A. Plead the Fifth. [RUDY’S COUNSEL:] — I would object to this. I think that [Rudy] has a right to exercise his Fifth Amendment if we’re going to talk about the statement. THE COURT: Well, the question was: Were you questioned about that Murder? [DEFENSE COUNSEL:] Yeah, I’m not going to get into— THE COURT: Overruled. You may answer. Were you questioned about that murder when you were arrested back in '04 in this case? BY THE WITNESS: A. I was asked about it. [BY DEFENSE COUNSEL:] Q. Okay. And have you been — are there any charges resulting from that murder against you currently? A. No, ma'am. Q. Okay. So you — do you have any cases at all pending anywhere else but the case that’s here right now? A. Traffic, traffic, ma'am. Q. Okay. Now, are you aware if the federal government has spoken to any of the assistant state’s attorneys out in Maywood regarding that case? A. No, ma'am. Q. Do you believe that you are going to be indicted in that Maywood case? A. No, ma'am. Q. Do you believe that your cooperation in this case, meaning your testimony against other people in this case and in other federal cases, is going to help you so you won’t be charged in that Maywood case? A. No, ma'am. [DEFENSE COUNSEL:] Nothing further. THE COURT: All right. Do we need to take any further steps with this witness? [DEFENSE COUNSEL:] I do not. Trial Tr. at 566-69, Jul. 16, 2007. The voir dire concluded, and Rudy was excused. The trial resumed, and Mr. Terrell’s defense counsel did not raise the Rudy cross-examination issue again. Mr. Terrell ultimately was convicted. Mr. Terrell filed a post-trial motion for acquittal, contending that the district court’s earlier ruling circumscribed improperly his cross-examination of Rudy. See R.1875. The motion stated that Mr. Terrell was prevented from determining whether Rudy “may have had [a subjective belief] regarding any promise the state made to him regarding possible murder charges not being brought in exchange for his testimony in this conspiracy trial.” Id. at 1. The motion continued, “In light of the fact [that Rudy] was arrested on this conspiracy charge and immediately brought to the Maywood Police Department in reference to the murder charge, the substance of the conversation [he] had with the May-wood police would be relevant as to the reasonableness of his subjective belief.” Id. at 2. The motion did not allege specifically that the district court’s ruling violated Mr. Terrell’s constitutional rights. Soon thereafter, Mr. Terrell substituted counsel, and his new counsel filed an amended post-trial motion, renewing the contention that the district court’s ruling limiting the cross-examination of Rudy about the Maywood murder investigation was erroneous. Specifically, Mr. Terrell contended, “By denying Mr. Terrell the right to investigate this weakness in [Rudy’s] testimony, the [district court] violated Mr. Terrell’s right under the Confrontation Clause. U.S. Const. Amnd. V[sie].” R.1890 at 3. The Government opposed the motion, contending that Mr. Terrell had waived his opportunity to challenge the district court’s ruling. See R.2026 at 9. The Government noted that, when it had sought the same evidentiary ruling that the district court had made in the previous Martin/Bell trial, Mr. Terrell’s trial counsel never objected and only requested that a voir dire occur. See id. at 10. The Government stated that “defense counsel even confirmed after the voir dire that the voir dire questioning was all that counsel sought.” Id. at 11 (citing Trial Tr. at 569, Jul. 16, 2007). The Government further argued that, in any event, Mr. Terrell’s complaint was meritless because Rudy had denied any expectation of benefit related to the Maywood murder investigation and that Rudy’s alleged motive to lie was purely speculative. Id. at 11-12. The Government also contended that “cross-examination on this topic would [have] ... cause[d] much confusion and waste of time,” “precisely the sort of confusion and waste that Federal Rule of Evidence 403 would prohibit.” Id. The Government noted that “[o]f course, [the district court] did not even have to make a specific Rule 403 determination during Terrell’s trial because he waived the issue after the satisfactory voir dire.” Id. at 12. The district court denied the motion; it ruled that Mr. Terrell’s right to confrontation had not been violated by the ruling limiting cross-examination of Rudy. See R.2130. The district court explained, “The right of confrontation does not require that a defendant be permitted to explore any and all avenues of bias. Nor was [Rudy’s] testimony the only (or even the most important) evidence against the Defendant. The court concludes that a new trial is not warranted due to this evidentiary ruling.” Id. at 2 (internal citations omitted). 3. Messrs. Martin, Bell and Terrell appeal the district court’s rulings limiting their ability to cross-examine Rudy about the Maywood murder investigation. They contend that the Sixth Amendment guaranteed them the right to cross-examine Rudy in front of the jury about whether he was biased in favor of the prosecutors because of his desire to secure their assistance with the pending Maywood murder investigation. See Martin/Bell Appellant’s Br. 9-10; Terrell Appellant’s Br. 13. The defendants suggest that they should have been permitted to establish the following facts before the jury: “1) that [Rudy] was suspected of murder in state court; 2) that [Rudy] had not yet been prosecuted for that murder; 3) that [Rudy] was first informed of that murder investigation immediately following his arrest by the federal government in this case; 4) that the federal authorities delivered [Rudy] to the state officials for interrogation regarding that murder; 5) that [Rudy] had made a statement to state authorities admitting his involvement in the murder; and 6) that [Rudy] was never prosecuted for the murder to which he confessed after he began cooperating with federal authorities.” Martin/Bell Appellant’s Br. 10. They explain that, “[b]ased on these facts, a reasonable juror could infer that [Rudy] was manufacturing incriminating testimony against the defendant-appellants in order to minimize his culpability in the investigation and avoid prosecution for the murder.” Id.; see also id. at 13-14, 17-19. Messrs. Martin, Bell and Terrell emphasize that Rudy’s alleged bias arising from his expectation of a benefit in the Maywood murder investigation was a “core” concern of the Sixth Amendment because it represented “an entire source of bias” that the jury never heard about. Id. at 11-14. They point to Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986), and Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974), decisions establishing that cross-examination regarding a witness’s bias created by the threat of prosecution for matters unrelated to the crime about which the witness testifies is a core concern of the Sixth Amendment. See Martin/Bell Appellant’s Br. 14. They contend that all of Rudy’s testimony should have been stricken or a mistrial declared because Rudy relied on the Fifth Amendment when he was asked about the Maywood murder investigation. Id. at 21-23. They believe that Rudy’s bias was a core concern of the Sixth Amendment, and, therefore, his Fifth Amendment right should not have trumped the defendants’ Sixth Amendment rights. The Government contends that the Sixth Amendment does not guarantee an unfettered right to cross-examine and that the right may be limited by courts to avoid causing prejudice, confusion or delay. Appellee’s Br. 31. In the Government’s view, the Maywood murder investigation was strictly a collateral matter because there was no evidence showing that Rudy expected or hoped for any benefit in the Maywood murder investigation. Id. at 31-32. The Government notes that the defendants had ample opportunity to and did establish Rudy’s bias arising from his cooperation plea agreement and that the defendants impeached Rudy by asking him about his prior convictions and inconsistent statements. Id. at 31-32, 34-35. Additionally, the Government contends that Rudy’s invocation of his Fifth Amendment right not to incriminate himself insulated the district court’s ruling circumscribing questioning about the Maywood murder investigation; the Government believes that such questioning involved a collateral matter and therefore paled in comparison to Rudy’s important Fifth Amendment right. Id. at 33, 36. 4. The Sixth Amendment to the Constitution of the United States ensures that a defendant be given an opportunity for effective cross-examination. See Pennsylvania v. Ritchie, 480 U.S. 39, 51-53, 107 S.Ct. 989, 94 L.Ed.2d 40 (1987); Delaware v. Van Arsdall, 475 U.S. 673, 678-79, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986). Never theless, trial courts retain wide discretion to impose reasonable limits on cross-examination in order to curb harassment, prejudice, confusion of issues, threats to witness safety and testimony that is repetitive and only marginally relevant. Van Arsdall, 475 U.S. at 679, 106 S.Ct. 1431; United States v. Smith, 454 F.3d 707, 714 (7th Cir.2006). When a district court’s limitation of cross-examination directly implicates the values protected by the Confrontation Clause of the Sixth Amendment, we review the district court’s ruling de novo; otherwise, we review the district court’s limitation of cross-examination under the more deferential abuse of discretion standard. See Smith, 454 F.3d at 714. At issue here is the district court’s limitation of the defendants’ cross-examination of Rudy about his alleged pro-Government bias because of a desire to curry favorable treatment in connection with the Maywood murder investigation. “Bias is a term used in the ‘common law of evidence’ to describe the relationship between a party and a witness which might lead the witness to slant, unconsciously or otherwise, his testimony in favor of or against a party.” United States v. Abel, 469 U.S. 45, 52, 105 S.Ct. 465, 83 L.Ed.2d 450 (1984). Cross-examination designed to elicit witness bias directly implicates the Sixth Amendment. See Abel, 469 U.S. at 49-52, 105 S.Ct. 465; Davis v. Alaska, 415 U.S. 308, 316-17, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974); Alford v. United States, 282 U.S. 687, 691-92, 51 S.Ct. 218, 75 L.Ed. 624 (1931). Consequently, our review is de novo. If a Sixth Amendment violation occurred, we shall set aside the verdict unless the Government establishes that the error was harmless beyond a reasonable doubt. See Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431; United States v. Nelson, 39 F.3d 705, 710 (7th Cir.1994). The exposure of a witness’s bias directly implicates the Sixth Amendment. See Abel, 469 U.S. at 52, 105 S.Ct. 465 (“Proof of bias is almost always relevant because the jury, as finder of fact and weigher of credibility, has historically been entitled to assess all evidence which might bear on the accuracy and truth of a witness’ testimony.”). As we noted in United States v. Recendiz, 557 F.3d 511, 530 (7th Cir.2009), “[a] core value [of the Sixth Amendment] is the ability to expose a witness’s motivation for testifying, his bias, or his possible incentives to lie.” Proof of bias “is the ‘quintessentially appropriate topic for cross-examination.’ ” United States v. Manske, 186 F.3d 770, 777 (7th Cir.1999) (quoting Bachenski v. Malnati, 11 F.3d 1371, 1375 (7th Cir.1993)). We believe that the situation before us today clearly implicates the defendants’ rights to meaningful cross-examination with respect to witness bias. The Government had made Rudy available to state prosecutors for questioning about the Maywood murder. Rudy conceded that he had given a statement to those prosecutors with respect to that murder and that he never was charged with that murder. He denied the existence of a quid pro quo with the state or federal prosecutors. The district court took the view that the Maywood murder was “unrelated” to the issues on trial. See Trial Tr. at 1622, Sept. 18, 2006 (“I’m not — I don’t think it’s appropriate to ask about this, as I understand it, unrelated murder.”). We respectfully take a different view from the one taken by our colleague in the district court. Upon examination, the record makes clear that defense counsel sufficiently articulated a link between Rudy’s involvement in the pending state murder investigation and his testimony in the federal action. The conceded facts that Rudy was interrogated by state investigators soon after he was arrested, that he gave a statement about the murder of Curtis Rios and that he might have been charged with the murder — a serious offense that carries a severe punishment — could have been linked to Rudy’s decision to cooperate with the Government in this action. Cf. Lindh v. Murphy, 124 F.3d 899, 901 (7th Cir.1997) (“[The witness] may have believed that testimony helping the prosecution in this ease, which achieved notoriety throughout Wisconsin, would aid his [unrelated, pending criminal] cause, if only because it was bound to come to the attention of the judge who presided in the prosecution against him.”); United States v. Anderson, 881 F.2d 1128, 1139 (D.C.Cir.1989) (“To require evidence of an actual cooperation agreement between [the Government] and [the allegedly biased witness], as the district court in this case di