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TABLE OF CONTENTS Page I. Variance: Single Versus Multiple 1391 Conspiracies A. Permissible Variance. 1391 B. Establishing a Single Conspiracy... 1392 C. Sufficiency of the Evidence of a 1393 Single Conspiracy 1. Bums.1394 2. Black.1395 3. Tarantino .1397 4. Bell.1398 II.Severance. 1398 A. Disparity in Evidence. 1398 B. Conflicting Defense Theories. 1399 III. Jury Instructions. 1400 A. Single Versus Multiple Conspira- 1400 cies B. The Travel Act. 1401 C. The Cash Transaction Reports 1403 Instruction D. The Missing Witness Instruction ... 1404 E. Strickland’s Guilty Plea. 1404 IV. Restrictions on Cross-Examination. 1405 A. Strickland’s Plan to Murder Ku- 1405 pits B. Strickland’s Benefits from the 1407 Witness Protection Program C. Strickland’s Payment of Attor- 1407 neys’ Fees for Nicholls D. Miscellaneous Restrictions on 1408 Cross- Examination V. Evidentiary Rulings. 1408 A. Admission of Cocaine. 1408 B. Limitations on Collateral Im- 1409 peachment C. Prior Consistent Statements. 1411 D. Co-conspirators’ Statements. 1411 VI. The Reference to Black’s Being 1413 Named in Another Indictment VII. Disclosure of Witness Statements. 1414 A. Jencks Act. 1414 B. Sixth Amendment. 1415 C. Brady. 1416 D. Statements by Co-conspirators. 1417 VIII. Contingent Plea Arrangements. 1418 IX. Burns’ Desire to Represent Himself 1419 X. The Error in Sentencing Bell. 1422 XI. Conclusion. 1422 Before SILBERMAN, BUCKLEY and WILLIAMS, Circuit Judges. Opinion PER CURIAM. PER CURIAM: This is an appeal from criminal convictions following a complex, two-month trial before U.S. District Judge Thomas F. Hogan. All appellants were convicted on count one of the twenty-five count indictment: conspiracy to distribute and to possess with intent to distribute cocaine, in violation of 21 U.S.C. §§ 841(a)(1) and 846 (1982). In addition, John C. Tarantino was convicted as a principal, 18 U.S.C. § 2 (1982), of four counts of violations of the Travel Act, 18 U.S.C. § 1952 (1982). Fred B. Black, Jr. was also convicted of violating the Travel Act, and Wilfred Samuel Bell of distribution of cocaine. Viewing the evidence in the light most favorable to the government, Glosser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942), these appellants and others conspired to import, possess, and distribute large quantities of cocaine in various locales, and to launder the proceeds of this illegal activity. Lawrence (“Lonnie”) Strickland, the main player in the conspiracy, testified for the government in exchange for a favorable recommendation to the sentencing judge who would consider Strickland’s guilty plea. The government’s evidence essentially established that (1) Black assisted Strickland in launching his drug operation and in laundering the resulting profits; (2) Robert H. Burns was instrumental in introducing Strickland to major drug importers (for which Burns received commissions) and laundering his illicit profits; (3) Tarantino participated heavily in distributing Strickland’s cocaine and laundering his profits; and (4) Bell was Strickland’s main distributor in the Washington, D.C. area. Following guilty pleas by various defendants not now béfore us, a trial of the charges against Tarantino, Black, and Burns began on May 14, 1984. Judge Hogan declared a mistrial on June 13, 1984, and a new trial, in which Bell was joined, began on January 11, 1985. The jury returned the convictions on March 8, 1985. We commend Judge Hogan on his conduct of this long and difficult trial. Apart from a few errors that we conclude did not deprive appellants of their right to a fair trial, Judge Hogan’s management of the proceedings was admirable. We affirm in all respects, except that we remand Bell’s sentence for compliance with Federal Rule of Criminal Procedure 32(c)(3)(D). I. Variance: Single Versus Multiple Conspiracies Each appellant argues that the evidence at trial varied impermissibly from the allegations of the indictment, and that the resultant prejudice deprived him of his right to a fair trial. A. Permissible Variance A variance between the allegations of the indictment and the proof at trial constitutes grounds for reversal only if the appellant proves (1) that the evidence at trial established facts materially variant from those alleged in the indictment, and (2) that the variance caused substantial prejudice. See, e.g., United States v. Caporale, 806 F.2d 1487, 1499-1500 (11th Cir.1986), cert. denied, — U.S. -, 107 S.Ct. 3265, 97 L.Ed.2d 763 (1987). In a conspiracy prosecution, for example, the appellant may prove (1) that the evidence established the existence of multiple conspiracies, rather than the one conspiracy alleged in the indictment, and (2) that because of the multiplicity of defendants and conspiracies, the jury was substantially likely to transfer evidence from one conspiracy to a defendant involved in another. Id. The existence of a single conspiracy or multiple conspiracies is primarily a question of fact for the jury. E.g., United States v. Erwin, 793 F.2d 656, 662 (5th Cir.), cert. denied, — U.S. -, 107 S.Ct. 589, 93 L.Ed.2d 590 (1986); United States v. Molt, 772 F.2d 366, 369 (7th Cir.1985), cert. denied, 475 U.S. 1081, 106 S.Ct. 1458, 89 L.Ed.2d 715 (1986); United States v. Potamitis, 739 F.2d 784, 787 (2d Cir.), cert. denied, 469 U.S. 934, 105 S.Ct. 332, 83 L.Ed.2d 269 (1984). The verdict must be upheld if the evidence adequately supports a finding that a single conspiracy existed. Potamitis, 739 F.2d at 788; United States v. Arbelaez, 719 F.2d 1453, 1457-58 (9th Cir.1983), cert. denied, 467 U.S. 1255, 104 S.Ct. 3543, 82 L.Ed.2d 847 (1984); cf. Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979) (verdict upheld if any rational trier of fact could have found elements of offense beyond reasonable doubt). B. Establishing a Single Conspiracy Appellants Bell and Bums urge us to follow the analysis of conspiracies used in Kotteakos v. United States, 328 U.S. 750, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946). Kotteakos involved multiple conspiracies to defraud the Federal Housing Administration. The key figure, Brown, arranged with various defendants to submit false loan applications. None of the applicants had any connection with the others, although each had a relationship with Brown. Nevertheless, the government charged all the applicants with participation in a single conspiracy. On appeal, the government acknowledged that the proof established multiple conspiracies. Brown was the hub of a wheel, and the various applicants were the spokes. Without a rim to enclose the spokes, however, the evidence made out multiple conspiracies, not the single one alleged. 328 U.S. at 755, 66 S.Ct. at 1243. The government granted this much, but merely argued that the variance was harmless, a position that the Supreme Court rejected. The wheel metaphor has not been strictly applied as the method of analysis for all conspiracies, and particularly not for drug conspiracies. Rather, courts have utilized a chain metaphor. An example is United States v. Gantt, 617 F.2d 831 (D.C.Cir.1980). The evidence established that the appellants had trav-elled from Washington, D.C. to Los Ange-les to purchase narcotics. Other evidence established that the narcotics were later sold in D.C. The defendants claimed that these transactions were entirely distinct, establishing two conspiracies. The court disagreed. Certain defendants went to California to purchase narcotics, others prepared the drugs for sale in D.C., others distributed the drugs, and still others actually sold them. “The activities of each member and group in the organization meshed with those of the other members and groups. In short, the evidence disclosed a classic example of a narcotics sale and distribution conspiracy.... In those cases [relied on by appellants, e.g., Kottea-kos ], the evidence showed ‘wheel-type’ conspiracies, whereas the conspiracy here was the ‘chain-type’ conspiracy common in narcotics cases.” 617 F.2d at 846 (citations omitted). Under the chain analysis, the government need not prove a direct connection between all the conspirators. A single conspiracy may be established when each conspirator knows of the existence of the larger conspiracy and the necessity for other participants, even if he is ignorant of their precise identities. When the conspirators form a chain, each is likely to know that other conspirators are required. E.g., United States v. Andrus, 775 F.2d 825, 840-41 (7th Cir.1985); United States v. Inadi, 748 F.2d 812, 817 (3d Cir.1984) (citing W. LaFave & A. Scott, Handbook on Criminal Law 480-81 (1972)), rev’d on other grounds, 475 U.S. 387, 106 S.Ct. 1121, 89 L.Ed.2d 390 (1986). The chain metaphor, while helpful, does not end our analysis. The existence of a chain is only an aid in answering the ultimate question: whether a single conspiracy was demonstrated. A single conspiracy is proven if the evidence establishes that each conspirator had the specific intent to further the common unlawful objective. United States v. Ras, 713 F.2d 311, 314 (7th Cir.1983) (whether defendants “knowingly embraced a common criminal objective”); see also Andrus, 775 F.2d at 840 (applying Ras to chain conspiracy); cf. United States v. Haldeman, 559 F.2d 31, 112 (D.C.Cir.1976) (specific intent to further unlawful object of conspiracy must be shown), cert. denied, 431 U.S. 933, 97 S.Ct. 2641, 53 L.Ed.2d 250 (1977). The existence of a chain helps us determine both the unlawful objective and the conspirators’ intent. Unlike a wheel conspiracy, in which the interest of each spoke is unrelated to the interests of the other spokes, each link in the chain may rely upon the other links in furtherance of the common interest. The street dealer relies upon his supplier; the supplier relies upon his supplier; and so on. The existence of such a "vertically integrated, loose-knit combination," United States v. Bynum, 485 F.2d 490, 495-96 (2d Cir.1973), vacated & remanded on other grounds, 417 U.s. 903, 94 S.Ct. 2598, 41 L.Ed.2d 209 (1974), may raise the inference that each conspirator has agreed with the others (some whose specific identity may be unknown) to further a common unlawful objective, e.g., the distribution of narcotics. Chain analysis must be used with care. Even in a vertically integrated combination, certain players may have performed activities wholly unrelated to the aims of the conspiracy. These unrelated activities may not be attributed to the co-conspirators, Pinkerton v. United States, 328 U.S. 640, 647-48, 66 S.Ct. 1180, 1184, 90 L.Ed. 1489 (1946), and those with whom the "freelancing" conspirator dealt do not necessarily become members of the main conspiracy. Thus, even if we determine that a chain conspiracy exists, we may still conclude that certain actions were outside the chain and formed a separate conspiracy. In determining whether the conspiracy was single or multiple, and which acts were committed in furtherance of the common conspiracy, we are aided by those courts that have isolated a variety of factors. The most important of these is whether the conspirators share a common goal, such as the possession and distribution of narcotics for profit. Caporale, 806 F.2d at 1500; United States v. Dickey, 736 F.2d 571, 582 (10th Cir.1984), cert. denied, 469 U.S. 1188, 105 S.Ct. 957, 83 L.Ed.2d 964 (1985). Another is the degree of dependence inherent in the conspiracy. United States v. Cerro, 775 F.2d 908, 914 (7th Cir.1985); United States v. Adamo, 742 F.2d 927, 932-33 (6th Cir.1984), cert. denied, 469 U.S. 1193, 105 S.Ct. 971, 83 L.Ed.2d 975 (1985); Dickey, 736 F.2d at 582. Some courts have permitted the jury to infer the conspirators' knowledge of their link to other conspirators from the nature of a narcotics conspiracy. United States v. Behrens, 689 F.2d 154, 160 (10th Cir.), cert. denied, 459 U.S. 1088, 103 S.Ct. 573, 74 L.Ed.2d 934 (1982); United States v. Smith, 609 F.2d 1294, 1300 (9th Cir.1979); United States v. Burman, 584 F.2d 1354, 1356-57 (4th Cir.1978), cert. denied, 439 U.S. 1118, 99 S.Ct. 1026, 59 L.Ed.2d 77 (1979); United States v. Moten, 564 F.2d 620, 624-25 (2d Cir.), cert. denied, 434 U.S. 942, 98 5.Ct. 438, 54 L.Ed.2d 304 (1977); United States v. Taylor, 562 F.2d 1345, 1352 (2d Cir.), cert. denied, 432 U.S. 909, 97 S.Ct. 2958, 53 L.Ed.2d 1083 (1977). For this reason, cases relied upon by appellants dealing with non-narcotics conspiracies, e.g., United States v. Camie4 689 F.2d 31 (3d Cir.1982); United States v. Butler, 494 F.2d 1246 (10th Cir.1974); United States v. Varelli, 407 F.2d 735 (7th Cir.1969), cert. denied, 405 U.S. 1040, 92 5.Ct. 1311, 31 L.Ed.2d 581 (1972), are of limited relevance. A final factor of lesser significance is the overlap of participants in the various operations claimed to comprise a single conspiracy. Caporale, 806 F.2d at 1500; Erwin, 793 F.2d at 662-63. A single conspiracy conviction has been upheld, however, despite a "lack of significant overlap of some participants" when strong evidence established that a main player coordinated the narcotics importation and distribution enterprise. United States v. Champion, 813 F.2d 1154, 1166-67 (11th Cir.1987). C. Sufficiency of the Evidence of a Single Conspiracy In this case, the evidence presented to the jury was sufficient to establish the existence of a chain conspiracy whose aim was to accumulate wealth by distributing cocaine. The identity and relationship of the major players in the conspiracy is summarized in the chart below. All appellants shared the conspiracy's objects and knew of their dependence on other conspirators, even though they may not have known the precise identity of all the other conspirators. Each appellant played a vital role in the conspiracy's success. Burns facilitated purchase, Tarantino and Bell facilitated distribution, and Black and Tarantino facilitated laundering of the profits into usable form. As will become apparent, however, each of the appellants also played other roles in the conspiracy, and all knew of the collaboration of others. We hold that the evidence was sufficient for the jury to conclude that the appellants joined in a single conspiracy. The defendants’ activities relating to the purchase, distribution, and laundering of funds did not constitute separate conspiracies, but were undertaken in furtherance of the overarching objectives of the single conspiracy. Accordingly, we find no basis for appellants’ claim that they have been substantially prejudiced by a material variance between the evidence introduced at trial and the facts alleged in the indictment. 1. Bums Strickland was introduced to Bums by Black, Tr. 123-29, with whom Bums had had numerous prior dealings. Tr. 5391-93. At their first meeting in Miami, Bums asked Strickland if he was in town to buy cocaine. An extensive discussion of the cocaine trade ensued. Bums stated that he had confidence in Strickland because of their mutual friendship with Black. Tr. 166-71. Strickland returned to Bums’ apartment the next day, when Bums introduced him to two men, Gene Cello and an unidentified Colombian, who could supply cocaine. Bums offered to broker cocaine deals for Strickland for a commission of $2,000 per kilogram. Strickland then purchased a single kilo from Cello and the Colombian, which was transported to and distributed in Washington, D.C. Tr. 173-77. After a subsequent purchase from Cello produced poor quality cocaine, Burns introduced Strickland to Armando Marulanda, a major Colombian importer. Marulanda offered to sell Strickland ten kilos of cocaine on credit, with a $2,000 per kilo commission to Burns. Marulanda’s extension of credit to Strickland was a turning point in Strickland’s cocaine trade. Never before had he been able to obtain such large quantities on consignment. Tr. 182-91. Burns thus was essential to the expansion and success of the conspiracy, and he benefitted directly by receiving commissions on each sale by Marulanda to Strickland. Burns apprised Black of these transactions. Tr. 323-34. Strickland’s purchases from Marulanda and Marcos Cadavid, an associate of Marulanda’s, escalated over the course of the next months, which increased Burns’ commissions. Tr. 197-213. Soon after the first transaction, Strickland introduced his partner and co-conspirator, Steve Kupits, to Burns. Strickland stated that he and Kupits were distributing the cocaine “in different parts of the country.” Burns responded: “Fine, no problem.” Tr. 195-96. Burns knew of and endorsed the nationwide scope of the conspiracy. Burns also was directly involved with the other conspirators. When Ribera, one of Strickland’s distributors, took over Strickland’s customers in the D.C. area while Strickland took an extended “vacation,” Burns dealt directly with Ribera. Under Strickland’s prodding, Bums “fronted” cocaine to Ribera, i.e., gave him cocaine on consignment. Bums also supplied Ribera with a courier to transport cocaine to the conspiracy’s distributors in California. Tr. 1769-72,1791. Burns himself directly provided the California conspirators with three kilos of cocaine. Tr. 2223-25. Bums also dealt with the Texas conspirators working with Kupits. Tr. 272-75. There was even evidence linking Bums to Tarantino’s plan to launder money by investing it in a Haitian casino, Tr. 472, and Black’s plan to launder money through investments in a New Jersey casino (the “Gateway Project”). Tr. 353-55. The evidence was sufficient for a jury to conclude that Bums was an essential link in the distribution chain. He shared the conspiracy’s goals, and knew of the nature and scope of the enterprise. Burns argues that the government’s evidence was based entirely on perjured testimony, a claim which the jury was entitled to reject. Brief for Bums at 7-21. He also argues that every act of the conspirators was a separate conspiracy of which he was no part. Id. at 37. The evidence was sufficient, however, for the jury to conclude that Bums was an essential link in a single chain. We have considered carefully Bums’ claim that prosecutorial misconduct “permeated the entire proceedings.” Id. at 21. To a large extent, Bums’ claim reiterates his other assignments of error, e.g., use of perjured testimony, attempt to deprive Burns of his “pro se status,” and suppression of evidence favorable to him and material to guilt or punishment under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). We discuss each of these arguments separately elsewhere in this opinion. We merely note here that we have found no obvious perjury on any material matter, much less knowing use of perjured testimony by the prosecutor. See Mooney v. Holohan, 294 U.S. 103, 55 S.Ct. 340, 79 L.Ed. 791 (1935) (prosecutor’s knowing use of material perjured testimony, along with deliberate suppression of impeachment evidence, justifies collateral attack). The prosecutor was entitled to argue his interpretation of the evidence, and the jury was entitled to accept that interpretation. 2. Black Strickland met Black after Black indirectly received a $13,000 loan from Strickland. At their first meeting, Strickland informed Black that he was a marijuana dealer, upon which Black suggested that Strickland meet Burns (who later proved to be a major cocaine broker). Tr. 128. Black urged Strickland to transform the loan into an investment in Black’s Gateway Project, and to increase the amount of the investment to $70,000. Black also stated he could help Strickland “clean up” his money, that is to say, to disguise its illegal source. Tr. 129-30. Strickland soon invested a total of $140,000 in the Gateway Project, all of it in cash. Tr. 5025-26. Later, Black asked Strickland to “come out of retirement” to generate an additional $800,000, and a further cash payment by Strickland of $500,000 followed shortly. Tr. 362-69. Black claims that he was unaware of the illicit source of Strickland’s funds. Brief for Black at 24-28. The jury was entitled to infer, however, that Black was well aware that Strickland’s investment represented his cocaine profits: according to Strickland’s testimony, (1) Black knew from the first that Strickland was involved in the drug trade; (2) Black introduced Strickland to Burns, a major cocaine broker; (3) Black knew of the developing relationship between Strickland and Burns (Black told Strickland he had heard from Burns that “things are going well with you two” (Tr. 323-24)); (4) Black touted the Gateway Project as a good way for Strickland to “clean up” his money (Tr. 129-30); (5) Strickland provided huge sums of cash to Black (Tr. 362-69), a fact that should have at least aroused suspicion (cf. United States v. Nicholson, 677 F.2d 706, 709 (9th Cir.1982), holding that large cash transactions without documentation, combined with refusal to describe investment, established sufficient circumstantial evidence to infer conspiracy); and (6) Black twice arranged for attorneys to represent conspirators arrested on cocaine charges (Tr. 668-69, 672). Black was also involved in a series of financial transactions that the jury was entitled to conclude were “washes.” Black offered to issue a check for cash provided by Strickland in order to permit Strickland to show a legitimate source of income. Black twice issued a Dunbar Corporation check for $3,000 in exchange for $3,000 cash (proceeds of cocaine sales) provided by Strickland. Tr. 338-43. Black also washed $60,000 to permit the financing of a land development project of Strickland, Kupits, and Maddux. Tr. 343-48. Two final pieces of evidence are decisive in establishing Black’s involvement in the conspiracy, if credited by the jury. First, in 1980, Black asked Strickland if he was still dealing in drugs. Strickland said he was not, because of a capital shortage. Black offered to arrange the necessary financing. Tr. 426-28. Second, in 1981, Black asked Strickland whether the Texas federal grand jury’s investigation centered on the land development plan only, or if it also concerned the drug network. Because of the two $60,000 washes he provided in connection with that project, he feared he might be indicted. Tr. 397-403. We have little trouble concluding that the jury was entitled to find that Black knew of the nature and scope of the conspiracy, joined in its aims, and facilitated its success. Black further claims that even if he knew of the conspiracy, he only dealt in an “article of free commerce, i.e., money.” Brief for Black at 28. He argues that a “conspiracy conviction under 21 U.S.C. §§ 841 and 846 requires more evidence of involvement in the conspiracy than mere handling of the proceeds of an illegal drug scheme.” Brief for Black at 29. In a related argument, Black maintains that money laundering is not a proscribed offense under section 841; laundering is specifically criminalized by other statutes (e.g., 18 U.S.C. §§ 1952(a) (1982), 1956(a)(1) (Supp. IV 1986), 1962(a) (1982), and 21 U.S.C. § 854 (Supp. III 1985)), under which Black was not charged. Id. at 31-37. This claim misconstrues the nature of the conspiracy as charged. The conspiratorial agreement was proscribed by section 841 because one of its essential aims was the distribution of cocaine. The laundering of funds was a part of the plan to distribute cocaine; the conspirators, including Black, well knew that the cocaine money had to be “cleaned up” to be useful to them. Tr. 129-30. Black’s aid in launder-the attainment of the conspiracy’s goals; money launderers play an essential part in a narcotics chain conspiracy. See, e.g., United States v. Dela Espriella, 781 F.2d 1432, 1436 (9th Cir.1986); United States v. Orozco-Prada, 732 F.2d 1076, 1080 (2d Cir.), cert. denied, 469 U.S. 845, 105 S.Ct. 154, 83 L.Ed.2d 92 (1984); United States v. Metz, 608 F.2d 147, 153 (5th Cir.1979), cert. denied, 449 U.S. 821, 101 S.Ct. 80, 66 L.Ed. 2d 24 (1980). The government is not required to prove that every act taken in furtherance of the conspiracy is illegal, much less that it is specifically proscribed the conspiracy statute. See Braverman United States, 317 U.S. 49, 53, 63 S.Ct. 99, 101, 87 L.Ed. 23 (1942). 3. Tarantino Tarantino participated in two aspects of the conspiracy: the distribution of cocaine and the laundering of proceeds. Tarantino’s involvement in the distribution of cocaine for Strickland began in the summer of 1980, when he introduced Strickland to Sonny Croughn, with the remark that Croughn could “sell a lot of coke.” Tr. 438-40. Strickland agreed to provide cocaine to Croughn through Tarantino. Tr. 444-46, 458. Following a phone call from Tarantino, Strickland travelled from the District of Columbia to New Jersey to deliver cocaine to Croughn. Strickland “fronted” the cocaine to Croughn, who later paid Strickland through Tarantino. Tr. 457-61. Similar transactions followed. Tr. 462-66. In some of these, Strickland was accompanied by other members of the conspiracy, e.g., Baker (Tr. 2412-19) and Kohn (Tr. 477-78). In all of these instances, Tarantino was present at the delivery of the cocaine. Tarantino also was aware of the national scope of the conspiracy. At the end of 1980, Strickland called Croughn from Houston and asked if Croughn could dispose of an excess kilo of cocaine. Tarantino immediately called back and arranged for a courier to pick up the cocaine. Strickland met the courier, and Croughn and Tarantino confirmed the delivery. Tr. 479-83. Tarantino’s second level of involvement was his role in attempting to launder the proceeds of the conspiracy’s cocaine sales. Strickland first met Tarantino in connection with Black’s casino project (the Gateway Project; see supra at 1395). At first, Strickland concealed from Tarantino the source of the funds he was investing in the Gateway Project. But when Tarantino met Strickland in Las Vegas in 1980, he told Strickland he was aware that Strickland and Burns had been selling drugs. He thanked Strickland for his help in supporting the Gateway Project, and later advised him to make further investments in the casino. Tr. 437-38, 1208, 375-76. At a subsequent meeting in New Jersey concerning the Gateway Project, Tarantino introduced Strickland to Croughn as a man who could “sell a lot of coke.” Tr. 438-40. Tarantino at least knew of, and arguably urged and facilitated Strickland’s investment in the Gateway venture. Given Tarantino’s knowledge of the nature of Strickland’s business, he also would have known that Strickland’s investments in Gateway were made to clean up his money. Tarantino knew of and condoned this aspect of the conspiracy’s goals. Tarantino managed a separate casino project in Haiti. He encouraged Strickland to invest in this project as well and credited the proceeds of Strickland’s sales to Croughn to the Haitian project. Tr. 470, 475-77. Strickland invested $300,000 in the Haitian project, thinking it a good laundering device. Tr. 470-71. Tarantino was familiar with other major players in the conspiracy. He knew Black through the Gateway Project. Tr. 434-36. He was acquainted with Bell, and was working with him on a separate investment project. Tr. 538-538A. Tarantino and Kohn, the conspiracy’s bookkeeper, also had extensive discussions concerning the Haitian and other potential investment projects. Tr. 521, 3302-10. Tarantino argues that, at most, the evidence established a conspiracy between Strickland, Croughn, and Tarantino to distribute cocaine, and an agreement by Strickland to invest $300,000 in the Haitian project. This conspiracy, says Tarantino, did not involve Black and Burns and was therefore totally separate from the conspiracy alleged in the indictment. Brief for Tarantino at 44. The jury concluded otherwise, however, and the evidence is sufficient to support its verdict. Tarantino was aware of Strickland’s acquisition and distribution of cocaine; it is immaterial that he did not know the precise identities of all the other conspirators. As we discuss elsewhere in this opinion, Black and Bums were sufficiently aware of and entered into the goals of the conspiracy, even if they did not know the full extent of Strickland’s dealings with Tarantino. 4. Bell The evidence clearly established that Bell was the conspiracy’s major distributor of cocaine in Washington, D.C. See, e.g., Tr. 98-118, 526-29. Bell does not seriously dispute this now, but claims he was unaware of other aspects of Strickland’s operations, including the distribution of cocaine elsewhere in the nation and the laundering of the cocaine profits. Brief for Bell at 35-39. The government was not obliged to prove that Bell knew every detail of the conspiracy. All that is required is that the evidence establish that he knew others were involved and that his own benefits depended upon the success of the entire venture. See United States v. Sisca, 503 F.2d 1337, 1345 (2d Cir.), cert. denied, 419 U.S. 1008, 95 S.Ct. 328, 42 L.Ed.2d 283 (1974) (cited in Brief for Bell at 35), and supra at 1392-93. Bell had extensive dealings not only with Strickland, but also with other players in the conspiracy’s distribution chain. He received cocaine deliveries from Ribera (Tr. 1726, 1740-43), acted as a money courier between Strickland and Kastrenakes (Tr. 532-33), and distributed cocaine supplied by Kastrenakes (Tr. 535-36). Bell was at least acquainted with Kupits and Kohn in Texas (Tr. 3269-70) and Tarantino in New Jersey (Tr. 588-538A). From this evidence, a jury could conclude that Bell was aware of the nationwide conspiracy and his dependence on its continued success. The existence of multiple distribution points does not, in itself, establish multiple conspiracies. See, e.g., United States v. Jenkins, 779 F.2d 606, 616-17 (11th Cir.1986); United States v. Bibbero, 749 F.2d 581, 587 (9th Cir.1984), cert. denied, 471 U.S. 1103, 105 S.Ct. 2330, 85 L.Ed.2d 847 (1985); United States v. Vila, 599 F.2d 21, 24 (2d Cir.), cert. denied, 444 U.S. 837, 100 S.Ct. 73, 62 L.Ed.2d 48 (1979). Finally, although the evidence did not establish that Bell directly participated in the laundering phase of the conspiracy, he was aware that the continued success of the conspiracy depended upon effective means of “cleaning up” its funds. The laundering of funds was a further link in the chain of which Bell was a part, and the conspirators’ acts in laundering the funds were thus attributable to Bell. Pinkerton, 328 U.S. at 646-47, 66 S.Ct. at 1183-84. II. Severance Each appellant argues that the trial court should have granted his motion for severance. We review the denial of a motion to sever under an abuse of discretion standard. United States v. Butler, 822 F.2d 1191, 1194 (D.C.Cir.1987). A. Disparity in Evidence Severance is required in two situations. First, when the evidence against the other defendants was “far more damaging,” the prejudicial spillover may have deprived a defendant of a fair trial. Id. (quoting United States v. Sampol, 636 F.2d 621, 645 (D.C.Cir.1980)). The trial judge is usually in the best position to evaluate the resulting degree of prejudice, and jury instructions generally are sufficient to minimize any disparities in evidence. Butler, 822 F.2d at 1194; United States v. Wright, 783 F.2d 1091, 1096 (D.C.Cir.1986). Although each appellant claims the government’s case against him was far weaker than that against the other appellants, the evidence was not so dramatically disparate that the judge abused his discretion in denying the motions to sever. We have rarely held that a district court improperly denied a motion to sever. In United States v. Mardian, 546 F.2d 973 (D.C.Cir.1976) (en banc), Robert Mardian was tried along with the other Watergate conspirators. Mardian’s participation in the conspiracy was brief, and the evidence against him was slight. Nevertheless, we held that severance was not required until Mardian’s lawyer became ill during the trial. 546 F.2d at 979-80. In Sampol, 636 F.2d 621, Ignacio Sampol was tried only for misprision of a felony and making false statements, whereas his co-defendants were tried for conspiracy and murder. Because of the quantity and inflammatory nature of the testimony against the co-defendants, the risk of a transference of their guilt was significant. Moreover, the testimony created a false impression that Sampol was involved in the conspiracy. 636 F.2d at 644-48. In United States v. Bruner, 657 F.2d 1278 (D.C.Cir.1981), however, the kingpin of the conspiracy was tried along with his confederates. Lynch directed the operation, in which groups of overweight women were sent to doctors in various cities to obtain prescriptions for Dilaudid and Prelu-din. These drugs were later illegally resold. Although the evidence against Lynch was “substantial,” there was also “independent and substantial evidence” that the co-defendants participated in the conspiracy. The disparity in the weight of the evidence was not so dramatic as to require a severance. 657 F.2d at 1290-91. We also distinguished Mardian and Sampol in United States v. Sutton, 801 F.2d 1346 (D.C.Cir.1986). There, we held the trial judge did not abuse his discretion in denying a motion for severance when the charges required the “presentation of much of the same evidence, testimony of the same witnesses, and involve[d] two defendants who [were] charged, inter alia, with participating in the same illegal acts.” 801 F.2d at 1365. Here, too, there was substantial and independent evidence of each appellant’s significant involvement in the conspiracy. Once each appellant was tied to the conspiracy, the acts of each conspirator in furtherance of the conspiracy’s aims were attributable to all. The evidence and the charges were substantially overlapping, but the overlap was caused by the involvement of each appellant in a single scheme. In these circumstances, severance was not required. B. Conflicting Defense Theories Severance may also be required in cases in which co-defendants rely on defenses that are mutually contradictory. “[T]he denial of a severance motion generally constitutes an abuse of discretion when 'the defendants present conflicting and irreconcilable defenses and there is a danger that the jury will unjustifiably infer that this conflict alone demonstrates that both are guilty.’ ” Wright, 783 F.2d at 1094 (quoting Rhone v. United States, 365 F.2d 980, 981 (D.C.Cir.1966)). In Wright, two men were charged with kidnapping. Wright intended to claim insanity, and Moss duress, but this in itself did not establish the requisite conflict requiring severance. Wright further claimed that a substantial factor contributing to his mental illness was the murder of his lover. But Moss claimed that Wright had said that he himself had killed his lover. According to Moss, Wright’s statement lent plausibility to his alleged threats, which forced Moss to join in the kidnapping plan. Although we recognized the conflict to be “a real one,” the defenses were not “so contradictory as to raise an appreciable danger that the jury would convict because of the inconsistency.” The inconsistency “would not logically require a jury to find Wright guilty if it acquitted Moss.” 783 F.2d at 1095. The conflicts between appellants in the instant case are far less severe, and not such as to require severance. For example, Black claims that restrictions placed on impeachment of Strickland resulted from conflicts with co-defendants. Black’s counsel was not permitted to inquire about Strickland’s knowledge of the murder of a Colombian drug source. But this restriction was imposed by the district court not because of the tendency to implicate Burns (as Black claims), but because it was “not probative of anything.” Tr. 713. Similarly, the court restricted inquiry on cross-examination as to witnesses’ fears of other defendants. See, e.g., Tr. 3574-77. The court imposed these restrictions partly to avoid unfair prejudice to the co-defendants, but mainly because the probative value of the evidence was slight. Finally, although the trial court refused to allow Bell’s counsel to cross-examine Strickland regarding an alleged plot to kill Kupits because the probative value was outweighed by the danger of prejudice to Black, see infra at 1405-07, we cannot say that the decision not to sever Bell (or Black) from the other defendants based on this prejudice was an abuse of discretion. The conflicts between the defendants in this respect were not so severe as to require severance. III. Jury Instructions A. Single Versus Multiple Conspiracies After a thorough instruction on the elements of conspiracy, the trial judge told the jury: [I]n the context of that instruction as to the elements of a conspiracy, you’re further instructed with regards [sic] to this. alleged conspiracy offense, that proof of several separate conspiracies is not proof of the single, overall conspiracy charged in the indictment unless one of the several conspiracies which is proved is the single conspiracy which 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, not the one charged in the indictment, then you must acquit the defendant. In other words, to find a defendant guilty you must find that he was a member of the conspiracy charged in the indictment and not some other, separate conspiracy. Tr. 6444-45. Taking the instructions as a whole, this charge was proper. E.g., United States v. Darby, 744 F.2d 1508, 1542 (11th Cir.1984) (approving identical instruction), cert. denied, 471 U.S. 1100, 105 S.Ct. 2322, 85 L.Ed.2d 841 (1985); cf. United States v. Gantt, 617 F.2d 831, 846 (D.C.Cir.1980) (approving substantially similar instruction). Appellant Bell nevertheless complains that Judge Hogan did not adopt the precise language of his proposed instruction, especially the following: A conspiracy may ... include two or more separate agreements ... providing the participants in the separate agreements are joined together by their knowledge of the essential features and scope of the overall conspiracy and by the common goal. Where the participants in separate agreements are not so joined, they are not members of a single, overall conspiracy. ... See United States v. Bailey, 607 F.2d 237, 243 n. 14 (9th Cir.1979) (the source of the instruction), cert. denied, 445 U.S. 934, 100 S.Ct. 1327, 63 L.Ed.2d 769 (1980). Bell argues that the instruction given “provided no guidance to the jury as to how to determine whether, in fact, there was more than one conspiracy.” Brief for Bell at 42. We do not decide the correctness of the Bailey instruction, as the instruction given here was adequate. The trial court is required to give a proper instruction, and to instruct on the defendant’s theory of the case if supported by the evidence. United States v. Payne, 805 F.2d 1062, 1067 (D.C.Cir.1986). The court is not required to give the instruction in the specific language requested by the defendant. Id. Judge Hogan did instruct the jury on the elements of conspiracy, Tr. 6432-35, so that the jury had a proper basis for determining whether the agreements between the various conspirators comprised one or several conspiracies. The adequacy of the instructions must be determined by looking at the charge as a whole. E.g., United States v. Douglas, 818 F.2d 1317, 1321-22 (7th Cir. 1987). The slight variation from the proposed instructions did not substantially prejudice the appellants, particularly in view of the strength of the evidence of a single conspiracy. Cf. United States v. Davenport, 808 F.2d 1212, 1217-18 (6th Cir.1987) (because of strength of evidence and adequacy of instruction on elements of conspiracy, failure to give specific instruction on multiple conspiracies was harmless error). Finally, Bell’s claim that the court “fail[ed] to charge the jury that if it found that multiple conspiracies existed, it should disregard all evidence introduced by the government relating to conspiracies other than the one in which the defendant was involved,” Brief for Bell at 42, is inaccurate. Judge Hogan instructed the jury as follows: [I]n determining whether a particular defendant was a member of the conspiracy, if any existed, you may consider only his own acts and statements. A defendant cannot be bound by the acts or declarations of the other participants unless and until it is established that a conspiracy existed and the defendant was one of its members. Tr. 6434. This instruction adequately conveyed the importance of segregating evidence between defendants. Although the jury was not instructed in the precise terms Bell desires, it was told that the defendants were bound by co-defendants’ acts only if they were found to be members of the same conspiracy. B. The Travel Act The Travel Act, 18 U.S.C. § 1952 (1982), broadly forbids travel in interstate commerce or the use of facilities of interstate commerce for the purposes of furthering “any unlawful activity.” 18 U.S.C. § 1952(a). The statute defines “unlawful activity” as “any business enterprise” involving narcotics or controlled substances, 18 U.S.C. § 1952(b)(1), and the courts have construed “business enterprise” to require “a continuing course of conduct rather than sporadic casual involvement in a proscribed activity.” United States v. Kendall, 766 F.2d 1426, 1434 (10th Cir.1985), cert. denied, 474 U.S. 1081, 106 S.Ct. 848, 88 L.Ed.2d 889 (1986); United States v. Corbin, 662 F.2d 1066, 1072 (4th Cir.1981). See also H.R.Rep. No. 966, 87th Cong., 1st Sess. 3 (1961) (“[Individual or isolated violations would not come within the scope of this bill since they do not constitute a continuous course of conduct so as to be a business enterprise.”) Black attacks his conviction under the Travel Act on the ground that the trial judge’s charge failed to tell the jury of the need to find a continuous course of conduct. Because Black failed to object at trial we could reverse only if we found “plain error,” which we do not. The trial court’s instructions to the jury on the “unlawful activity” element of the Travel Act did not specifically mention the “business enterprise” aspect of the offense: In this case, the unlawful activity is alleged to be the distribution of cocaine and other controlled substances and the conspiracy to distribute cocaine and other controlled substances.... You are instructed as a matter of law that the distribution of cocaine and other controlled substances are violations of the laws of the United States. Tr. 6462-63. Because this instruction did not mention the “business enterprise” requirement or make clear that the jury had to find a continuous course of criminal conduct, it was an incomplete discussion of the “unlawful activity” element of the Travel Act. United States v. Rinke, 778 F.2d 581, 586 (10th Cir.1985) (specific findings as to the existence of a “business enterprise” essential to conviction at bench trial); United States v. Kaiser, 660 F.2d 724, 731 (9th Cir.1981) (error to refuse to instruct the jury that it must find a continuous course of criminal conduct to convict on Travel Act counts), cert. denied, 455 U.S. 956, 102 S.Ct. 1467, 71 L.Ed.2d 674 (1982); cf. United States v. Gallo, 782 F.2d 1191, 1195 (4th Cir.1986) (error to fail to give any definition of “unlawful activity”). The defendant did not, however, object at trial to this definition of “unlawful activity.” Consequently, reversal of the trial court would require a finding of plain error. United States v. DeBango, 780 F.2d 81, 84 (D.C.Cir.1986). See also Fed.R.Crim. P. 30 (“No party may assign as error any portion of the charge or omission therefrom unless he objects thereto before the jury retires to consider its verdict, stating distinctly the matter to which he objects and the grounds of his objection.”); Fed.R. Crim.P. 52(b) (“Plain errors or defects affecting substantial rights may be noticed although they were not brought to the attention of the court.”) The Supreme Court has recently admonished that the plain error exception is an exceedingly narrow one, to be used only “ 'to correct particularly egregious errors,’ United States v. Frady, 456 U.S. 152, 163, 102 S.Ct. 1584, 1592, 71 L.Ed.2d 816 (1982), those errors that ‘seriously affect the fairness, integrity or public reputation of judicial proceedings,’ United States v. Atkinson, 297 U.S. [157,] 160, 56 S.Ct. 391, 392, 80 L.Ed. 555 [(1936)].” United States v. Young, 470 U.S. 1, 15, 105 S.Ct. 1038, 1046, 84 L.Ed.2d 1 (1985). The inadequacy of the court’s charge on the “unlawful activity” aspect of the Travel Act does not rise to the level of plain error. First, although the instruction did not contain the specific words “business enterprise” or “continuous course of conduct,” the references to “distribution of cocaine” and the “conspiracy to distribute cocaine” indirectly expressed those concepts. Although both distribution and conspiracy may, of course, consist of sporadic activities, we think that in the context of this case the jury could only understand the instructions to refer to the massive ongoing conspiracy alleged in the indictment. Second, and more fundamentally, the jury convicted all of the defendants— including Black and Tarantino — on Count One of the indictment, which alleged a continuous, vertically integrated, geographically widespread operation to acquire, distribute and sell cocaine, and to launder the proceeds. The conspiracy spanned several years, and the jury heard evidence showing that Black and Tarantino were each involved in more than a few sporadic transactions during this period. The convictions for this wide-ranging conspiracy render it essentially inconceivable that Black or Tarantino was harmed by the court’s failure to more clearly emphasize the “continuous course of conduct” aspect of “unlawful activity.” Finally, in evaluating whether the instructions constituted plain error, we may ourselves evaluate the strength or weakness of the evidence against the defendants on the Travel Act. Young, 470 U.S. at 19-20,105 S.Ct. at 1048 (plain error reversal unwarranted because overwhelming evidence of defendant’s fraud showed that prosecutor’s improper remarks did not undermine the fairness of the trial). In this case the evidence showed beyond any reasonable doubt that Tarantino and Black were each a vital actor in an ongoing criminal business enterprise to acquire, distribute, sell, and profit from illicit drugs. See supra at 1395-98. That the error involved an omission of essential ingredients of the crimes makes no difference in this analysis. In the related area of “harmless error” analysis, applicable where proper objection has been made and where accordingly the standards must be more stringent, the Supreme Court has made clear a conviction may be sustained even when the trial court’s instructions allow the jury to convict without finding “each element of the crime under the proper standard of proof.” Pope v. Illinois, - U.S.-, 107 S.Ct. 1918, 1922 n.' 7, 95 L.Ed.2d 439 (1987), citing Rose v. Clark, 478 U.S. 570, 106 S.Ct. 3101, 92 L.Ed.2d 460 (1986). As the facts that the jury necessarily found established guilt beyond a reasonable doubt, cf. Pope, 107 S.Ct. at 1922, the convictions on the Travel Act counts must stand. C. The Cash Transaction Reports Instruction Defendant Black also objects to the trial court’s instructions regarding the filing of cash transactions reports (“CTR”s) under the Currency Transaction Reporting Act (“CTRA”), 31 U.S.C. § 5313(a) (1982). This requires banks to report certain transactions as specified by the Treasury Department, which has set a threshold of $10,000. See 31 C.F.R. § 103.22 (1987). Black's objections are that the court did not make it sufficiently clear, first, that only the financial institution has a duty to file CTRs, and second, that the depositors are completely free to structure their transactions so as to keep under the threshold. We find no error. The court instructed the jury as follows: The law provides that a financial institution shall file a report of each transaction in currency of more than $10,000. The duty and the responsibility to obtain the required information, fill out and file the required currency transaction report is on the banking institution in the case of bank deposits exceeding $10,000. The depositor, that is the person making the deposit, does not file the report. Tr. 6421. These instructions obviously make it clear that depositors do not have a duty to file CTRs, so we turn to the second objection. Here Black specifically objects to the trial court’s refusal to give his Requested Instruction No. 8, to the effect that the law does not prohibit a person from structuring his transactions in such a way as to avoid the filing of CTRs. We note at the outset that Black’s view of the law is hotly disputed in the courts of appeal. Compare United States v. Nersesian, 824 F.2d 1294, 1311 (2d Cir.1987); United States v. Puer-to, 730 F.2d 627, 631 (11th Cir.), cert. denied, 469 U.S. 847, 105 S.Ct. 162, 83 L.Ed. 2d 98 (1984); United States v. Tobon-Builes, 706 F.2d 1092, 1098 (11th Cir.1983) with United States v. Larson, 796 F.2d 244, 246 (8th Cir.1986); United States v. Reinis, 794 F.2d 506, 508 (9th Cir.1986); United States v. Varbel, 780 F.2d 758, 762 (9th Cir.1986); United States v. Anzalone, 766 F.2d 676, 681 (1st Cir.1985). Even if we assume that the depositor has no legal duty not to structure his transactions so as to avoid the filing of CTRs, however, we still conclude that omission of the requested instructions was not error. The prosecution did not charge Black with substantive violations of the CTRA. Though the prosecutor made references to Black’s evident efforts to keep below the trigger amount, he did so exclusively to support the inference that Black wished to avoid the governmental scrutiny that would follow if the bank filed a CTR with the federal government each time he deposited proceeds of drug sales. Tr. 6082-83, 6085-90, 6354-55. Thus the government claim was that these otherwise apparently lawful acts were unlawful only because they were carried out in furtherance of a conspiracy. Clearly many acts that are by themselves perfectly legal may constitute overt acts manifesting participation in an illegal conspiracy, C. Torcía, 4 Wharton’s Criminal Law § 728 at 538 (1981). The jury need not be informed that all such acts are in the normal course of things perfectly legal. For instance, where conspiracy to rob a bank is charged and one member is assigned to “case the joint” by driving around the bank, it would be absurd to argue that the trial court must explain that driving a car near a bank is legal. In the absence of either a charge against Black under the CTRA itself or insinuations by the prosecutors or the court that Black’s actions were illegal apart from their connection to the conspiracy, we find no error in denial of the proposed instructions. D. The Missing Witness Instruction Burns argues that the trial court should have given a “missing witness” instruction (suggesting an inference adverse to the government), or allowed Bums’ counsel to note for the jury the absence of Steve Kupits, Nancy Strickland and many other witnesses that counsel at trial vaguely characterized as having a special “relationship” with the government. See, e.g., Tr. 5985. The decision to refuse a missing witness instruction rests within the discretion of the trial court. United States v. Montoya, 676 F.2d 428, 431 (10th Cir.), cert. denied, 459 U.S. 856, 103 S.Ct. 124, 74 L.Ed.2d 108 (1982), and nothing in this case suggests any abuse of that discretion. First, an instruction or inference that the missing witness’ testimony would be unfavorable to the government is generally permissible only when it is within the government’s exclusive power to call the witness to testify. Id. In the instant case, Bums had every opportunity to call these witnesses; indeed, the trial court at one point specifically questioned Burns as to why he could not call them. Tr. 5859. Bums has made no specific allegation that any of these potential witnesses were in fact unavailable to the defense, and, contrary to Burns’ assertion, no automatic inference of exclusive government control arises from the fact that witnesses are acting as government informants, DeBan-go, 780 F.2d at 84 (informant equally available to prosecution and defense); Montoya, 676 F.2d at 431 (same), or from a grant of immunity from prosecution, United States v. Keplinger, 776 F.2d 678, 702 (7th Cir. 1985), cert. denied, 476 U.S. 1183, 106 S.Ct. 2919, 91 L.Ed.2d 548 (1986). Second, the trial court itself was responsible for the non-appearance of at least some of these possible witnesses; it restricted the government’s intended presentation in the interest of avoiding cumulative evidence. Tr. 5864, 5990-91. Cf. United States v. Jennings, 724 F.2d 436, 446 (5th Cir.) (missing witness instruction not justified if testimony of witness not called is likely to have been cumulative or corroborative), cert, denied, 467 U.S. 1227, 104 S.Ct. 2682, 81 L.Ed.2d 877 (1984). On these facts the trial court plainly did not abuse its discretion in declining to invite, or to allow defendants to invite, an inference against the government. E. Strickland’s Guilty Plea Strickland testified at trial that he had pleaded guilty to the same conspiracy counts for which the defendants were being tried. Tarantino contends that the trial court should have informed the jury that they should not consider Strickland’s guilty plea in assessing the defendants’ guilt or innocence. A government witness’ guilty plea obviously may not be used as substantive evidence of the guilt of defendants, but the plea is equally obviously admissible to show the witness’ acknowledgement of his role in the offense and to reflect on his credibility. United States v. Roth, 736 F.2d 1222, 1226 (8th Cir.), cert. denied, 469 U.S. 1058, 105 S.Ct. 541, 83 L.Ed.2d 429, 433 (1984). In some instances — most obviously where there is a serious risk that the plea itself may be taken by the jury to support the defendants’ guilt — a limiting instruction may be necessary to avoid prejudice. Wallace v. Lockhart, 701 F.2d 719, 725-26 (8th Cir.), cert. denied, 464 U.S. 934, 104 S.Ct. 340, 78 L.Ed.2d 308 (1983). At trial, however, Tarantino’s counsel neither requested limiting instructions nor objected to the court’s failure to give such instructions. Therefore, we could reverse only if the omission were plain error. De-Bango, 780 F.2d at 84; Fed.R.Crim.P. 30; Fed.R.Crim.P. 52. See also supra at 1402. Here the defendants were not disadvantaged in any significant way by the omission of the instructions. The government never attempted to argue or even hint that Strickland’s guilty plea had any bearing on the defendants’ guilt or innocence. Wallace v. Lockhart, 701 F.2d at 726; cf. United States v. Fleetwood, 528 F.2d 528, 532-33 (5th Cir.1976) (government’s emphasis on witness’ guilty plea was prejudicial). Moreover, the overwhelming evidence of Tarantino’s involvement in the conspiracy negates any possible harm from Strickland’s statement. Failure to instruct on the issue was not plain error. United States v. Martin, 790 F.2d 1215, 1219 (5th Cir.), cert. denied, — U.S.-, 107 S.Ct. 231, 93 L.Ed.2d 157 (1986); United States v. Smith, 790 F.2d 789, 793-94 (9th Cir.1986); Roth, 736 F.2d at 1226-27. IV. Restrictions on Cross-Examination The defendants have challenged several rulings of the trial court restricting the scope of cross-examination of government witnesses. We address the various arguments separately below. We note at the outset, however, that “trial judges retain wide latitude insofar as the Confrontation Clause is concerned to impose reasonable limits on ... cross-examination based on concerns about, among other things, harassment, prejudice, confusion of the issues, the witness’ safety or interrogation that is repetitive or only marginally relevant.” Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 1435, 89 L.Ed.2d 674 (1986). See Fed.R.Evid. 611. Appellate review under the harmless error doctrine is to “focus[] on the underlying fairness of the trial rather than on the virtually inevitable presence of immaterial error.” Van Arsdall, 106 S.Ct. at 1436-37. In Van Arsdall the Supreme Court found a breach of the Confrontation Clause when the trial court “prohibited all inquiry into the possibility that [a key prosecution witness] would be biased as a result of the State’s dismissal of his pending public drunkenness charge.” 106 S.Ct. at 1435 (emphasis in original). But it also made clear that “the Confrontation Clause guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish.” Id. at 1435 (quoting Delaware v. Fensterer, 474 U.S. 15, 106 S.Ct. 292, 295, 88 L.Ed.2d 15 (1985) (emphasis in original)). Of course one might find a prohibition of “all inquiry” into almost any specific subject simply by defining the subject narrowly, but such a reading would plainly conflict with the Court’s observations on the trial court’s right to impose reasonable limits. Limits imposed in the interest of avoiding prejudice to a defendant (as in one instance here) are especially likely to cut off what might be loosely called a “subject,” since such limits will typically foreclose reference to some discrete event that carries a risk of prejudice. Accordingly, we believe that we must conduct our Confrontation Clause inquiry with some consideration of the countervailing values. A. Strickland’s Plan to Murder Kupits The trial court refused to allow Bell’s counsel to cross-examine Strickland about an alleged plot, involving Strickland, Black, Kohn, Ribera and Kastranakes, to hire a hit man to murder Kupits in Texas. The supposed rationale for the plan was to prevent Kupits from testifying as a government witness. Tr. 1256-72. Bell asserts that this ruling was an abuse of the trial court's discretion. Under Fed.R.Evid. 608(b), specific instances of conduct may, in the discretion of the trial court, be inquired into on cross-examination “if probative of truthfulness or untruthfulness.’’ Although the government argues that the plan to kill Kupits is not probative at all of Strickland’s credibility, we cannot agree. To be sure, the planning or commission of a crime of violence without more is not usually thought to bear on a witness’ veracity. See J. Weinstein & M. Berger, 3 Weinstein’s Evidence § 608(05) at 608-45 to 608-46 (1987). For instance, in United States v. Young, 567 F.2d 799 (8th Cir.1977), a case heavily relied upon by the government, the Eighth Circuit held that it was not an abuse of discretion to refuse to allow cross-examination of a witness regarding her attempt to have her ex-husband killed. There the court held that the attempted murder was “not relevant to veracity and honesty.” Id. at 803. The viewpoint suggests a strong judicial concern over the drawbacks of allowing such inquiries; surely readiness to kill others for one’s personal advantage, of any kind, signifies an egotism that in turn signifies a readiness to blur the truth when it is personally advantageous to do so. Judicial exclusion of such material is not sufficiently explained by any lack of logical connection to credibility. Nonetheless, we think that a murder plan aimed at stamping out evidence impugns a witness’ credibility more directly than murder plans generally. Young is therefore not controlling; nowhere in that case was there any suggestion that the