
    UNITED STATES of America, Appellee, v. Dwayne A. WASHINGTON, Appellant.
    Nos. 95-3097, 95-3098 and 95-3099.
    United States Court of Appeals, District of Columbia Circuit.
    Argued Nov. 14, 1996.
    Decided Feb. 21, 1997.
    
      Stanley J. Reed, Bethesda, MD, appointed by the court, argued the cause and filed the briefs, for appellant John C. Harmon.
    Allen E. Burns, Washington, DC, appointed by the court, argued the cause, for appellant Troy E. Taylor, with whom A.J. Kramer, Federal Public Defender, was on the briefs.
    Steven R. Kiersh, Washington, DC, appointed by the court, filed the briefs, for appellant Dwayne A. Washington.
    Mary-Patrice Brown, Assistant U.S. Attorney, Washington, DC, argued the cause for appellee, with whom Eric H. Holder, Jr., U.S. Attorney, John R. Fisher, Leslie A. Blackmon, Carol A. Fortine and Steven W. Pelak, Assistant U.S. Attorneys, were on the brief.
    Before: WALD, GINSBURG and ROGERS, Circuit Judges.
   Opinion for the Court filed PER CURIAM.

PER CURIAM:

In these consolidated appeals, appellants are three officers of the Metropolitan Police Department (“MPD”), who, with others, were caught in a reverse-sting operation. They challenge their convictions and sentences for a variety of drug-related charges, raising numerous claims both jointly and individually. In Part I, we summarize the . relevant evidence. In Part II, we address the challenges to the jury instructions on entrapment, specifically, the district court’s refusal to instruct the jury on derivative entrapment as well as-the sufficiency of the general entrapment instructions. We also address appellant Washington’s challenge to the refusal to admit evidence of his prior commendations and appellant Harmon’s challenge to the ex-elusion of his prior consistent statement. Further, we address appellants Taylor and Washington’s challenge to the instructions on attempted possession of cocaine with intent to distribute, both as to the sufficiency of the evidence and the jury instructions themselves, as well as appellant Hannon’s challenge to the bribery instruction. In Part III, we address the exclusion of expert testimony and appellants’ various challenges to their firearms convictions under 18 U.S.C. § 924(c). Finally, in Part IV, we address appellants’ sentencing challenges. For the reasons that follow, we affirm the judgments of convictions in all respects save for one of the firearms convictions of each appellant; we remand the cases for resentencing in light of the vacation of these convictions.

I.

In December 1992, undercover FBI Agent Jose Olivier, posing as a member of a Miami-based narcotics organization, told MPD Officer Nygel Brown that he was interested in obtaining protection from Brown and other willing police officers for his illegal narcotics activities while in the District of Columbia. Olivier explained that he was working for a cocaine dealer named Juan, and they wanted to set up a “drug base” in the District of Columbia. Brown, who was already on a list of suspected corrupt officers, expressed his interest and stated that he knew other potential recruits. On two separate occasions during February and March 1993, Brown accompanied and “protected” Olivier while Olivier delivered $250,000 in cash, ostensibly for a drug purchase on one occasion and for money laundering on the other. Brown was paid $1000 on each occasion.

On March 4,1993, Brown introduced Olivier to Officer Sean Wiggins. Brown told Olivier that Wiggins had dealt drugs both before and after becoming a police officer, which Wiggins later confirmed. Upon learning from Olivier the same account of his plans to use the District of Columbia as a transit point for his drug operation, Wiggins was enthusiastic to join. On March 23, Brown and Wiggins escorted Olivier on another staged money laundering run. Olivier paid Wiggins $1000, but this time gave Brown $1500, telling Brown the bonus was for recruiting Wiggins.

On April 25, 1993, Brown and Wiggins were flown by Olivier to Miami, Florida, to be introduced to Olivier’s boss “Juan,” undercover FBI agent Robert Williams. After wining and dining the officers, Williams informed them that he intended to fly large quantities of cocaine into the District of Columbia area, and that he wanted police officers to “protect” those shipments until couriers took possession of the cocaine and left the District of Columbia. Williams stated that the officers would receive $2000 for each run, but that Wiggins and Brown would receive $7500 a run for their leadership roles. Williams told them that he wanted “dirty police officers, people who were used to protecting drugs.” Wiggins and Brown agreed to this proposal without reservation.

On June 8 and 9,1993, Brown and Wiggins introduced Olivier to Officers Ronald Bailey, William Hackney, and Kyle Davis. After meeting with Olivier individually and learning of the drug operation, they each agreed to join. On July 13,1993, the officers participated in the first of three staged drug runs. Olivier, Brown, and Wiggins drove to the airport, picked up a shipment of cocaine, and drove it back to Olivier’s house in Northwest Washington. “Couriers” subsequently arrived to pick up the drugs, and Wiggins, Bailey, and Hackney escorted them from Olivier’s house to the Capital Beltway, which encircles the District of Columbia. Bailey and Hackney each received $2000, and Brown and Wiggins, $7500.

On August 9, 1993, Brown and Hackney brought Roland Harris and John Harmon to meet Olivier. After making sure that Harris and Harmon were interested, Olivier asked each of them whether he had any prior experience with the drug world. Both officers responded affirmatively. Harmon stated that he had sold drugs with Hackney and that he had done “rips” on the street, picking up drugs or money dropped by fleeing dealers. After explaining that the officers would be expected to drive behind the couriers and to be prepared to “use their badges” if necessary, Olivier stated that his organization had successfully employed police officers in numerous other cities. Neither Harris nor Harmon expressed any reluctance to join the endeavor, and on August 10, 199B, both joined in the second of the three runs. Harmon and the other escorts received $2000, while Wiggins and Brown each received $7500 for their day-long services.

On August 25, 1993, Olivier told Hackney and Brown that Juan'wanted to set up a second team, and asked Hackney to lead it and recruit as many new officers as he could. Hackney readily agreed, and on September 16, 1998, Brown and Hackney brought Officers Dwayne Washington, Darryl Lawson, Mark Reid, and Vikki Childress to meet Olivier. Officer Troy Taylor, who was also invited, did not attend because he was working. After Olivier engaged in his standard introduction and questions, Washington told Olivier not only that he had worked in vice and was used to being around drugs, but that he had stolen drugs from street dealers because “they ain’t gonna say nothing.” Washington also told Olivier that he was told by Hackney that he would not have to touch the drugs and that he was comfortable with the arrangement. After similar discussions with Olivier, the other three officers also agreed to join the operation.;

On October 4, 1993, Taylor was introduced to Olivier. After being given the standard pitch from Olivier, Taylor agreed to participate. Taylor described his former experience “running the coke” and “shipping it out to the little people” for a local drug dealer. Although he claimed to have shot people in the course of his illegal activities, and stated that he would “take somebody’s life, pointblank” if things went wrong, he said he had never killed anyone. He also said that he knew a “hit man” if Olivier encountered “any problems with anybody.” The next day, on October 5, after attending a morning meeting with all the officers, Washington and Taylor joined in the third and final drug run.

On November 16, 1993, Olivier held separate meetings with two groups of the officers to update them on the operation. Olivier informed the officers that the next run, which would be conducted around Thanksgiving, would include a larger shipment and would be conducted from a hotel room, rather than his townhouse. During the meeting, Olivier mentioned the high crime rates and murders connected with drug trafficking, and referencing a newspaper article, discussed at length an actual case in Puerto Rico where two bodies had been found in a car trunk; cut up into “seven pieces.” At trial, Olivier testified that the story was idle conversation; Harmon testified that he understood it to send a message about the consequences of betrayal. On duty during the time 'of the meeting, Taylor learned of the plans from Olivier over the telephone the next day.

On December 14, 1993, Taylor, Washington, and Harmon, along with eight other officers, assembled in two hotel rooms with Olivier and another courier to prepare for the cocaine shipment scheduled for that day. While they were discussing their runs, FBI agents and MPD senior officers rushed in to the hotel rooms with guns drawn, and arrested the officers.

Officers Wiggins, Hackney, Harmon, Washington, and Taylor were charged on April 26, 1994, in a superseding indictment with the following crimes: conspiracy to commit bribery, in violation of 18 U.S.C. § 371; conspiracy to distribute and possess with intent to distribute cocaine, in violation of 21 U.S.C. § 846; bribery, in violation of 18 U.S.C. § 201; attempted possession with intent to distribute cocaine, in violation of 18 U.S.C. § 2 and 21 U.S.C. §§ 841(a)(1), (b)(l)(A)(ii), 846; and two counts per defendant of using or carrying a firearm during and in relation to a drug trafficking offense, in violation of 18 U.S.C. § 924(c)(1). The indictment alleged that the conspiracies existed between March and December 1993. Following the example of seven other defendants, Wiggins and Hackney ultimately pleaded guilty and agreed to cooperate with the government.

In a jury trial, appellants Washington, Taylor, and Harmon presented an entrapment defense. Each of them stated that before meeting with Olivier, he knew only of the opportunity to do some private security work, not of the work’s connection with drug operations. Each further testified that upon learning of the nature of the operations, he was too scared to back out. Each also testified that he carried a gun during the drug runs.

The jury found Washington and Taylor guilty of all six charges; it acquitted Harmon of attempted possession with intent to distribute cocaine but convicted him of the five remaining. charges. Appellants were each sentenced to prison terms totaling 592 months (49 years, 4 months), aggregating concurrent terms of up to 292 months (24 years, 4 months) for the bribery and drug offenses with consecutive terms of 300 months (25 years) for the firearms offenses.

II.

A. Sufficiency of the Jury Instructions on Entrapment Issues. With two exceptions, the jury instruction on entrapment given by the district court adhered to the standard Redbook instruction. See Criminal Jury Instructions for the District of Columbia, No. 5.05 (4th ed.1993). The two exceptions were that the jury was instructed that (1) “it is not a defense to the crimes charged that the defendants were induced to commit the crimes by their co-conspirators,” and (2) “if you find that a defendant was entrapped as to one offense, you may but are not required to find the defendant was also entrapped as to the other offenses.” Appellants challenge these two deviations from the standard instructions, and they also object to the district court’s refusal to include various additions to the standard instructions they proposed.

1. Refusal to Instruct the Jury on Derivative Entrapment. Appellants first contest the district court’s decision to preclude consideration of a “derivative entrapment” defense. Whereas a regular entrapment instruction is generally given when the evidence shows that the defendant was directly induced to commit a crime by a government agent, the evidence in the present ease showed that the three appellants were not directly recruited by Olivier (the undercover agent), but by Hackney (an “unwitting” intermediary who had previously been recruited by Olivier). All three appellants testified at trial that Hackney approached them claiming that a Miami businessman who carried lots of cash and needed protection while in the area was looking for officers to work private security. On the basis of this testimony, the defense requested an entrapment instruction that would have permitted the jury to consider the conduct of and inducement offered by Hackney in determining whether the defendants had been entrapped.

The district court rejected the request for an instruction on derivative entrapment. The jurors were instructed that “they could consider only the representations or actions of the FBI agent” himself, and that “as a matter of law it is not a defense to the crimes charged that the defendants were induced to commit the crimes by their co-conspirators, such as William Hackney or Nygel Brown.” Appellants challenge this instruction, contending that this circuit has recognized the derivative entrapment defense (at least in dicta), Johnson v. United States, 317 F.2d 127 (D.C.Cir.1963), that other circuits have also recognized it, and that the defense should have been available here because otherwise the government would be allowed to shield itself from regular entrapment claims by designing sting operations to shift the task of recruiting additional sting targets onto the original targets of the operation. Joint Brief for Appellants, at 59-60. The government, on the other hand, asserts that, even if derivative entrapment is a legitimate defense under the law of this circuit, there was “no legal or factual basis” for allowing it in this case. Final. Brief for Appellee, at 96. We review the district court’s decision not to give the derivative entrapment instruction de novo. United States v. Layeni 90 F.3d 514, 517 (D.C.Cir.1996); United States v. Ortiz, 804 F.2d 1161, 1164 (10th Cir.1986) (“[W]hether there is evidence sufficient to constitute a triable issue of entrapment is a question of law.”).

This case involves a difficult question in the field of entrapment law, and one on which courts around the country have reached vastly different conclusions: to what extent is a derivative entrapment instruction merited in cases where the government acts through an unwitting agent. Although all circuits appear to be in agreement that “[p]ersuasion, seduction, or cajoling by a private party does not qualify as entrapment,” United States v. Burkley, 591 F.2d 903, 911 n. 15 (D.C.Cir.1978), and some circuits appear to have rejected the derivative entrapment defense in all its forms, nevertheless a number of circuits have recognized the defense under some circumstances when “government agents act through private citizens.” Of those jurisdictions permitting the defense, some have allowed it only in cases in which the government acts through a knowing agent (e.g., an informant), whereas others have also allowed its application in cases of unwitting (that is, de facto) agents.

After carefully examining case law in this and other jurisdictions, we conclude that a limited form of the “derivative entrapment” theory is recognized in this circuit, and extends to cases in which unwitting intermediaries—at the government’s direction—deliver the government’s inducement to a specified third party. In Johnson v. United States, this court first stated that, although “[t]he entrapment defense does not extend to inducement by a private citizen,” nevertheless “it has found general application to cases where the officer acts through a private citizen.” 317 F.2d 127, 128 (D.C.Cir.1963). More recently, in United States v. Layeni we further explained that:

[T]he.entrapment defense can be raised by a defendant who was induced by an unknowing intermediary at the instruction or direction of a government official or third party acting on behalf of the government (e.g., an informant). The defense should not apply if, in response to pressure put on him by the government, the unknowing intermediary on his own induces the defendant to engage in criminal activity.

90 F.3d 514, 520 (D.C.Cir.1996) (emphasis in original). The Layeni court made explicit what was implicit in Johnson—that a derivative entrapment defense could be based on the actions of an “unknowing intermediary.” Then, most recently, in United States v. Spriggs, this court again confirmed the existence of the defense (as well as its application in cases of unknowing, de facto government agents), when it cited Layeni for the proposition that “it may be possible to establish indirect entrapment through an unwitting intermediary.” 102 F.3d 1245, 1261 (D.C.Cir.1996). The combined weight of the decisions in Johnson, Layeni, and Spriggs persuades us that situations may arise in which this court would be obligated to give an instruction on derivative entrapment, even if the intermediary involved did not know that he was acting as a de facto government agent.

Of course, the fact that derivative entrapment is a legally cognizable defense in this circuit does not mean that an instruction on the defense was merited on the facts of this case. We do, however, reject the notion that the intermediary’s ignorance of the fact that he is acting as go-between for the government by itself negates a derivative entrapment defense, and so disagree with the district court’s ruling to the extent it suggests a blanket rule against a derivative entrapment instruction in cases where “the defendants were induced to commit the crimes by their co-conspirators.” Indeed, the purpose behind allowing such a defense is to prevent the government from circumventing rules against entrapment merely by deploying intermediaries, only one degree removed from the officials themselves, who carry out the government’s explicit instructions to persuade a particular individual to commit a particular crime using a particular type of inducement. This purpose could too easily be defeated by allowing the government to target specific individuals through unwitting go-betweens. In the present case, nonetheless, for the reasons outlined below we agree with the district court that—regardless of what view of the facts is adopted—there is no basis for the derivative entrapment defense.

The facts of the so-called “entrapment” scenario were hotly disputed in the proceedings below. The defense asserted that the appellants were not aware that the “private security work” was illegal until they actually met with Olivier. The prosecution, in contrast, claimed that' the appellants knew from the outset that they were hired to participate in illegal drug-running activities. Generally speaking, “[i]n deciding whether-the trial judge should have given the jury an entrapment instruction, this court must consider appellant’s version of the facts as true.” United States v. McKinley, 70 F.3d 1307, 1310 (D.C.Cir.1995) (citing United States v. Borum, 584 F.2d 424, 427 (D.C.Cir.1978)). However, if we assume the facts alleged by the defense on appeal, then appellants clearly are not entitled to a derivative entrapment defense. According to appellants, Joint Brief for Appellants, at 58-59 (footnotes and citations omitted). Appellants argue that a derivative entrapment instruction was warranted despite the fact that the “inducement” communicated by Hackney to his recruits was allegedly different than the inducement that Olivier directed Hackney to relay. This assertion conflicts with established law in this circuit. Under our precedents, the derivative entrapment defense may only be raised if the alleged inducement communicated by the unwitting intermediary is the same inducement, directed at the same target, as the inducement that the government agent directs the intermediary to communicate. If the intermediary deviates from the government’s plan, and therefore acts, “on his own,” then the inducement cannot be attributed to the government agent. United States v. Layeni, 90 F.3d at 520. Accordingly, even if it were true (as appellants themselves allege) that Hackney modified the alleged inducement, telling the appellants that they would be engaging in legitimate private security work in exchange for $2000 per run, then he would have deviated from the government’s original inducement (offering money in exchange for drug-running), and a derivative entrapment instruction would not be supported by the evidence. Assuming that appellants did not know they were to commit a crime until after they met with Olivier himself, then the only issue for the jury would be whether Olivier himself entrapped them. But the jury was instructed on the issue of direct entrapment, and it was up to the jury to decide whether the elements of the derivative entrapment defense were shown.

The three defendants herein had all been recruited by Hackney. Each officer testified, with some variation, that Hackney had approached them under the same- pretext—a Miami businessman who carried lots of money and needed protection while in the area was looking for officers to work private security, a scenario consistent with what Hackney, in his [Pre-Sentencing Report], claimed he had been told by Brown. Based on that testimony, the jury could have concluded that Hackney duped the defendants into meeting with Olivier, by causing them to believe that the work for Olivier involved legal, albeit unauthorized, private security work.

On the other hand, because the McKinley rule is based on the principle that, “[i]n deciding whether a jury question is raised, the trial judge must consider the evidence in the light most favorable to the defendant,” and because, ironically, all three appellants might have made a stronger case for a derivative entrapment instruction had they conceded that they were aware from the outset that they would be working for a “drug dealer,” we give appellants every benefit of the doubt on this question and go on to consider whether they would have been entitled to a derivative entrapment instruction under that view of the facts. This second scenario is much closer to a paradigmatic example of derivative entrapment: the undercover agent explicitly directed his initial recruit (who acted as an unwitting government agent) to recruit more “corrupt” officers—and to offer these new recruits a monetary incentive ($2000 per drug run) that Olivier had set. One could argue that, by recruiting the three appellants, Hackney unwittingly acted as a conduit, directly communicating an incentive dictated by a government agent to other sting targets, at the direction of that government agent. Given this scenario, a derivative entrapment instruction almost certainly would have' been necessary, except for the crucial fact that Olivier did not designate particular police officers to whom the intermediaries should offer the $2000 incentive per drug run. Rather, Olivier instructed Hackney and Brown more generally to offer the incentive to undesignated cops whom they knew to be corrupt or “dirty.”

Such a general instruction by a government agent to an intermediary is not sufficient to support a derivative entrapment defense. As Layeni made clear, “[t]he defense should not apply if, in response to pressure put on him by the government, the unknowing intermediary on his own induces the defendant to engage in criminal activity.” 90 F.3d at 520. In Layeni, this court held that a derivative entrapment instruction was not required in a case where a government informant (directed by the government) attempted to apprehend a known heroin dealer by persuading the dealer’s girlfriend to arrange for the dealer to sell drugs to the informant. On the day of the proposed sale, however, the dealer happened to be out of town, and the girlfriend instead sent defendant Layeni to make the sale. In affirming the denial of the defendant’s request for an entrapment instruction, we reasoned that, because the girlfriend had acted “on her own” (rather than at the explicit direction of the government) in sending Layeni (rather than her boyfriend) to make the sale, the government had not entrapped the defendant.

The meaning of acting “on one’s own” was further expounded upon in Spriggs, where this court noted that, although government agents conducting a money-laundering sting operation had indirectly communicated monetary incentives to the defendant through a go-between, the actual inducement of that particular defendant “was not specifically contemplated by the Government, which had not targeted any particular salesperson.” 102 F.3d 1245, 1261 (D.C.Cir.1996). In this way, Spriggs elaborated on the reasoning of Layeni, making clear that a derivative entrapment theory should only apply to sting operations conducted through unwitting intermediaries if the intermediaries are directed to target specific individuals and follow these instructions. Here, in contrast, Hackney acted independently—that is, on his own—in deciding who would be targets of Olivier’s offer. Because appellants were not specifically targeted by the government’s scheme, they are not entitled to a derivative entrapment defense. We therefore conclude that appellants were not entitled to a derivative entrapment defense under any possible version of the facts that the jury could have found.

2. Sufficiency of the General Entrapment Instructions. In addition to the claim that the district court should have given an instruction on a derivative entrapment defense, appellants also challenge the general entrapment instructions actually given on four grounds, arguing that the district court erred when it refused to add the appellants’ suggested language. In reviewing jury in-struetions for legal error, “we consider not just the challenged phrases, but the instruction as a whole.” United States v. Merlos, 984 F.2d 1289, 1242 (D.C.Cir.1993) (citation omitted). We conclude that, viewed as a whole, the instructions given by the district court correctly informed the jury about the entrapment defense and about the legal standards to be applied in this case.

Appellants first contend that the entrapment instruction in its entirety was “severely imbalanced” because it “exhaustively catalogued a veritable litany of proper government actions while failing” to mention that the government cannot “create the crime” under Jacobson v. United States, 503 U.S. 540, 548-49, 112 S.Ct. 1535, 1540-41, 118 L.Ed.2d 174 (1992). See Joint Brief for Appellants, at 65. Although it is true that the instruction did not specifically use the Jacobson language that the government may not “create the crime,” this fact alone is not sufficient to demonstrate that the instruction was flawed. On the contrary, the instruction did include—in standard Redbook form—the functional equivalent of the Jacobson language by stating that, “[a] person is entrapped if law enforcement officials induced or persuaded a person to commit a crime which he would not otherwise have committed.” Nor in our view were the instructions “severely imbalanced” in any other way. Although the instruction did dte many examples of proper police conduct, it also suggested numerous examples of improper conduct, explaining that inducement “may take many forms, including persuasion, fraudulent representations, threats, coercive tactics, harassment, promises of reward, or pleas based upon need, sympathy, or friendship.” We therefore find that the court fairly and adequately described the legal meanings of improper inducement; ultimately, it was the jury’s province to decide whether Olivier’s specific conduct fit this model.

Second, appellants challenge the district court’s denial of defendants’ request that the jury “be instructed that it could consider Olivier’s actions as relating to the scope and nature of the inducement, and its effect on the defendants’ states of mind.” Joint Brief for Appellants, at 65 (citing United States v. Williams, 705 F.2d 603, 617 (2d Cir.1983), as an example of a case where such an instruction was given). According to the defense, it was necessary so to instruct the jury because Olivier accompanied the monetary inducement with constant reassurances that it was “easy money,” and because Olivier exerted subtle coercion over the defendants, presenting himself as “a ‘Columbian’ drug dealer—behind locked doors, and in the presence of other armed policemen, some of whom were not known to the officers, and all of whom appeared already to be in cahoots with Olivier.” Id. at 66. This argument is without merit. As the government rightly points out, the entrapment instruction included standard Redbook language which adequately conveyed to the jury that it could consider both the impact that Olivier’s words and actions may have had on the appellants’ states of mind, as well as the various forms that “inducement” by a law enforcement officer might take. Moreover, adding the precise language requested by the appellants could have misled the jury into judging the defendants’ predisposition on a subjective basis, when the established standardfor predisposition is objective. United States v. Kelly, 748 F.2d 691, 698 (D.C.Cir.1984) (for entrapment defense, relevant issue is whether the government agent’s conduct was likely to overcome “a law-abiding citizen’s will to obey the law”).

Third, appellants argue that, despite the repeated objections of defendants at trial, the judge’s entrapment instruction misconstrued the legal principles set forth in Sherman v. United States, 356 U.S. 369, 374, 78 S.Ct. 819, 821-22, 2 L.Ed.2d 848 (1958). They contend that the jury should have been allowed to consider that the sting operation and the resulting actions of the participants constituted a single continuing course of conduct such that once a defendant was entrapped, he may have stayed entrapped throughout the duration of the conspiracy. However, appellants’ reliance on this theory (and on the nearly forty-year old Sherman case) ignores the fact that we recently rejected the “once-entrapped-always-entrapped” theory. See United States v. Vaughn, 80 F.3d 549, 552 (D.C.Cir.1996) (interpreting Jacobson to permit “a jury to consider the possibility that a defendant’s disposition to commit a crime changed over time”); United States v. Layeni, 90 F.3d 514, 517 n. 1 (D.C.Cir.1996) (explaining that “the continuing entrapment theory” was rejected by Vaughn); Spriggs, 102 F.3d 1245, 1260 (D.C.Cir.1996) (finding that an instruction on continuing entrapment was foreclosed by Vaughn, and reasoning that the fact “[tjhat a particular defendant might have lacked predisposition to launder money once does not mean he lacked it at a later time.”). As the Vaughn court explained, “Sinners may become saints and saints may become sinners. Nothing is necessarily permanent about either state. A person might be disposed to commit a crime one day and not disposed to do so some time later.” 80 F.3d at 552. Here, the challenged instruction, which properly required the jury to find predisposition for each separate offense, but which also stated that, “if you find that a defendant was entrapped as to one offense, you may but are. not required to find the defendant was also entrapped as to the other offenses,” was entirely consistent with Vaughn, Layeni, and Spriggs.

Fourth and finally, appellants claim the entrapment instruction did not inform the jury adequately about the essential timing of a finding of predisposition. According to appellants, “[i]t is fundamental that a defendant’s predisposition to engage in the crime must precede or arise simultaneously with the proffered inducement.” Joint Brief for Appellants, at 66 (emphasis in original) (citing cases). Contrary to appellants’ assertion, we conclude that‘the court did not err (let alone plainly err) - by omitting an instruction that the jury must find that the defendant was ready and willing to commit the crime before being approached by. government agents. Although at least one of our sister circuits has stated that, “[a] defendant’s predisposition is not to be assessed ‘as of that time when he committed the crime,’ ” and that “predisposition refers to the state of mind of a defendant before government agents make any suggestion that he should commit a crime,” United States v. Williams, 705 F.2d 603, 618 (2d Cir.1983) (emphasis added), the government is correct in arguing that this circuit has interpreted the “prior to” language of some of our cases “to mean only that the government must prove that the defendant’s disposition was ‘independent and not the product of the attention that the Government’ directed at the defendant.” Vaughn, 80 F.3d at 552. The district court explained to the jury that inducement and predisposition were two distinct elements of the entrapment defense, and that the jury was required to make a finding that “the defendant was otherwise ready and willing to commit the crimes charged.” These instructions made clear to the jury that the defendants’ predisposition to commit the crime, or lack thereof, was a separate and independent element from the government’s inducement. An additional instruction emphasizing that the predisposition must be “prior to” the alleged inducement was not required by current law and would have been superfluous.

B. Refusal to Admit Evidence of Appellant Washington’s Prior Commendations. In the proceedings below, the government was permitted to present “other crimes” evidence under Rule 404(b) of the Federal Rules of Evidence in order to rebut the defendants’ entrapment defense, and to “prove that [the officers’] betrayal of trust was done intentionally and knowingly and not done mistakenly or accidentally” and that they were predisposed to abuse their authority as police officers. Government’s Notice of Rule 404(b) Evidence, at 1-2. Washington, in turn, sought to have evidence admitted under Federal Rule of Evidence 405(b) of several commendations he had received for his work on the police force. He proffered this evidence in an attempt to rebut the instances of alleged criminal activity raised by the government, and to disprove predisposition. Washington argued at trial that the jury could then contrast prior good with pri- or bad acts and be better able to determine the presence or absence of criminal intent.

The district court refused to admit the commendations into evidence, explaining that they did not fit the criteria for any exception from the hearsay rule for character evidence, that they did not constitute rebuttal evidence, and that neither Rules 404 nor 405 provided a basis for their admission. We review the district court’s refusal' to admit evidence of the commendations for abuse of discretion. United States v. Watson, 894 F.2d 1345, 1349 (D.C.Cir.1990).

On appeal, Washington complains that the district court was expansive in its admission of the government’s evidence of prior bad acts, while at the same time it was unfairly strict in its admission of evidence of prior good acts. In arguing that the commendations were admissible, he relies on Michelson v. United States, in which the Supreme Court stated that a defendant “may introduce affirmative testimony that the general estimate of his character is so favorable that the jury may infer that he would not be likely to commit the offense charged.” 335 U.S. 469, 476, 69 S.Ct. 213, 219, 93 L.Ed. 168 (1948). In some eases, the Court explained, “such testimony alone ... may be enough to raise a reasonable doubt of guilt.” Id. The defense contends that the letters “would have rebutted the government’s repeated declaration that Washington was prepared to ‘sell his badge’ and clearly cast doubt on whether the evidence of prior bad acts established a predisposition” on Washington’s part. Individual Brief for Appellant Washington, at 16.

We conclude that the district court did not abuse its discretion in refusing to admit the commendations. It is true that the accused may introduce-evidence of a “pertinent trait of character” under Federal Rule of Evidence 404(a)(1). Such evidence generally must be in the form of testimony as to reputation or by testimony in the form of an “opinion,” Fed:R.Evid. 405(a), but “[i]n cases in which character or a trait of character of a person is an essential element of a charge, claim, or defense, proof may also be made of specific instances of that person’s conduct.” Fed.R.Evid. 405(b). Under these Rules, the district court acted well within its discretion when it excluded the evidence at issue here. As the government persuasively argues, the commendations were not admissible under either Rule because appellant’s “dedication, aggressiveness and assertiveness” in investigating drug dealing and carjacking is neither “pertinent” to nor an “essential element” of his supposed lack of predisposition to engage in the corrupt criminal activity with which he was charged. Cf. United States v. Nazzaro, 889 F.2d 1158, 1168 (1st Cir.1989) (excluding evidence of police officer’s prior commendations because “the traits which they purport to show—bravery, attention to duty, perhaps community spirit—were hardly ‘pertinent’ to the crimes [of perjury and conspiracy to commit mail fraud] of which [the defendant] stood accused”).

In addition, even if the exclusion amounted to error, it would have been harmless. When a court reviews a nonconstitu-tional trial error, it must determine “whether the error ‘had a substantial or injurious effect or influence in determining the jury’s verdict.’” Brecht v. Abrahamson, 507 U.S. 619, 637, 113 S.Ct. 1710, 1722, 123 L.Ed.2d 353 (1993) (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 1253, 90 L.Ed. 1557 (1946)). Any error that might have occurred here would not have had a substantial effect on the jury’s verdict because (1) the government produced overwhelming evidence of Washington’s predisposition, and because (2) the commendation evidence was cumulative of other “good character” evidence that was admitted. First, the government produced reliable evidence that Washington told Olivier that he had previously sold marijuana, and that, while Washington was a police officer, he had stolen money and drugs. Second, appellant was permitted to call four witnesses who attested to his “good character.” The commendations that were excluded from evidence were unlikely to be more effective in rebutting the government’s predisposition evidence than the testimony of these live witnesses. For these reasons, any conceivable error committed in declining to admit the commendations was harmless.

C. Refusal to Admit Evidence of Appellant Harmon’s Prior Consistent Statement. At trial, appellant Harmon (like Washington and Taylor) claimed that at the time he entered his first meeting with Olivier, he still believed that Olivier was offering the opportunity to do legitimate private security work. Harmon attempted to establish that, by the time he learned at the first meeting that the work involved illegal drug-running, he was already too scared to get out of the conspiracy. In support of his story, he sought admission of testimony from his friend and mentor, Russell Hairston, that Harmon had told Hairston separately that he was going to be doing some part-time private security work, that he would be paid in cash for the work, and that other police officers would be working with him.

Although the court found that Harmon’s statement to Hairston was material, and that Hairston was a credible witness, it nevertheless ruled that the statement did not meet the specific criteria for admissibility under Federal Rule of Evidence 801(d)(1)(B). The court acknowledged that the government had challenged Harmon’s credibility, but found that Harmon had not been directly impeached with prior inconsistent statements, or expressly or impliedly charged with recent fabrication, or improper influence or motive, as required by the Rule. We review the court’s refusal to admit the statement for abuse of discretion (although the court’s ruling on the residual hearsay exception may not be overturned unless this court has a “definite and firm conviction that the court made a clear error of judgment,” United States v. North, 910 F.2d 843, 909 (D.C.Cir.1990) (as amended) (internal quotation marks omitted)).

Hannon argues that the district court erred by refusing to admit evidence of the prior statement. Individual Brief of Appellant Harmon, at 7-8. He claims that the issue of what he knew before entering the townhouse for the initial interview with Olivier was crucial in the jury’s determination of his predisposition at the time that he was induced to join the conspiracy. He asserts three alternative theories of admissibility: (1) the statement was admissible non-hearsay under Federal Rule of Evidence 801(d)(1)(B) because it was offered to rebut an implied charge of improper motive; (2) it was admissible to rehabilitate Harmon’s trial testimony even if it did not meet the requirements of Rule 801(d)(1)(B); and (3) it was admissible under the residual hearsay exceptions set forth in Federal Rules of Evidence 803(24) and 804(b)(5). The government, on the other hand, argues that the statement should have been excluded both for lack of rebutting force under Rule 801(d)(1)(B) and for insufficient probative value under Rule 403.

We conclude that the district court did not err in excluding Hairston’s statement from evidence. First, it was not an abuse of discretion for the court to exclude the statement . under Rule 801(d)(1)(B) because, even if there had been a charge of recent fabrication or improper incentive or motive by the prosecution, Hairston’s statement had no rebutting force against such a charge. The statement would only have established that appellant told Hairston he was going to be doing private security work, not that he did not know that his employer was a drug dealer. Second, the district court did not abuse its substantial discretion in finding that the statement was inadmissible for rehabilitation purposes because the credibility of Harmon’s testimony was subjected only to a “generalized attack,” and more than this is required for admission under this rationale. United States v. Pierre, 781 F.2d 329, 333 (2d Cir.1986) (prior consistent statements must have some rebutting force “beyond showing that the witness had at an earlier time been consistent with his trial testimony”). Finally, we do not have the requisite “definite and firm conviction that the [district] court made a clear error of judgment” in refusing to admit the statement under the residual hearsay exceptions of Rules 803(24) or 804(b)(5). North, 910 F.2d at 909. These two exceptions to the hearsay rule are extremely narrow and require testimony to be “very important and very reliable.” United States v. Kim, 595 F.2d 755, 766 (D.C.Cir.1979); see also Securities & Exchange Comm’n v. First City Financial Corp., 890 F.2d 1215, 1225 (D.C.Cir.1989) (stating that “the legislative history of the [Rule 803(24) ] exception indicates that it should be applied sparingly” and “acknowledg[ing] the broad discretion a trial court enjoys in assessing the probity and trustworthiness of documents”). Thus, the proponent of the statement bears a heavy burden to come forward with indicia of both trustworthiness and probative force, neither of which appellant has succeeded in doing, here. Despite the fact that the district court found Hairston to be a “credible” witness, the prior statement was not trustworthy because of the unlikelihood that Harmon would have disclosed the true, illegal nature of the security work he was performing to a friend who was not involved in the conspiracy. See, e.g., Tome, 61 F.3d at 1453 (explaining that, in order to find the statement trustworthy, a court must find that the declarant of the prior statement “was particularly likely to be telling the truth when the statement was made.”) (internal quotation marks omitted). Moreover, the statement was not “more probative on the point for which it [was] offered than any other evidence which the proponent [could have] procure[d] through reasonable efforts.” Fed.R.Evid. 803(24). As the government pointed out, the prior consistent statement was too vague to be inconsistent with the prosecution’s theory. Even if the jury believed the statement to be true, it only established that appellant said he was going to be involved in some security work and that other officers would be involved. It did not show that appellant had no knowledge that his prospective employer was a drug dealer. Thus, the statement did not meet the requirements of these residual hearsay exceptions.

For similar reasons, even if there were any error here, it too would be harmless under the Brecht-Kotteakos standard. Brecht v. Abrahamson, 507 U.S. 619, 637, 113 S.Ct. 1710, 1722, 123 L.Ed.2d 353 (1993) (error is harmless unless it “ ‘had a substantial or injurious effect or influence in determining the jury’s verdict.’”). As noted above, the prior consistent statement was too vague to be inconsistent with the prosecution’s theory. Moreover, a rational juror would not expect any of the appellants involved in the conspiracy to tell their friends or mentors who were not involved in the conspiracy about its illegal nature. Thus, admission of the statement would not have significantly helped Harmon’s ability to prove his theory of the case, and in light of the overwhelming evidence against him, any error was harmless.

D. Sufficiency of Charge on Attempted Possession of Cocaine With Intent to Distribute. Appellants Taylor and Washington challenge their convictions for attempted possession of cocaine with intent to distribute on two grounds: (1) that there was insufficient evidence to convict them on this count; and (2) that the jury instructions were erroneous because they permitted the jury to convict based on insufficient evidence. Individual Brief for Appellant Taylor, at 8-11 (argument adopted by appellant Washington in his individual brief). We review the sufficiency of the evidence de novo to determine

whether, viewing the evidence in the light most favorable to the Government, according the Government the benefit of all legitimate inferences, and recognizing that it is the jury’s province to determine credibility and to weigh the evidence, a reasonable jury must necessarily entertain a reasonable doubt on the evidence presented.

United States v. Singleton, 702 F.2d 1159, 1163 (D.C.Cir.1983) (emphasis in original). In reviewing the jury instructions, we must determine whether, taken as a whole, they accurately state the governing law and provide the jury with sufficient understanding of the issues and applicable standards. United States v. Merlos, 984 F.2d 1239, 1242 (D.C.Cir.1993) (“[I]n reviewing a jury instruction we consider not just the challenged phrases, but the instruction as a whole.”). However, as appellants concede, see Individual Brief for Appellant Taylor, at 8, the jury instructions here will be reversed only for plain error because they were not challenged below. United States v. Whoie, 925 F.2d 1481, 1485 (D.C.Cir.1990).

1. Sufficiency of the Evidence. The record contains no evidence that appellants themselves attempted to possess the cocaine that was being transported by the undercover officers. Rather, the evidence (viewed in the light most favorable to the government for purposes of this appeal) showed that appellants willingly and knowingly helped Olivier, whom they believed to be a drug dealer, in what they believed to be his possession of cocaine with intent to distribute. Consistent with these facts, the prosecution put forth its charge of attempted possession on an aiding and abetting theory. In support of the proposed charge, the prosecution explained:

The fact that [appellant] Harmon never touched the suitcase, never touched any drugs is irrelevant under the government’s theory of aiding and abetting the possession with intent to distribute cocaine. What he did was take a substantial step in furtherance of his intended purpose to aid Jose Olivier in the transportation of [the drugs].

After some initial controversy raised by Harmon’s counsel, the judge ultimately allowed the attempt charge against all three appellants on the basis of this aiding and abetting theory.

Appellants now claim that there was insufficient evidence to convict them under an aiding and abetting theory because they did not possess “the same criminal intent as the principals.” United States v. North, 910 F.2d 843, 881 n. 11 (D.C.Cir.1990). They argue that their convictions must be reversed because the undercover FBI agents participating in Operation Broken Faith, who were the so-called “principals” to the attempted possession crime, had no criminal intent whatsoever. The government, on the other hand, argues that the “shared intent” requirement of accomplice liability refers not to the fact that the accomplice and the principal must have the same intent, but rather to the fact that “the accomplice must have some criminal purpose in mind.” Final Brief for Appellee, at 111. We conclude that there was sufficient evidence to instruct the jury on the attempted possession with intent to distribute charge.

It is true that in order to convict an accomplice of a completed substantive crime (rather than a mere attempt), “there must be a guilty principal before there can be an aider and abettor,” United States v. Staten, 581 F.2d 878, 887 (D.C.Cir.1978), and the accomplice and the principal must have a “shared intent.” United States v. Walker, 99 F.3d 439, 442 (D.C.Cir.1996). In United States v. Raper, we set forth the specific requirements for convicting an accomplice:

The elements of aiding or abetting an offense are (1) the specific intent.to facilitate the commission of a crime by another; (2) guilty knowledge on the part of the accused; (3) that an offense was being committed by someone; and (4) that the accused assisted or participated in the commission of the offense.

676 F.2d 841, 849 (D.C.Cir.1982) (citations omitted) (emphasis added). In purported reliance on these principles, appellants here claim that they could not legitimately be convicted of aiding and abetting attempted possession of drugs with intent to distribute because there was no guilty principal, and because there was no “shared intent” between the “principals” and the accessories (because the government agents, unlike the appellants, were only pretending to be drug dealers and therefore did not have the necessary mens rea for the offense). Whatever merit such arguments might have in another context, appellants’ reliance on these principles here is entirely misplaced—because they were not charged or convicted of the completed substantive crime, but only of an attempt.

The Model Penal Code has expressly addressed the question we face here. In a section on the law of criminal attempt, it states:

Section 5.01. Criminal Attempt.

(3) Conduct Designed to Aid Another in Commission of a Crime. A person who engages in conduct designed to aid another to commit a crime that would establish his complicity under Section 2.06 if the crime were committed by such other person, is guilty of an attempt to commit the crime, although the crime is not committed or attempted by such other person.

Model Penal Code and Commentaries (Official Draft and Revised Comments), Part I, § 5.01(3) (A.L.I.1985). In an explanatory note, the Code identifies the purpose behind subsection (3):

Subsection (3) fills what would otherwise be a gap in complicity liability. Section 2.06 [of the Model Penal Code] covers accomplice liability in situations where the principal actor actually commits the offense. In eases where the principal actor does not commit an offense, however, it is provided here that the accomplice will be liable if he engaged in conduct that would have established his complicity had the crime been committed.

Id. at 297-98 (explanatory note to § 5.01(3)). It is important to highlight the fact that this passage does not describe an offense of aiding and abetting an attempted crime (in that case, there would be a guilty principal and an offense, thus posing no problem under the traditional aiding-and-abetting framework), but rather refers to attempting to aid and abet a crime (an offense for which there may not be a guilty principal). See id. at 354-56 (comment to § 5.01(3)). But in either case, paradoxically, the crime ultimately charged is the same. If the principal had actually attempted to commit a crime but had failed, the aider and abettor would be charged with the same offense as the principal (attempt to commit the crime). If (as here), the principal had only pretended to commit the crime, and the accomplice attempted to aid the principal by “engag[ing] in conduct that would have established his complicity had the crime been committed,” the accomplice may also be charged with an attempt to commit the crime.

In the latter scenario, however, the prosecution need not show that an offense was actually committed, nor that the principal and accomplice had a “shared intent.” As with other attempt crimes, the focus of the court’s analysis shifts away from external circumstances to an examination of the defendant’s intent and actions in furtherance of that intent. Thus, the prosecution must show that the defendant “acted with the kind of culpability otherwise required for the commission of the crime which he is charged with attempting,” and that he “engaged in conduct which constitutes a substantial step toward the commission of the crime.” United States v. Mandujano, 499 F.2d 370, 376 (5th Cir.1974); accord 2 Wayne R. La Fave & Austin W. Scott, Jr., Substantive Criminal Law 18 (1986) (“The crime of attempt ... consists of (1) an intent to do an act or to bring about certain consequences which would in law amount to a crime; and (2) an act in furtherance of that intent which ... goes beyond mere preparation.”). Factual impossibility is no defense. United States v. Duran, 884 F.Supp. 577, 580 n. 5 (D.D.C.1995) (citing cases), aff'd, 96 F.3d 1495 (D.C.Cir.1996); see also 2 LaFave & Scott, Substantive Criminal Law 41 (“[F]actual impossibility, where the intended substantive crime is impossible of accomplishment merely because of some physical impossibility unknown to the defendant, is not a defense.”). The court looks instead to the question of whether, if the facts had been as the accomplice believed them, the principal would have been guilty. As with other attempt crimes, permitting convictions on the basis of the “attempt to aid and abet” theory is justified because, even if an offense was not actually committed, the defendant “manifests the same dangerousness of character as the actor who himself attempts to commit the offense.” Model Penal Code, supra, at 356.

In a ease very similar to the one we decide today, the Fifth Circuit reached a similar conclusion. United States v. Cartlidge, 808 F.2d 1064 (5th Cir.1987). In that case, a government informant and other undercover government agents posed as drug dealers in order to catch a corrupt police officer who “had solicited money from [the informant] in return for providing protection for drug deals.” Id. at 1065. The undercover agents recorded a conversation in which the defendant “demanded] $500 a month to provide protection for [the informant’s] involvement in what [the defendant] assumed to be a drug operation.” Id. at 1066. After several more recorded conversations in which the defendant accepted money from the undercover agents, assuring them that in exchange he would “provide security” to drug dealers, the defendant was arrested. Although the drug operation that the defendant intended to help did not really exist (since the undercover agents were only pretending to be drug dealers), the defendant was charged with and convicted of attempting to aid and abet in the federal crime of possession and distribution of marijuana.

On appeal, the Fifth Circuit upheld the conviction for attempted aiding and abetting of the drug offense. As the Cartlidge court pointed out, the federal Controlled Substances Act punishes “[a]ny person who attempts or conspires to commit any offense” enumerated in the Act. 21 U.S.C. § 846 (1994). Neither the statute itself nor its legislative history provides any other explanation of what constitutes an attempt, so “federal courts have, like state courts faced with a similar problem, followed the principles of attempt liability developed at common law.” Cartlidge, 808 F.2d at 1066. Under the common law model, the defendant could be convicted of attempted aiding and abetting possession with intent to distribute, despite the fact that no drug offense was actually committed by a principal, if he (1) had exhibited a criminal intent consistent with the crime of aiding and abetting a drug operation; and (2) had “moved beyond preparation” and completed the “requisite sub-, stantial step” toward committing that crime by accepting the money and by promising to protect the purported “drug dealers.” Id. at 106&-69.

Similarly here, the evidence construed in the light most favorable to the government showed that appellants had a criminal intent consistent with the crime of aiding and abetting possession of cocaine (based on the tapes of their discussions with Olivier, evidence of their discussions with each other, as well as their actions). Moreover, they took very substantial steps toward committing that crime {e.g., meeting with Olivier, agreeing to protect drug dealers and accepting cash payments for doing so, and protecting the “drug dealers”), and would have committed the crime, but for the fact that the crime was made factually impossible because the “principals” were really undercover government agents. As noted above, factual impossibility is no defense to an attempt crime. Under these circumstances, there clearly was sufficient evidence to convict appellants of attempted possession with intent to distribute.

2. Jury Instructions. Although we have established that there was sufficient evidence to convict appellants of the attempted possession with intent to distribute charge, we must still address the question of whether the jury instructions on that charge were plainly erroneous. United States v. Gatling, 96 F.3d 1511, 1524 (D.C.Cir.1996).

Most of appellants’ objections to the jury instructions are based on their erroneous view that, for a charge of attempted aiding and abetting possession with intent to distribute, the accomplice and the “principal” must have a “shared intent.” Individual Brief for Appellant Taylor, at 10-11. Those arguments were addressed and rejected in the previous section on the sufficiency of the evidence. However, appellants do correctly point out that the district court included some language in the jury instructions that was not supported by the evidence. For example, although the language of the second to last paragraph of the charge is drawn from the Redbook, that particular version of the instruction is explicitly designed for situations like felony murder, in which there is originally a shared intent between the principal and the accessory, but where the accessory may not actually have intended the crime which the principal ultimately committed. Id. at 10 (citing D.C. Bar Association, Criminal Jury Instructions (1993 ed.) (Instr. 4.02 Comment)). Similarly, some of the district court’s instructions (for example, those that explain the requirements for convicting a person of attempted possession, without referring to an aiding and abetting theory) seem to lay the groundwork either for a charge of direct attempted possession, or for aiding and abetting attempted possession, neither of which was supported by the evidence here.

Yet, in spite of the fact that the district court included some superfluous language describing legal theories that were not supported by the evidence, we cannot conclude that these inclusions constituted plain or reversible error. We will find plain error “only if the defendant has shown a clear or obvious error occurred that affected substantial rights.” Gatling, 96 F.3d at 1525. The defense must show that this error “was prej-udieial and actually affected the outcome below,” and that it was an error that “seriously affeet[s] the fairness, integrity or public reputation of judicial proceedings.” Id. (quoting United States v. Olano, 507 U.S. 725, 735-86, 113 S.Ct. 1770, 1778, 123 L.Ed.2d 508 (1993)) (internal quotation marks omitted). This standard is not met here.

First, no error was committed that seriously affected the fairness of the trial. Although the instructions included descriptions of theories of liability that were not necessarily supported by the evidence, this does not constitute reversible error because the instructions viewed as a whole provided an entirely adequate explanation of all of the elements that go into a proper attempt to aid and abet charge. The court began by laying out the requirements for the offense of possession of cocaine with intent to distribute. The court also correctly advised the jury of the requirements for convicting a defendant of an attempt crime, and of the requirements for finding accomplice liability. Thus, the district court succeeded in explaining to the jury each of the elements of the crime of attempting to aid and abet possession of cocaine with intent to distribute. Moreover, although the instructions also suggested some theories of liability that were not supported by the evidence, it is a well-established principle that when a jury is instructed on multiple acts that may legally form the basis for a conviction, a general verdict must be sustained so long as “the evidence is sufficient with respect to any one of the acts charged.” Griffin v. United States, 502 U.S. 46, 56-57, 112 S.Ct. 466, 473, 116 L.Ed.2d 371 (1991) (internal quotation marks omitted); see also United States v. Collins, 56 F.3d 1416, 1421 (D.C.Cir.1995) (upholding conviction in a case where one basis of charge was factually unsupported but other basis was supported), cert. denied, — U.S. —, 116 S.Ct. 737, 133 L.Ed.2d 687 (1996).

Second, the error, if any, did not rise to the level of plain error because the defendants were not prejudiced thereby. For one thing, a rational jury presumably would ignore those charges that were unsubstantiated by the facts of the case. Moreover, the prosecution presented overwhelming evidence that the defendants were guilty of attempting to aid and abet possession with intent to distribute. In light of this overwhelming evidence, the appellants’ only chance of acquittal was if the jury believed their entrapment defense. But the elements of that defense (ie., inducement and predisposition) were completely separate from and independent of the elements of the attempted possession charge. Thus, the defendants did not show any error in the instructions which possibly could have “actually affected the outcome below.” We therefore conclude that there was no reversible error in the jury instructions on the attempt charge.

E. Permissibility of Bribery Instructions. In defining an essential element of the bribery count, the district court instructed the jury: “the defendant demanded, sought, received, accepted, or agreed to receive or accept a thing of value corruptly in return for being influenced in the performance of any official act, or being persuaded to omit an act in violation of his official duty.” Harmon contends that there was no evidence that he received payments in exchange for omitting an act in violation of his duty, and therefore, the district court erred in instructing the jury on a charge unsupported by the evidence. This contention is without merit.

When a jury is instructed on multiple acts that may form the basis of a conviction, “ ‘the verdict stands if the evidence is sufficient with respect to any one of the acts charged.’” Griffin v. United States, 502 U.S. 46, 56-57, 112 S.Ct. 466, 473, 116 L.Ed.2d 371 (1991) (quoting Turner v. United States, 396 U.S. 398, 420, 90 S.Ct. 642, 654, 24 L.Ed.2d 610 (1970)). The fact that the district court may have instructed the jury on an additional ground not warranted by the evidence thus would not in itself establish grounds for reversing the bribery conviction. In the instant ease, in any event, the instruction was supported by the evidence. The evidence showed that the defendants did “omit an act” in violation of their duties as police officers: they failed to arrest or even investigate a drug trafficker. Each appellant acknowledged that he thought “Jose” was a drug dealer, yet none arrested him, began an investigation into his activities, or reported him to the police department. Moreover, Harmon admitted that he accepted a bribe rather than taking appropriate “police procedures and arrest[ing] [Jose] or mak[ing] some type of report,” and Taylor testified that he had accepted $2000 in return “for not arresting Jose.” Based on this testimony, the jury reasonably could have concluded that the bribes were an inducement for the officers to keep quiet, as well as a payment for their affirmative misconduct. The district court’s jury instruction on bribery thus comported with the evidence.

III.

We turn to appellants’ contention that the district court abused its discretion in excluding the testimony of their expert witnesses, and then address their challenges to their convictions under 18 U.S.C. § 924(c)(1).

A. Expert téstimony. Appellants contend that the district court abused its discretion in granting the government’s motion to exclude the proposed expert testimony of Dennis Fitzgerald and George Smith. Fitzgerald, an advisor to law enforcement agencies on corruption training, would have testified that MPD police training was insufficient to prepare young police officers to identify and resist corrupt overtures. Smith, a member of the Tucson, Arizona, police force who had set up many sting operations, would have testified that the design and implementation of Operation Broken Faith, as manifest by the language used by Agent Olivier, created a coercive environment and effectively limited the young officers’ realistic options to resist. Because the proposed expert testimony would allegedly have permitted the jurors to understand the “unique culture of law enforcement” and the particular pressures and difficulties faced by young police officers in confronting police corruption, appellants maintain that the district court’s exclusion of such testimony prejudiced their ability to present an entrapment defense.

Under Rule 702 of the Federal Rules of Evidence, the district court may admit expert testimony that “assist[s] the trier of fact to understand the evidence or to determine a fact in issue.” Fed. R. Evid. 702. But “[expert] testimony should ordinarily not extend to matters within the knowledge of lay[persons].” United States v. Boney, 977 F.2d 624, 628 (D.C.Cir.1992). In other words, “[wjhere the jury is just as capable of drawing correct conclusions as the witness possessed with special training, expert testimony is unnecessary.” United States v. Fadayini, 28 F.3d 1236, 1241 (D.C.Cir.1994). Even when testimony may assist the trier of fact for purposes of Rule 702, the district court may nonetheless exclude such testimony on the grounds that it is unduly prejudicial under Rule 403 of the Federal Rules of Evidence. United States v. Hall, 969 F.2d 1102, 1109 (D.C.Cir.1992). “A trial court has ‘broad discretion’ in deciding both issues, and its decision to admit or exclude expert testimony will be sustained unless the court has in fact abused that discretion.” Id. at 1109-10 (internal citations omitted); see also Fadayini, 28 F.3d at 1241.

In considering Fitzgerald’s proffered testimony, the district court found that the testimony, which “focuse[d] on something the government failed to do in its training program,” was not “relevant to the issue of whether the defendants were either predisposed to commit the crime or not predisposed to commit the crime charged.” In evaluating Smith’s proffered testimony, the district court concluded that his interpretation of the conversations and interaction among Agent Olivier and appellants would not assist the jury because it pertained to matters well within the jurors’ knowledge. Not only was the proposed testimony unnecessary, the district court explained, but its admission would have presented the risk that the jurors would substitute the expert’s interpretation of the conversations and interaction for their own. Finally, the district court stated that the proffered testimony of both experts was too general—about training or sting operations in general—to be of assistance to the jury.

We find no abuse of discretion by the district court in excluding the proffered experts’ testimony. The district court could reasonably conclude not only that the jurors were capable of understanding the evidence in the instant case and determining facts in controversy simply by evaluating the agents’ and appellants’ own words and demeanor on tape and in the courtroom, see United States v. Mitchell, 49 F.3d 769, 780 (D.C.Cir.), cert. denied, — U.S. —, 116 S.Ct. 327, 133 L.Ed.2d 228 (1995); see also United States v. Devine, 787 F.2d 1086, 1087-88 (7th Cir.), cert. denied, 479 U.S. 848, 107 S.Ct. 170, 93 L.Ed.2d 107 (1986), but that the general expert testimony on corruption training and sting operations risked distracting the jury from the true issues of the trial. See United States v. Rouco, 765 F.2d 983, 995 (11th Cir.1985), cert. denied, 475 U.S. 1124, 106 S.Ct. 1646, 90 L.Ed.2d 190 (1986). As the Eleventh Circuit stated in United States v. Evans, 910 F.2d 790 (11th Cir.1990); which affirmed the exclusion of a linguist’s expert testimony interpreting recorded conversations as evidence of entrapment:

[Questions regarding the defendant^’] understanding of the illegality of the operation and the extent of government inducement were at the center of the trial. The jury’s task was to determine, on the basis of its collective experience and judgment, what [the defendants’] state of mind was when [they] accepted the money and whether [they were] entrapped into committing the crime for which [they were] charged.

Id. at 803. The defendants, after all, were members of the MPD, and the jury was in a position to understand that as police officers they would be alert to unlawful conduct even more readily than most persons. Expert testimony essentially to excuse their status as members of the MPD would have been misleading. Moreover, it would have had little bearing on the central issue relevant to appellants’ entrapment defense: whether they had a predisposition to commit the crimes with which they were charged. Hence, we reject appellants’ contention that the district court abused its discretion in excluding the proffered expert testimony.

B. Firearms Convictions. Appellants challenge their convictions under 18 U.S.C. § 924(c)(1) on five independent grounds, including the sufficiency of the evidence; the jury instructions on co-conspirator liability, unanimity, and “use”; and the permissibility of their second firearms convictions in light of United States v. Anderson, 59 F.3d 1323 (D.C.Cir.) (en banc), cert. denied, — U.S. —, 116 S.Ct. 542, 133 L.Ed.2d 445 (1995). Only the last challenge has merit.

1. Sufficiency of the evidence. Appellants contend that, even assuming that they could be held vicariously liable for the acts of their co-conspirators, the evidence was insufficient to support any of their firearms convictions. In order to convict under § 924(c)(1), the government must show that the defendant “use[d] or carrie[d] a firearm,” and that the use or carrying was “during and in relation to” a “crime of violence or drug trafficking crime.” Smith v. United States, 508 U.S. 223, 227-28, 113 S.Ct. 2050, 2053-54, 124 L.Ed.2d 138 (1993). “The phrase ‘in relation to’ thus, at a minimum, clarifies that the firearm must have some purpose or effect with respect to the drug trafficking crime; its presence or involvement cannot be the result of accident or coincidence.” Id. at 237-38, 113 S.Ct. at 2058-59. “[T]he gun at least must facilitate, or have the potential of facilitating, the drug trafficking offense.” Id. at 238, 113 S.Ct. at 2059 (internal quotation marks and brackets omitted). According to appellants, no rational juror could have found that they or any of the other officers, all of whom were required by police regulations to carry their guns at all times, had an intent or purpose to make illegal use of the weapons for the purpose of facilitating a drug trafficking offense.

In reviewing a sufficiency challenge, we view the evidence in the light most favorable to the government. United States v. Fennell, 53 F.3d 1296, 1298 (D.C.Cir.1995). Given Olivier’s instructions to the defendants that their guns and badges would be necessary to the drug runs, and the defendants’ compliance in carrying their guns while escorting the couriers, there was sufficient evidence to support appellants’ § 924(c) convictions, notwithstanding appellants’ self-serving testimony that they did not intend to use their guns. Not only was appellants’ testimony significantly discredited throughout the trial, but their co-conspirators, Officers Hackney, Wiggins, and Harris, admitted that they carried, and were prepared to use, their guns to ensure the couriers’ safe passage through the District of Columbia. In light of this evidence, a reasonable juror could find that appellants carried their guns in relation to the drug operations.

2. Instruction on co-conspirator liability. In Pinkerton v. United States, 328 U.S. 640, 647—48, 66 S.Ct. 1180, 1184, 90 L.Ed. 1489 (1946), the Supreme Court held that a co-conspirator may be held vicariously liable for reasonably foreseeable substantive offenses committed by other co-conspirators in furtherance of the conspiracy. In the instant ease, when the district court advised that it intended to instruct the jury on the Pinkerton theory of liability with respect to the § 924(c)(1) counts, appellants objected, stating “It may be the law, but it was not what the government argued, and it was not consistent with the evidence presented in the case.” Over defense objection, the district court instructed the jury:

If you find that any or all of the defendants were members of a conspiracy, you may find each defendant guilty of carrying or using a firearm during and in relation to a drug trafficking offense if any of their fellow co-conspirators committed this offense during the existence of the conspiracy and in furtherance of the conspiracy. This is because each member of a conspiracy is considered to be responsible for any offense committed by a co-conspirator that could have been reasonably expected or anticipated as a necessary or a natural consequence of the conspiracy.

Appellants’ initial contention that Pinkerton liability ought not apply to § 924(c)(1) charges in drug conspiracy eases is meritless. Consistent with the decisions in numerous other circuits, see, e.g., United States v. Wacker, 72 F.3d 1453, 1464 (10th Cir.1995); United States v. Dean, 59 F.3d 1479, 1489-90 (5th Cir.1995), cert. denied, — U.S. —, 116 S.Ct. 748, 133 L.Ed.2d 696 (1996); United States v. DeMasi, 40 F.3d 1306, 1319-20 (1st Cir.1994), cert. denied, — U.S. — , 115 S.Ct. 947, 130 L.Ed.2d 890 (1995); United States v. Williams, 31 F.3d 522, 526-27 (7th Cir.1994), this court has assumed the applicability of Pinkerton liability to § 924(c)(1) counts. United States v. Long, 905 F.2d 1572, 1577 n. 8 (D.C.Cir.), cert. denied, 498 U.S. 948, 111 S.Ct. 365, 112 L.Ed.2d 328 (1990). As long as the use or carrying of a firearm in relation to a drug trafficking offense was done in furtherance of the conspiracy and was reasonably foreseeable to the co-conspirators, Pinkerton, 328 U.S. at 647-48, 66 S.Ct. at 1184, we see no reason, and appellants offer none, that would render Pinkerton liability inapplicable to § 924(c)(1) offenses.

Appellants’ further contention that by instructing the jury on Pinkerton liability the district court constructively amended the indictment is also meritless. Count Two of the indictment, the drug conspiracy count, incorporated by reference the “Overt Acts” and “Manner and Means” sections of Count One, the bribery count. The “Overt Acts” section, which included 59 specifications, did not include any allegations of use of a firearm during and in relation to drug trafficking. Only the “Manner and Means” sections mentioned that appellants and their co-conspirators used their badges and their guns to protect shipments of cocaine. The fact that the use of firearms was not mentioned in the “Overt Acts” section of the conspiracy count does not mean, as appellants maintain, that the court should not have instructed the jury on the Pinkerton theory of liability.

Contrary to appellants’ view that co-conspirators may be held liable only for the overt acts of their co-conspirators specifically alleged in the indictment, a theory of defendant liability need not be pleaded in the indictment. United States v. Roselli, 432 F.2d 879, 894-95 (9th Cir.1970), cert. denied, 401 U.S. 924 (1971). Nor can appellants prevail because the indictment did not specifically list the use or carrying of a firearm as an overt act in the conspiracy count. With respect to the § 924(c)(1) counts, the indictment clearly stated that appellants and their co-conspirators knowingly used and carried a firearm during and in relation to a drug conspiracy. As the court stated in United States v. Edmond, 924 F.2d 261, 269 (D.C.Cir.), cert. denied, 502 U.S. 838, 112 S.Ct. 125, 116 L.Ed.2d 92 (1991): “Indictments do not recite the government’s theory of proof, which is what the Pinkerton theory is.... [T]he function of a federal indictment is to state concisely the essential facts constituting the offense, not how the government plans to go about proving them.” The indictment here stated the essential facts, and submission of the Pinkerton theory to the jury did not change the charges. Moreover, because appellants were charged with the firearms offenses in relation to the drug conspiracy, they had sufficient notice that they could be held liable for the substantive offenses of their co-conspirators. Finally, while Pinkerton did mention, as appellants maintain, that an overt act is an “essential ingredient” of a conspiracy, 328 U.S. at 647, 66 S.Ct. at 1184, its reasoning in support of finding co-conspirator liability did not depend on it. As long as a substantive offense was done in furtherance of the conspiracy, and was reasonably foreseeable as a “necessary or natural consequence of the unlawful agreement,” then a conspirator will be held vicariously liable for the offense committed by his or her co-conspirators. Pinkerton, 328 U.S. at 647-48, 66 S.Ct. at 1184.

Likewise, we reject appellants’ contention that the Pinkerton instructions im-permissibly allowed the jury to convict them for acts prior to their membership in the conspiracy. Appellants maintain that the instruction that each conspirator is liable for eo-eonspirators’ offenses, as long as the acts could have been “reasonably expected or anticipated,” rather than “reasonably foreseen,” coupled with the instruction that the relevant time-frame was “the existence of the conspiracy,” may have led the jury to attribute to each appellant liability for the conduct of others that took place before his membership in the conspiracy. Harmon was hired on August 9, 1993, Washington, on September 16,1993, and Taylor, on October 4,1993, and the indictment charged that the conspiracy lasted from about March to December 1993. Although it is not inconceivable that the jury instructions could lead to the danger suggested by appellants, the record makes clear that no such danger existed in the instant case. At appellant Harmon’s request, the jury verdict form was revised to reflect the specific dates upon which appellants were alleged to have committed the substantive firearms offense. As marked by the jury, the special verdict form reflects findings of guilt on the firearms offenses for Harmon on acts committed on August 10, and December 14, 1993, and for Washington and Taylor, on October 5, and December 14, 1993. Under the circumstances, there is no basis for concern that the jury instructions caused the jury to believe that it could convict appellants based on the actions of their co-conspirators that took place before appellants joined the conspiracy. Hence, the instructional error, if any, was harmless.

3. Unanimity instruction. Appellants’ contention that the instructions violated the requirement that criminal verdicts be unanimous is also flawed. In instructing the jury on the unanimity requirement, the district court stated, “In order to return a verdict as to any count, it is necessary that each juror agree to the verdict as to that count. In other words, your verdicts must be unanimous as to each defendant and as to each count.” Appellants maintain that this instruction violated both the Sixth Amendment and Federal Rule of Criminal Procedure 31(a). Because the district court did not require the jury to agree as to the principal factual elements for any of the § 924(c)(1) convictions, they contend that the jury may have rendered impermissibly non-unanimous verdicts of guilt on the firearm counts. Because they raise this contention for the first-time on appeal, we review for plain error.

In United States v. Mangieri, 694 F.2d 1270, 1281 (D.C.Cir.1982), the court noted with approval the rule announced by the District of Columbia Court of Appeals in Hack v. United States, 445 A.2d 634, 641 (D.C.1982), that “when one charge encompasses two separate incidents, the judge must instruct the jury that if a guilty verdict is returned the jurors must be unanimous as to which incident or incidents they find the defendant guilty.” Despite its endorsement of this rule, the Mangieri court held that, in light of the circumstances of that ease, the failure of the district court to give a special unanimity instruction was not plain error. Similarly, the general unanimity instruction in the instant case was adequate because there was sufficient evidence of each act that could form the basis of the verdict, and in the context of the entire charge and whole trial, a conscientious juror would have understood the prerequisite of agreement on the essential facts. Mangieri, 694 F.2d at 1281. The co-conspirators admitted that they carried their guns in order to facilitate the drug conspiracy, and it is uneontested that appellants carried their guns during the drug runs after Oliver told them that their guns and badges were necessary for protection, i.e., to facilitate the conspiracy.

4. “Use” instruction. In instructing the jury on the “use” prong of the § 924(c)(1) count, the district court stated,

[U]se is not limited to firing or brandishing or displaying a gun. Eather, a defendant uses a firearm whenever he puts or keeps a gun in a particular place from which he or his agent can gain access to it if and when the gun is needed to facilitate a drug crime.

Relying on the Supreme Court’s decision in Bailey v. United States, — U.S. —, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995), which held that a conviction under the “use” prong of § 924(c) requires proof that the defendant “actively employed” the firearm, appellants contend, and the government concedes, that the district court erred in instructing the jury on the “uses” prong of § 924(c)(1). We agree. See United States v. Hung Shun Lin, 101 F.3d 760, 771 (D.C.Cir.1996) (citing United States v. Washington, 12 F.3d 1128, 1139 (D.C.Cir.1994)).

“A verdict [is required] to be set aside in cases where the verdict is supportable on one ground, but not another, and it is impossible to tell which ground the jury selected.” Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1073, 1 L.Ed.2d 1356 (1957); see also Griffin v. United States, 502 U.S. 46, 58-59, 112 S.Ct. 466, 473-74, 116 L.Ed.2d 371 (1991); United States v. Collins, 56 F.3d 1416, 1421 (D.C.Cir.), cert. denied, — U.S. —, 116 S.Ct. 737, 133 L.Ed.2d 687 (1996). Appellants contehd that, particularly in light of the fact that co-conspirator Harris stated that he was willing to “use” his gun to protect the drug shipments on August 10 and December 14, it is possible that the jury, without even considering the “carry” prong, convicted appellants for “use” of the firearm. Yet the only evidence in support of the firearms convictions showed that the officers wore their service pistols on their persons during the drug trafficking offenses; there was no evidence suggesting that the officers merely “possessed,” without carrying, the guns for protection or active use. Hence, regardless of whether the jury actually convicted appellants under the “use” or “carry” prong, it is clear that the jury’s reasoning included a finding that appellants, or their co-conspirators, carried their guns. Moreover, the fact that the jury convicted appellants necessarily means that the jury concluded that the guns were connected, or “related,” to the drug offenses. Because it was impossible, under these facts, for the jury to have found “use” without having concluded that the gun was “carried” in relation to the drug conspiracy, the erroneous “use” instructions do not require reversal of the convictions. See United States v. Feinberg, 89 F.3d 333, 339-40 (7th Cir.1996).

5. Second convictions in light of Anderson. All three appellants were charged and convicted of two violations of § 924(c)(1). Appellant Harmon was charged in Count Eight with using or carrying a firearm on or about August 10, 1993, during and in relation to a drug trafficking crime, that is, the drug conspiracy (Count 2) and attempted possession with intent to distribute cocaine on that same date (Count 7). Appellants Washington and Taylor were charged in Count Eleven with using or carrying a firearm on or about October 5, 1993, during and in relation to a drug trafficking crime, that is, the drug conspiracy (Count 2) and attempted possession with intent to distribute cocaine on that same date (Count 10). AH three appellants were charged in Count Twelve with using or carrying a firearm on or about December 14, 1993, during and in relation to a drug trafficking crime, that is, the drug conspiracy.

In Anderson, 59 F.3d at 1334, the in banc court held that “only one § 924(c)(1) violation may be charged in relation to one predicate crime.” Consequently, appellants contend, because each of their two § 924(c)(1) convictions may have been predicated on the narcotics conspiracy, one of each of their firearms convictions must be vacated. In light of Anderson, the Yates standard once again governs. 354 U.S. at 312, 77 S.Ct. at 1073; see also Griffin, 502 U.S. at 58-59, 112 S.Ct. at 473-74; Collins, 56 F.3d at 1421. Because it is “impossible to tell” whether the jury relied on the drug conspiracy as the predicate offense for each firearms conviction, we agree that one of the § 924(e)(1) convictions for each of the appellants must be vacáted.

The fact that the jury acquitted appellant Harmon of Count Seven, the attempted possession with intent to distribute charge, but nonetheless convicted him of two violations of § 924(c)(1) suggests that it is quite likely that his two firearms convictions were predicated on the same offense, the drug conspiracy. Although it is possible that one of Harmon’s firearms convictions was based on the attempt count, see Anderson, 59 F.3d at 1331 (“[T]he government need not convict of—but it must prove—the predicate crime ... ”), this conclusion, as the government acknowledges, cannot be made with sufficient confidence to warrant upholding the verdict. Thus, we agree with appellants and the government that one of Harmon’s firearms convictions must be vacated.

Unlike Harmon, Taylor and Washington were convicted of both of the underlying predicates to the firearms charge in Count Eleven. Yet, contrary to the government’s contention, it is impossible to tell whether the jury actually based its conviction for Count Eleven on the attempt or the conspiracy charge. In giving a unified charge concerning all three § 924(c) counts, the district court instructed the jury that each defendant was charged with both “the crime of conspiracy to distribute or possess with intent to distribute cocaine and the crime of attempted possession with intent to distribute cocaine,” and that both were “drug trafficking crimes” for purposes of § 924(c). The district court further instructed that the jury should consider the § 924(c) charge only if it “found beyond a reasonable doubt that a defendant committed one of those drug trafficking crimes.” In the absence of contrary record evidence, we assume the jury understands and follows its instructions. Richardson v. Marsh, 481 U.S. 200, 211, 107 S.Ct. 1702, 1709, 95 L.Ed.2d 176 (1987); Delli Paoli v. United States, 352 U.S. 232, 242, 77 S.Ct. 294, 300, 1 L.Ed.2d 278 (1957).

Because the verdict form indicated that appellants Taylor and Washington were charged in Count Eleven with “carrying or using a firearm during and in relation to a drug trafficking crime on or about October 5, 1993,” the government contends that the jury must have based its firearms convictions on the predicate offense of attempted possession with intent to distribute; it was the only offense charged for that specific date, and the only evidence presented concerned the conduct alleged in the attempted distribution count. Yet, the government’s reasoning is undermined by the fact of appellant Harmon’s two firearms convictions. The jury verdict form specified the date, August 10, 1993, of Harmon’s alleged activities with regard to the § 924(c)(1) count for which attempted possession or conspiracy could have formed the predicate offense. While the jury convicted Harmon of the August 10 firearms count, it nonetheless acquitted him of the specific conduct alleged on that date— the attempted possession with intent to distribute charge—thus suggesting the jury-considered conspiracy to be the predicate offense to the firearms count. Just as it was possible for the jury to convict Harmon on the firearms count with the conspiracy as the underlying offense, notwithstanding the date specification in the jury yerdict form and the evidence presented, it was possible that the jury convicted Taylor and Washington of the second firearms conviction with the conspiracy as the predicate offense. Under these circumstances we conclude that it is impossible to tell on which grounds appellants Washington and Taylor were convicted, and, therefore, one of each of their § 924(c)(1) convictions must be vacated. See United States v. Cappas, 29 F.3d 1187, 1188 (7th Cir.1994).

IV.

Each appellant argues that the district court should have departed from the strictures of the Sentencing Guidelines because of some unusual features of his case. In addition Taylor and Washington each challenge the district court’s decision to increase his offense level by two points for obstruction of justice. Finally, Taylor and Harmon each argue that the district court should have reduced his offense level by two points because he played only a minor role in the offense.

We review the district court’s decision not to grant a downward departure only to determine whether the sentencing judge misunderstood the scope of his authority to depart. United States v. Hazel, 928 F.2d 420, 423 (D.C.Cir.1991). We review the district court’s factual findings relating to reductions or enhancements of a defendant’s offense level under the “clearly erroneous” standard, giving due deference to the district court’s application of the Guidelines to the facts. United States v. Graham, 83 F.3d 1466, 1481 (D.C.Cir.1996).

A. Downward departure. A district court is not to depart from the Sentencing Guidelines unless it “finds that there exists an aggravating or mitigating circumstance of a kind, or to a degree, not adequately taken into consideration by the Sentencing Commission in formulating the guidelines that should result in a sentence different from that described.” 18 U.S.C. § 3553(b). As the Supreme Court has stated, “[b]efore a departure is permitted, certain aspects of the case must be found unusual enough for it to fall outside the heartland of cases in the Guideline.” Koon v. United States, — U.S. —, —, 116 S.Ct. 2035, 2046, 135 L.Ed.2d 392 (1996).

In sentencing the three defendants to 49> years and four months, the district court stated that it did “not believe that the length of the sentence equates to the wrongness of the actions of the defendants.” The district court declined, however, to depart from the Guidelines because it concluded that the circumstances involved in the case had all been adequately considered by the Sentencing Commission; hence there was “no principled] basis for the court to depart under the Guidelines.”

In Koon, the Supreme Court adopted as its own the approach that then-Chief Judge Breyer had taken in United States v. Rivera, 994 F.2d 942, 949 (1st Cir.1993), to determine whether to depart from the Guidelines. The court first asks what features of the case are unusual and potentially take it out of the Guidelines’ heartland. Then the court determines whether the Commission has specifically forbidden departures based upon those features. If not, then the court asks whether the Commission has encouraged or discouraged departures based upon those features. Koon, — U.S. at —, 116 S.Ct. at 2045. Although Koon had not yet been decided when these appellants were sentenced, thé district court expressly (and presciently) followed the framework of Rivera. Nevertheless, the appellants argue that the district court did not understand the full extent of its ireedom to depart from the Guidelines. Specifically, they argue that under Rivera the district court, looking at the totality of the circumstances, may depart based upon a combination of a number of factors no one of which by itself would be a ground to depart. See U.S.S.G. 5k2.0, comment. (“The Commission does not foreclose the possibility of an extraordinary case that because of a combination of such characteristics or circumstances, differs significantly from the ‘heartland’ cases covered by the guidelines in a way that is important to the statutory purposes of sentencing, even though none of the characteristics or circumstances individually distinguishes the case. However, the Commission believes that such cases will be extremely rare.”)

Clearly, however, the district court did not misunderstand its authority to depart from the Guidelines. The court expressly stated that under Rivera “courts are free to consider in an unusual case whether the factors that make it unusual are present in sufficient kind to warrant a departure, and I am free to do this whether or not such departures are encouraged, discouraged, or unconsidered by the Guidelines.” The district court also considered the totality of the circumstances: “none of the factors identified by the defendants at least, either individually or collectively, seem to me to raise this case to the unusual case ... that the Guidelines considers appropriate to take it out of the heartland type of cases.” We have repeatedly emphasized that “if the judge correctly understood the Sentencing Guidelines and the evidence, knew he could depart, and yet decided to stick to the guideline range, there has been no incorrect application of the Guidelines ... and so the resulting sentence cannot be set aside.” United States v. Sammoury, 74 F.3d 1341, 1343 (D.C.Cir.1996). We may not review the “court’s discretionary decision that the particular circumstances of a given, case do not warrant a departure.” United States v. Pinnick, 47 F.3d 434, 439 (D.C.Cir.1995); cf. Graham, 83 F.3d at 1481 (remand proper where district court erroneously thought it could not depart based upon defendant’s vulnerability to abuse in prison).

Even if the court were to review the district court’s decision not to depart, we would have to affirm because the appellants have provided no reason why their sentences fall outside the heartland—aside from their bald assertion that this case is “atypical.” In fact, the appellants point to only two factors that they claim warrant a downward departure. First, they contend that there was no connection between the police officers’ pay or conduct and the amount of drugs involved; thus, they argue, a sentence based upon the amount of drugs involved overstates each defendant’s culpability. Even assuming that there was no connection (which the Government disputes), the district court properly held that the lack of such a connection “does not provide a basis for departure.” See United States v. Walls, 70 F.3d 1323, 1329-30 (D.C.Cir.1995) (rejecting defense of “sentencing entrapment” where undercover police officer who had purchased powder cocaine from defendant asked him to cook it into crack cocaine in order to subject defendant to' greater penalty for distribution of crack cocaine). The appellants concede that Walls forecloses their claims of “sentencing entrapment and improper sentence factor manipulation,” but they argue that even if the Government’s alleged sentencing manipulation is not by itself sufficient to grant a downward departure it may be considered as part of the totality of the circumstances.

Unfortunately for the appellants, there is no other mitigating factor to throw into the mix. They argue that the district court should have considered that the second § 924(e)(1) convictions entail mandatory additional 20-year sentences. Because we reverse the second § 924(c)(1) convictions today, however, we need not address whether a sentencing judge may consider the impact of multiple § 924(c)(1) convictions upon a defendant’s total sentence in order to determine whether to depart from the Guidelines. Left only with the claim that the amount of drugs involved in the sting operation overstated each defendant’s culpability, neither appellant can show that the district court erred in refusing to grant a downward departure.

B. Upward adjustment for obstruction of justice. Section 3C1.1 of the Guidelines directs the district court to increase a defendant’s offense level by two if it is satisfied by clear and convincing evidence, United States v. Montague, 40 F.3d 1251, 1254-56 (D.C.Cir.1994), that “the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the investigation, prosecution, or sentencing of the instant offense.” In this case the district court found that Taylor and Washington had each committed perjury and ac-eordingly increased each defendant’s base offense level by two for obstruction of justice.

At trial Hackney testified that he told Washington, well before Washington’s first meeting with Olivier, that Olivier was a drug dealer and that working for him would involve the protection of cocaine. Washington, however, testified that he did not know Olivier was a drug dealer until he met him and that he went along with Olivier’s scheme only because he was afraid of him. In addition, Washington denied that he feared or suspected that the operation might be a set-up. The district court did not believe any of this. The videotape of Washington’s first meeting with Olivier clearly showed that Washington knew in advance that Olivier was a drug dealer and that Washington had no fear of Olivier. Videotape evidence and testimony also refuted Washington’s claim that he had not been worried about a set-up: Washington was concerned that there might be a video camera in the fireplace of the townhouse and surveillance equipment on the roof.

The district court further concluded that Washington also perjured himself when he denied his involvement in a previous crime. In order to establish Washington’s predisposition, the Government introduced evidence, through two witnesses, that Washington had seized and resold illegal nitrous oxide tanks while working as a security officer at a Grateful Dead concert. One witness was Darryl Lawson, who had pleaded guilty to his involvement in the scheme. The other was a “Deadhead,” a Grateful Dead fan who follows the group around the country, who had attended the concert and corroborated Lawson’s account. Thus does Washington attack the credibility of these witnesses: Lawson had reason to lie and the Deadhead was high. Despite this, the district court specifically found the testimony of these witnesses to be “credible” and “very convincing” and we have no reason to disturb the court’s credibility findings.

The district court found that Taylor also perjured himself by denying that he knew that Olivier was a drug dealer before he met with him in person; Taylor claimed that he did not know drugs would be involved in this part-time “security job” until he met Olivier. The court also found that Taylor lied about the meaning of his statement that he would kill Bailey, a member of the conspiracy who had been driven out because of his lack of discretion. The district court labeled “ludicrous” Taylor’s testimony that he had threatened to kill Bailey only because he was afraid that if Bailey did not keep his mouth shut then Taylor might get in trouble for engaging in unauthorized (but not unlawful) part-time security work.

The district court concluded that there was “clear and convincing” evidence that both Taylor and Washington testified falsely. Considering the weight of the evidence refuting each appellant’s testimony, we cannot say that this conclusion was clearly erroneous. The court also concluded that their lies were material and were intended to mislead. As such, we cannot say that the sentencing enhancement under § 3C1.1 of the guidelines was unwarranted.

C. Denial of downward adjustments for the defendants’ “minor role.” Under § 3B1.2(b) of the Guidelines the district court may reduce a defendant’s offense level by two if it finds that the “defendant’s culpability ... was relatively minor compared to that of the other participant(s)” in the offense. See United States v. Caballero, 936 F.2d 1292, 1299 (D.C.Cir.1991). The district court refused to grant Taylor and Harmon minor role adjustments because it concluded that each defendant actively participated in the offense:

They were active participants, whose participation ... level was consistent with the others. Nine out of twelve ... took $2,000 bribes....
Here among all of these nine defendants, it’s apparent to me they’re somewhat equally culpable.
Mr. Harmon actively recruited Mr. Taylor. Mr. Taylor indicated he would commit violence on anyone and actually was heavily involved. So it does not appear that either is entitled to a reduction.

Harmon complains that his participation totaled no more than four hours, consisting of one “run,” a few meetings and telephone calls, and his suggestion that Taylor contact Hackney. But the Guidelines do not indicate that a defendant’s sentence should be determined by reference to the amount of time in which he actively participated in a criminal enterprise. Great harm can be wrought in a short time. Harmon also argues that his role was no greater, and possibly less, than that of a drug cornier. The Guidelines, however, direct the sentencing judge to consider a defendant’s culpability relative to that of his comrades, not to that of a hypothetical courier or other prototypical criminal.

For his part Taylor argues that the district court should have considered that he was the “last recruit” in the operation and that, unlike several others, he never tried to recruit anyone else. For what it is worth, the record is unclear on the question whether Taylor was the last officer to join the scheme. He was the last officer to meet Olivier but there is evidence that he expressed an interest in the organization earlier in August 1993. Furthermore, although Taylor did not actually recruit any additional police officers, he freely offered to do so. More important, there was evidence that Taylor was willing to inject violence into the conspiracy: he offered to introduce to Olivier a hit man.

We have noted before that the district court need not make express findings of relative culpability so long as it is clear that the court assessed the defendant’s “role in the specific criminal conduct” and did not “gauge his culpability generically.” United States v. Edwards, 98 F.3d 1364, 1370 (D.C.Cir.1996). Here the court did make express findings concerning Taylor’s and Harmon’s relative culpability and those findings are based upon sufficient record evidence.

Accordingly, we affirm the judgments of conviction in all respects save for one of the firearms’ convictions of each appellant; we remand the eases for resentencing in light of the vacation of these convictions. 
      
      . Part II, except II.E, is authored by Judge Wald; Part IV is authored by Judge Ginsburg; Parts I, II.E, and III are authored by Judge Rogers.
     
      
      . Hackney was not aware that Olivier was a government agent at the time when Hackney recruited the appellants at Olivier's direction.
     
      
      . There is some dispute as to whether appellant Taylor was actually recruited by Hackney, or whether he was recruited by Harmon (another step removed from Olivier). Compare Joint Brief for Appellants, at 59 n.38 ("Harmon had mentioned to Taylor the prospect of some lucrative private security work, but referred Taylor to Hackney, who in turn provided Taylor with information and acted as a conduit to Olivier.”), with Final Brief for Appellee, at 103 ("Taylor was 'recruited' not by Agent Olivier or Hackney, but by his co-defendant, John Harmon.”). The district court did not make factual findings on this issue. For purposes of this analysis, we consider the facts in the light most favorable to the defense—and so we assume that Hackney did recruit Taylor. See infra, page 995.
     
      
      .The court .did not elaborate as to why a defendant could not, as a matter of law, be "entrapped” by “co-conspirators."
     
      
      . See, e.g., United States v. Martinez, 979 F.2d 1424, 1432 (10th Cir.1992) (claiming to be "among the majority of Circuits that have not recognized the defense of vicarious or derivative entrapment” and collecting cases).
     
      
      . United States v. Buie, 407 F.2d 905, 908 (2d Cir.), aff'd on other grounds sub nom., Minor v. United States, 396 U.S. 87, 90 S.Ct. 284, 24 L.Ed.2d 283 (1969); see also United States v. Hodges, 936 F.2d 371, 372 (8th Cir.1991); United States v. Valencia, 645 F.2d 1158, 1168-69 (2d Cir.1980) (as amended), reh’g denied, 669 F.2d 37 (1981).
     
      
      . See, e.g., United States v. Emmert, 829 F.2d 805, 809 (9th Cir.1987) (rejecting the "unwitting agent” theory and stating that “an approach to a defendant by a private citizen before he was [knowingly] cooperating with the government, [does] not constitute governmental solicitation or inducement for purposes of the entrapment defense”); United States v. Beverly, 723 F.2d 11, 12 (3d Cir.1983) ("[A]n entrapment defense cannot be predicated on the actions of a party who has not agreed explicitly or implicitly to help the government make its case against the person who complains of entrapment.”).
     
      
      . See, e.g., United States v. Jones, 839 F.2d 1041, 1054 (5th Cir.1988) (as corrected) (stating that "the government may entrap a defendant through the actions of an ‘ignorant pawn'").
     
      
      . Although the term "derivative entrapment” was not explicitly mentioned in Johnson, the court held that a defendant was entitled to a jury instruction on entrapment in a situation where an undercover police officer supplied an (apparently unwitting) intermediary with government money, instructed the intermediary to purchase narcotics with the money, and then drove the intermediary to a spot where said intermediary returned with the defendant. The defendant then instructed the undercover officer to drive to another spot, where the defendant purchased drugs as requested by the intermediary, who in turn gave the drugs to the officer.
     
      
      . See also United States v. Hodges, 936 F.2d 371, 372 (8th Cir.1991) ("[C]ourts have ... recognized that, under certain circumstances, an unknowing middleman ... can satisfy the element of governmental inducement in another's entrapment defense.”); United States v. Valencia, 645 F.2d 1158, 1168 (2d Cir.1980) (as amended) ("If a person is brought into a criminal scheme after being informed indirectly of conduct or statements by a government agent which could amount to inducement, then that person should be able to avail himself of the defense of entrapment just as may the person who receives the inducement directly.”), reh'g denied, 669 F.2d 37 (1981).
     
      
      . Indeed, appellant Harmon’s counsel conceded at trial that
      if the jury were to conclude that the defendants were all misled before they walked in [to meet Olivier] ... it would be difficult to sustain a derivative entrapment instruction, because it’s clear that Mr. Hackney did not say he was told to mislead anybody.
     
      
      . United States v. Borum, 584 F.2d 424, 427 (D.C.Cir.1978) (as amended) (quoting United States v. Boone, 543 F.2d 412, 414 (D.C.Cir.1976)) (internal quotation marks omitted). This principle, in turn, is based on the idea that an appellate court may not infringe upon the domain of the jury, and so may not "decide the factual question whether appellant was indeed entrapped, but only the legal question whether the trial judge should have given the jury an entrapment instruction.” Id.
      
     
      
      .In addition, the appellants were required to meet with Olivier himself before becoming official members of the scheme. Cf. United States v. Valencia, 645 F.2d 1158, 1169 n. 10 (2d Cir.1980) (as amended) (suggesting that a case for a derivative entrapment defense is more easily made in cases where the defendant is "made aware” of the government official’s inducement, or where the defendant has actually been introduced to the official), reh’g denied, 669 F.2d 37 (1981).
     
      
      . The Layeni court also observed that, "even if [the girlfriend] had induced [the boyfriend], the intended target of the government's sting,” nevertheless the boyfriend "would not be entitled to an entrapment instruction because there is no evidence that [the informant] suggested that [the girlfriend] should use inducements' to bring him to the table.” 90 F.3d at 518-19 (citations omitted). Presumably, however, if the government had told the girlfriend to offer a particular inducement to her boyfriend, and she had not deviated from this plan, he would have been entitled to an entrapment instruction. Similarly here, had the government designated particular officers that Hackney should target with particular inducements, and Hackney had followed this plan, the appellants might have been entitled to a derivative entrapment instruction.
     
      
      . Other courts have established somewhat different frameworks for the defense. Of these various theories, some are narrower than the one we set forth here, see, e.g., United States v. Hollingsworth, 27 F.3d 1196, 1204 (7th Cir.1994) (en banc) ("|T|here is a defense of derivative entrapment: when a private individual, himself entrapped, acts as agent or conduit for governmental efforts at entrapment, the government as principal is bound. This principle follows ... from the unquestioned principle that the entrapment defense will lie whether the government uses its own employee as the stinger or an informant.”); United States v. Hodges, 936 F.2d 371, 372 (8th Cir.1991) (permitting the derivative entrapment defense in cases where the unwitting intermediary is himself entrapped and then, at the behest of the government, induces others to join a criminal scheme), while others are potentially broader, see, e.g., United States v. Valencia, 645 F.2d 1158, 1168-69 (2d Cir.1980) (as amended) (“In general, we hold that a vicarious entrapment defense can be presented to a jury only where the defendant first introduces admissible evidence that the agent’s inducement was directly communicated to him by another.”), reh'g denied, 669 F.2d 37 (1981). See generally Note, Entrapment Through Unsuspecting Middlemen, 95 Harv. L.Rev. 1122 (1982) (surveying various theories of derivative entrapment).
     
      
      . Even if the district court had erred in its general entrapment instruction, such error would not constitute a basis for reversal unless the appellants could show that they were prejudiced by the error. The first three arguments were raised at trial and therefore would be reviewed for harmless error. Fed.R.Crim.P. 52(a). The fourth argument—pertaining to the timing of the finding of predisposition on the part of the defendants—was not raised below and therefore would be reviewed only for plain error. Fed R.Crim. P. 52(b).
     
      
      . The Sherman court stated that, *'[i]t makes no difference [for purposes of an entrapment defense] that the sales for which petitioner was convicted occurred after a series of [prior narcotics] sales. They were not independent acts subsequent to the inducement but part of a course of conduct which was the product of the inducement.” Id. at 374, 78 S.Ct. at 822.
     
      
      . The jury was informed that, "[j]ust as it's your responsibility to consider each offense and the evidence ... concerning each defendant separately, it is also your responsibility to consider the evidence concerning entrapment as to each offense and each defendant separately.”
     
      
      . Because no defendant took issue with this aspect of the instruction at the trial, this argument, unlike the previous three made by appellants, may only be reviewed for plain error.
     
      
      . During cross-examination, the government established that Washington had been paid by two employers for the same time period (double billing). Other cross-examination topics covered by the government were Washington’s removal from the motor tract unit for misconduct, his interaction with Officers Reid and Lawson (to impeach his claim that he didn't know or deal with any of the charged officers), and his alleged extortion and bribery on previous occasions .when he seized nitrous oxide containers to resell them, or accepted money not to seize them.
     
      
      . Washington objected to admission of this evidence, but the government countered that the evidence showed a previous criminal relationship between Washington and Lawson, and that Washington had placed his intent at issue by declaring that he participated in Olivier's operation because he had no realistic alternatives. The district court ruled that the government had met its burden of laying a foundation for Washington’s prior bad acts; it also ruled that the evidence was probative as to predisposition, and that this probative value was not outweighed by the prejudicial effect.
     
      
      . Evidence admitted against Hannon’s story included Hackney's testimony that Harmon did know prior to that first meeting of Olivier's drug dealer status and cross-examination in which the prosecutor questioned the likelihood that Harmon’s "good friend” Hackney (Harmon was a groomsman in Hackney’s wedding) would have led him into this situation without telling him the work was drug-related. The prosecutor also emphasized the fact that Harmon displayed no surprise when Olivier started their first discussion about the drugs, that Hannon unhesitatingly told Olivier that he had sold drugs in the past, and that Harmon conceded that he never confronted Hackney about introducing him to a drug dealer.
     
      
      . This subsection of the Rule provides:
      (d) Statements which are not hearsay. A statement is not hearsay if—
      (1) Prior statement by witness. The declarant testifies at the trial or hearing and is subject to cross-examination concerning the statement, and the statement is ... (B) consistent with the declarant's testimony and is offered to rebut an express or implied charge against the declar-ant of recent fabrication or improper influence or motive....
      Fed.R.Evid. 801(d)(1)(B).
     
      
      . Federal Rule of Evidence 801(d)(1)(B) provides that a statement is not hearsay if (1) the declarant testifies at trial and is subject to cross-examination about the statement, (2) the statement is consistent with the declarant's testimony, and (3) the statement is offered to rebut an express or implied charge against the declarant of recent fabrication or improper influence or motive.
     
      
      . Appellant conceded at trial that there had been no charge of recent fabrication, and does not raise that argument here. The district court additionally found that the government had made no charge of improper motive. We need not reach the question of whether this finding constituted an abuse of discretion because, in any event, the statement was inadmissible for lack of rebutting force.
     
      
      .Rule 803(24) provides:
      The following are not excluded by the hearsay rule, even though declarant is available as a witness: ... (24) Other exceptions. A statement is not specifically covered by any of the foregoing exceptions but having equivalent circumstantial guarantees of trustworthiness, if the court determines that (A) the statement is offered as evidence of a material fact; (B) the statement is more probative on the point for which it is offered than any other evidence which the proponent can procure through reasonable efforts; and (C) the general purposes of these rules and the interests of justice will best be served by admission of the statement into evidence....
      Fed.R.Evid. 803(24). Rule 804(b)(5) is identical, except that it applies to cases where the declar-ant is not available.
     
      
      
        . See, e.g.. United States v. Tome, 61 F.3d 1446, 1452 (10th Cir.1995) ("... Rule 803(24) should be used only 'in extraordinary circumstances where the court is satisfied that the evidence offers guarantees of trustworthiness and is material, probative and necessary in the interest of justice.'") (quoting United States v. Farley, 992 F.2d 1122, 1126 (10th Cir.1993)).
     
      
      . The government points out that it was especially likely that Harmon would be untruthful or omit important facts given the fact that "Mr. Hairston was an apparently law-abiding individual awaiting admission to the District of Columbia Bar.” Brief for Appellee, at 82.
     
      
      . Appellant Harmon was acquitted of this offense.
     
      
      . See, e.g., United States v. Loder, 23 F.3d 586, 591 (1st Cir.1994) (in order to show “shared intent,” government must present evidence that accomplice had knowledge he was furthering the crime); United States v. Parekh, 926 F.2d 402, 407 n. 9 (5th Cir.1991) (legal terms "community of unlawful intent” and "shared intent” are "simply different articulations of the usual requirement that the [accomplice] associated with a criminal venture ... and sought by his action to make the venture succeed") (citation and internal quotation marks omitted); United States v. Gomez, 733 F.2d 69, 73 (8th Cir.1984) (aider and abettor must voluntarily act “with bad purpose either to disobey or to disregard the law”) (citation and internal quotation marks omitted).
     
      
      . See also United States v. Zerbst, 111 F.Supp. 807, 810 (E.D.S.C.1953) (“There can be no accessory without a principal. One cannot be guilty of aiding and abetting in the perpetration of a crime without its first being shown that a crime was actually committed by another.... So one cannot render himself criminally liable as an aider and abettor for aiding in the commission of an act which is not in fact criminal.”). On the other hand, some courts have carved out significant exceptions to the rule that there must be a guilty principal and a substantive crime committed. For example, "it is now generally accepted that an accomplice may be convicted notwithstanding the fact that the principal in the first degree has not yet been tried or has been acquitted in a separate trial.” Wayne R. LaFave, Modern Criminal Law: Cases, Comments and Questions 754 (2d ed.1988) (collecting cases). Similarly, some courts have stated that an accomplice may be convicted despite the fact that the principal was found not guilty based on some defense not available to the accomplice, such as entrapment or insanity. See id. Finally, some courts have held that an aiding and abetting conviction for a completed substantive offense may stand even if the principal is a government agent with no guilty intent, and even if therefore no substantive crime was actually committed. See United States v. Meinster, 619 F.2d 1041, 1046 (4th Cir.1980) (upholding conviction for aiding and abetting drug smuggling and rejecting appellants’ claim that "the absence of a guilty principal precludes their conviction on aiding and abetting charges”); United States v. Gould, 
        419 F.2d 825, 826 (9th Cir.1969) (per curiam) (upholding conviction for aiding and abetting the smuggling of marijuana even though there was no "guilty principal” because the drugs were actually “smuggled” over the border by a government informant).
     
      
      . However, in Walker and our earlier decision in Edmond, we emphasized that the aider and abettor need not have the exact same intent as the principal. Rather, a finding of overlapping intent between accomplice and principal is sufficient to establish liability. See Walker, 99 F.3d at 442 (“fT]he intent of the aider and abettor must be shown, in crucial respects, to overlap with (but not necessarily match) the criminal intent of the principal”); United States v. Edmond, 924 F.2d 261, 266, 267 (D.C.Cir.1991) (holding that, although "the government must prove the criminal act the defendant is accused of abetting,” a jury "could consistently convict the [defendant-]abettor of first-degree murder while finding the actual perpetrator guilty only of the lesser offense" because "[t]he degree of murder in each case depends on the mens rea of the defendant who is on trial.”) (emphasis added).
     
      
      . Under 18 U.S.C. § 2 (in which the common law notion of accomplice liability was codified), "the acts of the perpetrator become the acts of the aider and abettor and the latter can be charged with having done the acts himself.” United States v. Kegler, 724 F.2d 190, 201 (D.C.Cir.1983).
     
      
      . That portion of the charge stated:
      It is not necessary that a defendant have had the same intent as a principal offender when the crime was committed or that he have intended to commit the particular crime committed by the principal offender. An aider and abettor is legally responsible for the acts of other persons that are the natural and probable consequences of the crime in which he intentionally participates.
      In the case of felony murder, unlike here, an actual crime (of murder) is committed, there is some overlapping intent between accomplice and principal, and the murder can be seen as a "natural and probable consequence" of the crime in which the accomplice intended to participate.
     
      
      . On the contrary, there was no evidence that the defendants themselves attempted.to possess the cocaine, only that they attempted to help others to do so. Moreover, the government agents did not meet the requirements for attempted possession because there was absolutely no factual basis for finding that they possessed the requisite criminal intent.
     
      
      . The court stated:
      The essential elements of the crime of possession with intent to distribute cocaine are:
      Again, that a person possessed a controlled substance;
      That a person did so knowingly and intentionally. This means consciously, voluntarily, and one purpose, not mistakenly, accidentally, or inadvertently;
      That when a person possessed a controlled substance, he had the specific intent to distribute it. Distribute means to transfer or attempt to transfer to another person.;..
     
      
      . The court explained in part that:
      In order to find the defendant guilty of the crime—I'm sorry, in order to find a defendant guilty of committing the crime of attempted possession with the intent to distribute cocaine as charged in the indictment, the government must first prove beyond a reasonable doubt that the particular defendant’s mental processes passed from the stage of thinking about the crime to actually intending to commit the crime, and secondly, that the physical conduct of the defendant went beyond the stage of mere preparation to some firm, clear, and undeniable action to accomplish that intent.
     
      
      . The court instructed the jury in part that:
      To find the defendant aided and abetted in committing a crime, you must find the defendant knowingly associated himself with the persons who committed the crime, that he participated in the crime as something he wished to bring about, and that he intended by his actions to make it succeed.
      Some affirmative conduct by the defendant in helping or carrying out the crime is necessary. ...
      It is not necessary that a defendant have had the same intent as a principal offender when the crime was committed or that he have intended to commit the particular crime committed by the principal offender....
     
      
      . In Collins, we explained that, whereas “|j]u-rors are not generally equipped to determine whether a particular theory of conviction submitted to them is contrary to law,” id. (citing Yates v. United States, 354 U.S. 298, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957)), nonetheless "a general verdict cannot be set aside merely because one of the possible bases of conviction is unsupported by substantial evidence” because jurors are presumed to be “well equipped, through their intelligence and expertise, to analyze the evidence and convict on the ground with sufficient evidence.” Id.
      
     
      
      . See D.C.Code § 4-142 (1988) (prescribing penalty for any officer who neglects to make an arrest for an offense committed in the officer’s presence); 6A DCMR § 200.4 (1988) ("[m]embers of the [MPD] force shall be held to be always on duty”); cf. Bauldock v. Davco Food, Inc., 622 A.2d 28, 31 (D.C.1993).
     
      
      . In interpreting the language of § 924(c), the in banc court stated that “Congress was focusing on the defendant's employment of a gun for the purpose of bringing about a crime." Anderson, 59 F.3d at 1326. Appellants' contention, that Anderson thus establishes that a conviction under § 924(c)(1) requires proof of carrying with a specific purpose or intent related to the drug trafficking crime, misconstrues this statement by removing it from its context. Holding that multiple § 924(c)(1) convictions could not be linked to only one underlying predicate offense, the Anderson court was merely clarifying that Congress did not intend to criminalize every discrete occasion that a defendant used or carried a gun during an ongoing drug crime, but instead intended only to criminalize the circumstance of "the defendant's advancement of his criminal ends by means of a gun." Id. at 1326-27.
     
      
      . “Members of the [MPD] force, when off duty any place in the District of Columbia, except in their residences, shall carry their badges, identification cards and service revolvers at all times.” District of Columbia v. Davis, 386 A.2d 1195, 1202 (D.C.1978) (quoting MPD Manual 2:3:1).
     
      
      . In support of the constructive amendment claim, appellants rely on United States v. Pedigo, 12 F.3d 618, 630-31 (7th Cir.1993). In that case, although the defendant was also convicted of conspiracy, the § 924(c) count charged him with using a firearm during and in relation to a substantive drug possession count, rather than the conspiracy count. Id. at 629. By contrast, the § 924(c) counts in this case specifically alleged that the defendants used or carried firearms during and in relation to a conspiracy. Moreover, the Seventh Circuit stated that “any broadening of an indictment, so that a trial jury is presented with more or different theories of conviction than charged by the grand jury is fatal." Id. at 631. This circuit, by contrast, has stated that the indictment need only state concisely the essential facts constituting the offense; it need not recite the government’s theory of proof. Edmond, 924 F.2d at 269.
     
      
      . Concurring in McKoy v. North Carolina, 494 U.S. 433, 449 n. 5, 110 S.Ct. 1227, 1237 n. 5, 108 L.Ed.2d 369 (1990), Justice Blackmon noted the "general agreement" of the federal courts of appeals that unanimity “means more than a con-clusory agreement that the defendant has violated the statute in question," but that "there is a requirement of substantial agreement as to the principal factual elements underlying a specified offense." While the juiy need not unanimously credit “each bit of evidence," it must unanimously agree as to “the nature of the defendant's violation.” Id.
      
     
      
      . The government contends that because both the conspiracy count and the attempt count may legally form the predicate for a violation of § 924(c), the court should not reach the "impossible to tell” analysis. Yet, the government errs by attempting to argue about what is legally permissible in the abstract. In the instant case, in light of the separate firearms conviction based on the predicate conspiracy offense, the-second firearm conviction was supportable on one ground, the predicate attempt offense, but not another, the predicate conspiracy offense. Hence, the Yates test controls.
     