[586]*586REINHARDT, Circuit Judge:
Raul Lopez-Alvarez, a former Mexican state police officer, and two co-defendants 1 were convicted after a two-month jury trial of charges stemming from the kidnappings and murders of DEA Special Agent Enrique Camarena-Salazar and DEA informant Alfredo Zavala. The principal evidence against Lopez-Alvarez consisted of videotaped admissions he made to Abel Reynoso, an undercover DEA agent, and Jose Reyes Garcia-Alvarez, a DEA informant. The defense argued that these statements were lies that Lopez-Alvarez had made up in order to convince the agents, who were posing as criminals, that he had ties to the drug underworld. His appeal raises the question, among many others, of the degree to which the government may rely on a defendant’s admissions in seeking to prove its case. We affirm four of Lopez-Alvarez’s six convictions.
Facts
On February 7, 1985, DEA Special Agent Camarena and Zavala, a pilot and DEA informant, disappeared from Guadalajara, Mexico. One month later, their bodies were found near Zamora, Michoacan, Mexico. They had been tortured and murdered. In connection with the murders, Mexican authorities arrested and imprisoned several Mexican police officers, including the defendant. He was later released.
In 1987, Lopez-Alvarez accompanied DEA informant Garcia on several trips to Los Angeles, where he met Reynoso, who, unknown to the defendant, was actually an undercover DEA agent. During their conversations, Lopez-Alvarez described to Reynoso his involvement in the Camarena abduction. These conversations were videotaped and/or audiotaped.
Lopez-Alvarez was arrested on October 27, 1987. At trial, Garcia, who had been in prison with the defendant, testified that Lopez-Alvarez had on several occasions spoken about his involvement in the Ca-marena affair. The prosecution introduced evidence that the abductions and murders were orchestrated by Rafael Caro-Quinte-ro, an alleged Mexican drug kingpin. Rey-noso testified that Lopez-Alvarez had described to him his involvement with, and loyalty to, Caro-Quintero as well as his role in Camarena’s abduction. Videotapes of Lopez-Alvarez’s conversations with Rey-noso were also admitted as evidence. The defendant’s statements related to three different incidents. Some statements provided details of the seizure of Camarena and his transportation to a house owned by Caro-Quintero. Other statements describe Camarena’s ordeal during the time he was being held. Finally, Lopez-Alvarez described an incident at the Guadalajara airport in which he claimed to have provided assistance to Caro-Quintero in a confrontation with DEA agents and Mexican federal police officers. Lopez-Alvarez’s defense was that he had, at Garcia’s urging, deliberately lied to Reynoso: that he pretended he had been involved in the Camarena affair in order to convince the agent that he was “a high level drug trafficker associated with ... Caro-Quintero.”
Lopez-Alvarez was convicted on all charges brought against him: one count of violent crimes in aid of racketeering for the kidnapping and murder of Camarena (18 U.S.C. §§ 1952B, 2) (Count One), another count of the same crime for the kidnapping and murder of Zavala (Count Two), of conspiracy to kidnap a federal agent (18 U.S.C. § 1201(c)) (Count Three), of kidnapping a federal agent (18 ..S.C. § 1201(a)(5)) (Count Four), of felony murder of a federal agent (18 U.S.C. §§ 1111, 1114) (Count Five), and of being an accessory after the fact (18 U.S.C. § 3) (Count Seven).2 He received four consecutive 60-year sentences plus one concurrent sentence of life and one of ten years.
[587]*587After the defendant’s motion for a new trial was denied, he filed this appeal. He contends that his conviction should be reversed for the following reasons: (1) the trial court improperly limited his cross-examination of Garcia, (2) his convictions are supported by insufficient evidence, (3) the prosecutor impermissibly referred to Lopez-Alvarez’s failure to testify, (4) the trial court lacked subject matter jurisdiction, (5) the felony-murder indictment was insufficient, (6) the trial court erroneously rejected his proposed jury instructions, (7) the prosecutor made improper prejudicial remarks to the jury, (8) the prosecution failed to disclose exculpatory evidence. We find all but one of these contentions to be without merit. As to the sufficiency of the evidence contention, we find it meritorious only with regard to Counts 2 and 7.
Discussion
1. Limitation of Lopez-Alvarez’s Cross-examination of Garcia
In the course of the case-in-chief against Lopez-Alvarez, the prosecution introduced testimony by Garcia that the defendant had on several occasions during their joint incarceration spoken of his involvement in the Camarena affair. Defense counsel sought to cross-examine Garcia regarding the fact that other persons in jail had also made statements in their presence about the Camarena affair. The trial court sustained the prosecution’s hearsay objections to this line of questioning. Lopez-Alvarez argues that the court misapplied the hearsay doctrine, thereby violating his rights under both federal law and the Sixth Amendment.
We agree that the court misapplied the hearsay rule. “Out of court statements constitute hearsay only when offered in evidence to prove the truth of the matter asserted.” Anderson v. United States, 417 U.S. 211, 219, 94 S.Ct. 2253, 2260, 41 L.Ed.2d 20 (1974). The purpose of defense counsel’s intended cross-examination was not to develop an alternate version of the Camarena affair, but merely to demonstrate that details of the crimes had been discussed in Lopez-Alvarez’s presence. Lopez-Alvarez did not seek to introduce Garcia’s testimony regarding these out of court statements in order to argue that those statements were true, just that he could have learned the specific details he related to DEA agents without having been a participant in the crimes. Therefore, the trial court should not have excluded the testimony on the basis of hearsay.
The trial court’s error did not, however, violate the defendant’s constitutional rights. First, defense counsel’s inability to pursue the desired line of cross-examination did not deny Lopez-Alvarez his right to confront Garcia in the traditional.sense because, even without the disputed questions, the cross-examination revealed sufficient information with which the jury could appraise Garcia’s reliability. See United States v. Bonanno, 852 F.2d 434, 439 (9th Cir.1988) (“Generally, once cross-examination reveals sufficient information with which to appraise a witness’s possible bias and motives, confrontation demands are satisfied.”). The testimony defense counsel sought to elicit did not undermine Garcia’s credibility in any substantial way, and certainly not in a manner different than that accomplished by evidence which was introduced.3 The jury’s perception of Garcia’s credibility would not have been significantly altered by the introduction of the additional testimony. Accordingly, Lopez-Alvarez’s traditional right to confrontation was not violated.
Second, and more pertinent, because the excluded testimony actually served the purpose of furthering the theory of the defense and not of impeaching the prosecution’s witness, the defendant’s arguments are better directed at demonstrating a denial of his constitutional guarantee of “a meaningful opportunity to present a com-[588]*588píete defense.” California v. Trombetta, 467 U.S. 479, 485, 104 S.Ct. 2528, 2532, 81 L.Ed.2d 413 (1984).4 Even when evidence is excluded on the basis of a valid application of the hearsay rules, such exclusion may violate due process if the evidence is sufficiently reliable and crucial to the defense. See Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 1049, 35 L.Ed.2d 297 (1973). When evidence is excluded on the basis of an improper application of the hearsay rules, due process concerns are still greater because the exclusion is unsupported by any legitimate state justification. See Crane v. Kentucky, 476 U.S. 683, 691-92, 106 S.Ct. 2142, 2147, 90 L.Ed.2d 636 (1986) (requiring introduction of evidence regarding the voluntariness of a confession because “[i]n the absence of any valid state justification, exclusion of this kind of exculpatory evidence deprives a defendant of thé basic right to have the prosecutor's case encounter and ‘survive the crucible of meaningful adversarial testing.’ ” (quoting United States v. Cronic, 466 U.S. 648, 656, 104 S.Ct. 2039, 2045, 80 L.Ed.2d 657 (1984)).
Nevertheless, not every hearsay error amounts to a constitutional violation. At a minimum, a defendant must demonstrate that the excluded evidence was important to his defense. Here, ,the line of questioning foreclosed by the trial court’s erroneous ruling fails this test, but only because the testimony sought to be ■ adduced would not have added substantially to the knowledge the jury gained during the course of the trial. Under cross-examination, Garcia acknowledged that “prisoners try to impress each other with things that they have done.” He also testified that he heard his cellmates discuss the Camarena affair. The jurors were thus aware that Lopez-Alvarez’s cellmates talked about the Camarena matter. The disallowed questions constituted inquiries as to specific details of their conversations. Because it was already established that Lopez-Alvarez’s cellmates could have been the source of his information, further evidence regarding exactly what the cellmates said would not have added significantly to the jury’s deliberations, particularly in light of the confusion surrounding the making of the prisoners’ statements. See note 3 supra. Accordingly, viewed in the context of the entire trial, the district court’s ruling did not deny Lopez-AIvarez a meaningful opportunity to present a complete defense.
Because the court’s erroneous ruling did not violate the defendant’s constitutional rights, we do not test the error against the stringent “beyond a reasonable doubt” harmless error standard of Chapman v. California, 386 U.S. 18, 21, 87 S.Ct. 824, 826, 17 L.Ed.2d 705 (1967), but rather against the more lenient standard of Fed.R.Crim.P. 52(a). As we have discussed above, the error excluded testimony that would have had limited probative value beyond that of other evidence before the jury. The primary evidence against Lopez-AIva-rez was his admissions, and the crux of the trial was the jury’s evaluation of the admissions’ trustworthiness. This evaluation would likely be influenced by the degree to which details of the admissions matched details of the crimes that could not have been easily learned by a non-participant. Because Lopez-Alvarez’s admissions contained many accurate details, an important part of his defense involved an attempt to demonstrate that he could have learned those details without being a participant. The defense was allowed to pursue this task; the excluded information affected only a portion of its effort. While it is true that the excluded testimony might have provided more concrete information regarding Lopez-Alvarez’s opportunity to learn information about the Camarena affair, appellant does not argue that the testimony [589]*589would have provided a specific source for the most damaging aspects of his admissions, such as his knowledge of the tape recording of Camarena’s interrogation or of the manner in which the agent was killed. Moreover, based -on Garcia’s actual testimony, it appears unlikely that additional probing would have elicited answers that would have been of significant value to Lopez-Alvarez. See note 3 supra. Although the question is close, we believe that on balance the trial court’s error did not have a substantial impact on the jury’s deliberation and that, for this reason, the error was harmless under Fed.R.Crim.P. 52(a). Accordingly, the limitation on defense counsel’s cross-examination of Garcia does not provide a basis for reversing the defendant’s convictions.
2. Sufficiency of the evidence
Lopez-Alvarez contends that the evidence is insufficient to support a verdict of guilty on any of the charges against him. Evidence is sufficient to support a convic-' tion if, viewing it in the light most favorable to the prosecution, “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979). On the other hand, we will reverse a conviction if our review of the evidence leads us to the conclusion that there are not sufficient probative facts from which a factfinder, applying the beyond a reasonable doubt standard, could rationally choose the hypothesis that supports a finding of guilt rather than the hypotheses that are consistent with innocence. See United States v. Bishop, 959 F.2d 820, 830 (9th Cir.1992).
The primary evidence against the defendant consists of his own admissions: statements he made to Garcia and to Reynoso describing his involvement in the crimes charged. On separate occasions, Lopez-Alvarez stated that he worked for Caro-Quintero, that he participated in the kidnapping of Camarena, that he participated in beating Camarena, and that he assisted in Caro-Quintero’s escape from DEA and Mexican authorities. It does not appear from the record that the defendant made any admissions concerning the kidnapping and murder of Alfredo Zavala. We must first consider the degree to which the government may rely on the defendant’s admissions to meet its burden of proof.
It has long been established that a defendant’s confession requires some independent corroborating evidence in order to serve as the basis for a conviction. See Opper v. United States, 348 U.S. 84, 89, 75 5.Ct. 158, 162, 99 L.Ed. 101 (1954) (citing Wigmore, Evidence (3d ed.) § 2071; Warszower v. United States, 312 U.S. 342, 345 n. 2, 61 S.Ct. 603, 606 n. 2, 85 L.Ed. 876 (1941)). The requirement of corroboration arises from the high incidence of false confessions and the resulting need to prevent “errors in convictions based upon untrue confessions alone.” Warszower, 312 U.S. at 347, 61 S.Ct. at 606.5 In Opper, the Supreme Court recognized that the same unreliability exists with respect to post-offense admissions, which therefore also require independent corroboration: “[A]n accused’s admissions of essential facts or elements of the crime, subsequent to the crime, are of the same character as confessions and ... corroboration should be required.” 348 U.S. at 90, 75 S.Ct. at 163. Under Opper, the prosecution must introduce independent evidence “tend[ing] to establish the trustworthiness of [a] statement” before it may rely on the statement as evidence of an element of the offense. Id. at 93, 75 S.Ct. at 164.6
[590]*590Opper also addresses the amount of evidence necessary to corroborate an admission. The Court rejected the proposition that independent evidence was necessary to establish the whole of the corpus delicti. See id. Instead, said the Court, “[i]t is sufficient if the corroboration supports the essential facts admitted sufficiently to justify a jury inference of their truth.” Id. The sufficiency requirement is complicated, however, by the fact that corroborating evidence may take two different, though related, forms. One type of corroborating evidence is the type just described; evidence that demonstrates that the offense for which the defendant was convicted did in fact occur. This type of corroboration ensures that the defendant is not convicted of a non-existent crime but does not otherwise tend to support the reliability of the admission or the guilt of the defendant. The other type of corroborating evidence relates to the admission itself; it is evidence that tends to suggest that the admission is truthful but does not otherwise demonstrate that the crime actually occurred.7 We must determine the degree to which the prosecution must introduce one, the other, or both types of corroborating evidence.
Prior to Opper, the corroboration requirement demanded only that the prosecution independently demonstrate the occurrence of the crime. See Smith, 348 U.S. at 153-54, 75 S.Ct. at 198 (“The corroboration rule, at its inception, served an extremely limited function. In order to convict of serious crimes of violence, then capital offenses, independent proof was required that someone had indeed inflicted the violence.” (emphasis in original)). This so called corpus delicti rule does not require the state to otherwise demonstrate the reliability of the confession, and a defendant can be convicted under that rule without any independent evidence of his involvement at all. See id. at 154, 75 S.Ct. at 198 (“Once the existence of the crime was established, however, the guilt of the accused could be based on his own otherwise uncorroborated confession.”).
The traditional corpus delicti rule presented certain difficulties. One obvious problem is that it failed to gúard against false confessions to actual crimes. See State v. Lucas, 30 N.J. 37, 152 A.2d 50, 60 (1959) (arguing that the corpus delicti rule is inadequate insofar as it does not protect against a false confession to a real crime, which is a greater likelihood than a false confession to a crime that never occurred); Wensley, Forty Years of Scotland Yard 57, 273 (1931) (same). Less obvious, however, is that its formalistic precision-requiring independent evidence of every element of the corpus delicti—sometimes prevented convictions due to an otherwise insignificant technicality. See, e.g., People v. Zwierkowski, 368 Mich. 56, 117 N.W.2d 179 (Mich.1962) (reversing conviction for breaking and entering at night because the prosecution had failed to introduce independent evidence that the crime had been committed during the nighttime). This problem has subjected the rule to criticism, see, e.g., Manning v. United States, 215 F.2d 945, 946 (10th Cir.1954), and arguably has induced courts to misapply the rule rather than reverse convictions that fail to meet [591]*591the traditional corpus delicti standard, see id.; State v. McGuire, 327 Mo. 1176, 39 S.W.2d 523 (1931) (upholding conviction for larceny at night even though the prosecution failed to introduce an essential element of the crime — that it was committed during the nighttime).
Opper attempted to cure both problems. First, it rejected the traditional corpus de-licti rule and held that the prosecution need not introduce independent evidence of every element of the crime. See 348 U.S. at 93, 75 S.Ct. at 164. Second, it adopted the new requirement that the prosecution introduce evidence “tendpng] to establish the trustworthiness of the statement.” Id. The Opper rule reduces the likelihood that a defendant will be convicted on the basis of a false confession or acqúitted on the basis of a slight technical error by the state.
While Opper clearly held that the prosecution need not introduce independent evidence of every element of the corpus de-licti, there has been some confusion over whether and to what degree independent evidence that a crime has been committed must be introduced. After Opper, must there be any independent verification that criminal conduct has occurred or may the prosecution rely entirely on admissions which it has shown to be reliable?
The answer is that independent verification is still required. However, the state no longer need introduce independent, tangible evidence supporting every element of the corpus delicti. Instead, the state is required to support independently only the gravamen of the offense — the existence of the injury that forms the core of the offense and a link to a criminal actor — with tangible evidence. The source of this modern corpus delicti rule is Wong Sun v. United States, 371 U.S. 471, 83 S.Ct. 407, 9 L.Ed.2d 441 (1963), in which the Supreme Court, albeit in dictum, stated that, even after Opper, the state remains obligated to introduce independent evidence that a crime has occurred. In an otherwise confusing footnote, the Court stated:
Where the crime involves physical damage to person or property, the prosecution must generally show that the injury for which the accused confesses responsibility did in fact occur, and that some person was criminally culpable. A notable example is the principle that an admission of homicide must be corroborated by tangible evidence of the death of the supposed victim. See 7 Wigmore, Evidence (3d ed. 1940), § 2072, n. 5. There need in such a case be no link, outside the confession, between the injury and the accused who admits having inflicted it. But where the crime involves no tangible corpus delicti, we have said that “the corroborative evidence must implicate the accused in order to show that a crime has been committed.” [Smith,] 348 U.S. at 154, 75 S.Ct. at 198.
371 U.S. at 489 n. 15, 83 S.Ct. at 418 n. 15. This footnote has proved somewhat misleading; it has led some courts and commentators to resurrect the traditional corpus delicti rule, see, e.g., Developments in the Law — Confessions, 77 Harv.L.Rev. 938, 1073 & n. 13 (1966) (citing Wong Sun for the proposition that the traditional corpus delicti rule is “presently being applied by many courts” and “does not seem to be in immediate danger of repudiation”), and to reject the requirement that the state introduce evidence demonstrating the reliability of the confession, see United States v. Johnson, 589 F.2d 716, 719 n. 32 (D.C.Cir.1978) (suggesting that Wong Sun allows the state to convict without independent evidence suggesting that a confession is reliable); in other words, the footnote has led some to suggest that Wong Sun overruled Opper implicitly.
We believe- that Wong Sun does not overrule Opper but that it does demonstrate that Opper’s creation of a requirement that the state introduce evidence as to the confession’s reliability does not wholly eliminate the requirement that it introduce evidence that a crime has occurred.
We begin with the question whether Wong Sun resurrects the traditional corpus delicti rule. Thie only specific requirement mentioned in the footnote is that the prosecution introduce into' a homicide trial [592]*592“tangible evidence of the death of the supposed victim.” Tangible evidence of the injury or loss that forms the gravamen of an offense is perhaps the most venerable aspect of the corroboration requirement, see Captain Green’s Trial, 14 How.St.Tr. 1199, 1246-47 (Scot.Ct.Adm. 1705), and it is unlikely that, even without Wong Sun’s reaffirmance, Opper’s rejection of the all-inclusive corpus delicti rule would have led courts to reject this part of the rule. At the same time, nowhere does Wong Sun state that the prosecution must introduce independent evidence of every element of the corpus delicti, and we think it clear that the Court had no intention to impose such a requirement, particularly in light of Op-per’s explicit rejection of it. We believe that Wong Sun merely reaffirms the elementary proposition that the prosecution must introduce independent evidence that the criminal conduct at the core of the offense actually occurred — “that the injury for which the accused confesses responsibility did in fact occur, and that some person was criminally culpable.”
We next turn to the question of whether the Court’s statement that “[t]here need in such a case [where the state has demonstrated that the homicide has occurred] be no link, outside the confession between the injury and the accused who admits having inflicted it” overrules Opper’s requirement that the state’s corroborative evidence fortify the truth of the defendant’s admissions. Even were there a clear conflict, we would not be inclined to give such disposi-tive effect to an ambiguous sentence in a single footnote. However, there is no conflict. Although Wong Sun states that there need be no independent evidence, other than the confession, linking the accused to a tangible crime, the footnote contains no discussion of the degree to which the state must introduce evidence substantiating the trustworthiness of that confession. We are obligated to read the Wong Sun statement in light of Opper. We read it, therefore, as referring to a confession that satisfies the corroboration requirements of the earlier decision. That is, the Wong Sun statement suggests that when the state has adequately demonstrated the occurrence of a tangible crime, an adequately trustworthy confession will suffice under the corroboration requirement without independent evidence linking the confessor to the crime..
To summarize, under our reading of Opper and Wong Sun, the corroboration requirement is two-pronged: first, although the state need not introduce independent evidence of the corpus delicti in conformance with the traditional test, it must introduce sufficient evidence to establish that the criminal conduct at the core of the offense has occurred. Second, it must introduce independent evidence tending to establish the trustworthiness of the admissions, unless the confession is, by virtue of special circumstances, inherently reliable. Only when both these prongs are satisfied will a jury be “sufficiently justified” in believing the truth of a criminal admission; only then will the evidence be deemed sufficient in a case in which the conviction depends in part on such admission.
Our two-pronged approach to the corroboration requirement is supported by circuit precedent. For example, in Rodriquez v. United States, 407 F.2d 832 (9th Cir.1969), we first noted that the crime was a tangible one and that the independent evidence demonstrating that the crime had occurred was sufficient even though it did not demonstrate a link to the defendant. See id. at 834. Next, we noted that “the government did introduce substantial evidence to establish the trustworthiness of the appellant’s confession.” Id. For these reasons, we held that the conviction, which was based primarily on the defendant’s confession, was supported by sufficient evidence. Other cases are similar.8 Accordingly, in re[593]*593viewing Lopez-Alvarez’s convictions for sufficient evidence, we must determine both whether there is independent evidence that the crimes actually occurred and whether the prosecution has demonstrated the trustworthiness of the defendant’s admissions. Because the convictions are dependent on the defendant’s admissions, we may affirm the convictions only if both requirements are met.
a. The crimes against Camarena
Four of the six counts on which Lopez-Alvarez was convicted involved crimes against Camarena. The primary evidence supporting these counts is the defendant’s admissions that he helped to kidnap and torture the agent. There is substantial independent evidence supporting the trustworthiness of these admissions. Preliminarily, we note that there is no doubt that the crimes were committed— that Camarena was kidnapped, severely beaten, and then killed and that the violent acts were committed to further the Caro-Quintero drug enterprise. There is sufficient independent evidence of these occurrences. As to the reliability of the admissions, the details of the crimes provided by the defendant are verified by independent evidence. For example, Lopez-Alvarez described using heated iron pipes to beat Camarena; this is consistent with the condition of the body, which had suffered broken ribs and a blow to the skull with a blunt instrument. In addition, Lopez-Alvarez stated that a tape recording existed in which several men questioned Camarena regarding the DEA’s knowledge of Caro-Quintero’s drug enterprise. This tape recording was introduced, and its contents matched the defendant’s general description. (The tape also constitutes circumstantial evidence of a conspiracy to kidnap Camarena and that the kidnapping and murder were committed in aid of Caro-Quintero’s racketeering activities.) Although the Camarena affair was well publicized, there is no indication that these specific details were so widely disseminated that the defendant’s knowledge of them would not constitute evidence of his participation in the crimes. The jury was free to reject the explanation that he learned of them from his cellmates. The erroneous limitation on cross-examination did not constitute reversible error. Accordingly, we believe that the admissions were supported by credible evidence, that a jury would be substantially justified in believing them, and that they were therefore sufficiently reliable to support a conviction. With the independent evidence regarding the existence of a crime and with the evidence of trustworthiness of the defendant’s admissions, the' Opper-Wong Sun test is met. Lopez-Alvarez’s inculpatory statements along with the evidence supporting their admission, are sufficient to support his convictions on the four counts involving Ca-marena: that the defendant committed violent crimes against the agent in aid of racketeering, that the defendant conspired to kidnap the agent, that he did kidnap the agent, and that he is guilty of the subsequent felony murder.
b. The crimes against Zavala
Lopez-Alvarez made no admissions regarding the kidnapping and killing of Zavala. Nor is there any other evidence linking him to those crimes. Instead, the only, evidence supporting his conviction for violent crimes against Zavala is that linking Zavala to the Camarena affair. There is evidence, that Zavala was held in the same location as Camarena, in a house belonging to Caro-Quintero. The DEA agent and the DEA informant were kidnapped at the same time, and their bodies were found together. In addition, the government argues that the defendant had the motive to kidnap and kill Zavala .because “[f]]inding out what [Zavala] knew about the [Caro-Quintéro] enterprise and/or killing [him] was ... essential to the continued operations of the enterprise.”.
[594]*594We find that this evidence is insufficient to uphold the defendant’s conviction. All the evidence merely supports the proposition that some members of Caro-Quintero's operation committed the violent acts against Zavala; there is no evidence specific to Lopez-Alvarez.9 While the government may have demonstrated that members of the Caro-Quinero drug operation committed the offenses against both Ca-marena and Zavala, it has offered no evidence that the same members were involved. Nor is the enterprise sufficiently small to permit a jury to draw such a conclusion. Accordingly, the defendant’s conviction for violent crimes against Zavala in aid of the Caro-Quintero racketeering enterprise must be reversed.
c. The conviction for being an accessory after the fact
Lopez-Alvarez was convicted of being an accessory after the fact regarding the kidnapping and murder of Camarena and Zavala. The government’s claim is that the defendant provided Caro-Quintero with assistance during an encounter at the Guadalajara airport between Caro-Quintero and DEA agents. The agents confronted Caro-Quintero but after a tense though non-violent stand-off permitted him to leave. In order for us to uphold the conviction, the government must have proved beyond a reasonable doubt that Caro-Quintero participated in the kidnappings and murders, that the defendant had knowledge of that participation, and that, with such knowledge, he assisted Caro-Quintero in avoiding apprehension, trial, or punishment. See United States v. Rux, 412 F.2d 331, 333 (9th Cir.1969). The difficult question is whether there is sufficient evidence supporting the jury’s finding beyond a reasonable doubt that Lopez-Alvarez provided some assistance to Caro-Quintero in connection with the Guadalajara incident.
The principal evidence against the defendant was his own admissions to Reynoso. He told the DEA agent that he assisted Caro-Quintero during the airport encounter. A group of Mexican state police officers, including the defendant, had been sent to the airport, ostensibly to support the Mexican federal police investigation of Caro-Quintero. The defendant claimed that, on the way to the airport, he had attempted without success to leave the caravan of automobiles in order to warn Caro-Quintero of the plan to capture him, and that he had managed to send that warning after he arrived. In addition, the defendant claimed that, during the encounter between Caro-Quintero and law enforcement officials, he had stood behind the DEA and Mexican federal officers and prepared himself to act in support of Caro-Quintero should fighting occur. No fighting occurred.
Aside from Lopez-Alvarez’s admissions, the evidence is slender. A DEA agent testified that he saw Lopez-Alvarez at the airport. However, the agent did not recall where Lopez-Alvarez had stood during the encounter with Caro-Quintero, and his testimony contained no details regarding Lopez-Alvarez’s activities at the airport. Although the agent suggested that law enforcement officials had collaborated with, and provided assistance to, Caro-Quintero during the encounter, his testimony impli[595]*595cated the Mexican federal police, not the Mexican state police.
We find that Lopez-Alvarez’s admission that he was an accessory after the fact is insufficiently corroborated. First, there is insufficient independent evidence that the crime actually occurred. The fact that Lopez-Alvarez was a member of the Caro-Quintero enterprise does not establish any element of the charge that he provided Caro-Quintero with assistance at the Guadalajara airport. The DEA agent’s testimony is equally inadequate. It merely places Lopez-Alvarez at the airport; it does not state that the defendant sent Caro-Quintero any signals or that Caro-Quintero received any signals; nor does it state that Lopez-Alvarez was in a position to help Caro-Quintero in a shoot out with the police; finally, it does not provide any other suggestion of how Lopez-Alvarez might have assisted Caro-Quintero. We note, furthermore, that the defendant’s presence at the airport is in no way incriminating as he was sent there as part of his duties with the Mexican state police. There is simply no tangible evidence that Caro-Quintero received the type of assistance Lopez-Alvarez claims to have provided or that Lopez-Alvarez sought to provide such assistance. In short, the only evidence that a crime occurred is Lopez-Alvarez’s statement that it did. The danger is too great that the defendant has admitted to non-existent criminal conduct.
Further, even if we were to assume that the government had sufficiently corroborated the occurrence of a crime, we would find that it had failed to establish adequately the trustworthiness of Lopez-Alvarez’s confession. The only elements of his admission that have been independently verified are those relating to his presence at the airport. There is no verification of any unlawful or inculpatory conduct: as we have noted, Lopez-Alvarez was at the airport for a legitimate reason. There is no independent evidence substantiating his claim that, while en route, he tried to warn Caro-Quintero, that he did manage to warn Caro-Quintero after he arrived, or that he stood ready to support Caro-Quintero in a shoot out with law enforcement officials. The government may not rely on the fact that Lopez-Alvarez’s admissions regarding the kidnapping and murder of Camarena appear trustworthy. That Lopez-Alvarez may have told the truth on some occasions does not establish that he was not exaggerating on others.
In sum, there is insufficient corroborating evidence supporting the defendant’s accessory after the fact admission. Because there is no independent evidence that the offense occurred, the danger is too great that the defendant has been convicted of non-existent criminal conduct. There is also insufficient evidence supporting the trustworthiness of the confession. For both reasons, the admission is inadequately corroborated. Because Lopez-Alvarez’s conviction for being an accessory after the fact is based primarily on that admission, the conviction is not supported by sufficient evidence, and must be reversed.
3. Reference to Lopez-Alvarez’s Failure to Testify
Lopez-Alvarez maintains that the prosecution committed prejudicial misconduct by making impermissible comments about his failure to testify at trial.10 It is misconduct for a prosecutor to comment on a defendant’s failure to testify. See United States v. Robinson, 485 U.S. 25, 108 S.Ct. 864, 99 L.Ed.2d 23 (1988). However, “ ‘a prosecutor may properly comment upon the defendant’s failure to present exculpatory evidence, as long as it is not phrased to call attention to defen[596]*596dant’s own failure to testify.’ ” United States v. Bagley, 772 F.2d 482, 494-95 (9th Cir.1985) (quoting United States v. Soulard, 730 F.2d 1292, 1306 (9th Cir.1984)), cert. denied, 475 U.S. 1023, 106 S.Ct. 1215, 89 L.Ed.2d 326 (1988). “ ‘A comment on the failure of the defense as opposed to the defendant to counter or explain the testimony presented or evidence introduced is not an infringement of the defendant’s Fifth Amendment privilege.’ ” United States v. Castillo, 866 F.2d 1071, 1083 (9th Cir.1988) (quoting United States v. Wasserteil, 641 F.2d 704, 709-10 (9th Cir.1981)) (emphasis in original).
The prosecutor’s remarks do not call attention to defendant’s failure to testify. As in United States v. Castillo, “[a]t no time was there any express reference to [the defendant’s] failure to testify. Instead, the Government asked the jury to consider, in weighing the evidence, that the defense did not rebut certain evidence presented by the prosecution.” 866 F.2d at 1083.
The defendant contends that despite the absence of express reference to his failure to testify, the prosecutor’s statement that there was no evidence that Lopez-Alvarez “did not mean what he said” amounted to the same thing because his testimony was the only form of evidence which could have indicated that he had lied about his role in the abduction. We do not agree with this contention. The defense itself attempted to show that he had lied in order to impress Agent Reynoso, by introducing circumstantial evidence consistent with that theory.11 Thus, the prosecutor’s statement likely referred to the inadequacy of that evidence and not to the fact that the defendant had not testified. Accordingly, we reject the defendant’s argument.
4. Subject Matter Jurisdiction
Lopez-Alvarez incorporates the argument raised by his co-defendant Jesus Felix-Gutierrez that the district court did not have subject matter jurisdiction to try the defendants for crimes committed outside the United States.12 It is unnecessary to discuss the' jurisdictional issue, however, because we have recently held in United States v. Felix-Gutierrez, 940 F.2d 1200 (9th Cir.1991), that the district court had extra-territorial jurisdiction over not only Felix’s charge of accessory after the fact, but also over the “underlying crime” — i.e., the abduction and murder, see id. at 1206. This holding is sufficient to dispose of Lopez-Alvarez’s contention.
5. Sufficiency of the Felony Murder Indictment
Lopez-Alvarez argues that Count Five of the indictment failed sufficiently to charge the offense of felony murder. It is well established that an indictment must state the elements of the offense charged in sufficient detail to allow the defendant to prepare his defense and to avoid double jeopardy. See Russell v. United States, 369 U.S. 749, 764, 82 S.Ct. 1038, 1047, 8 L.Ed.2d 240 (1962); United States v. Krasovich, 819 F.2d 253, 254-55 (9th Cir.1987). The indictment in the present case fulfilled these requirements. Because it stated the approximate date of the killing and the name of the victim, it enabled the defendant to determine whether double jeopardy concerns were implicated. Cf. Williamson v. United States, 310 F.2d 192 at 195-96 (9th Cir.1962) (indictment for marijuana smuggling was sufficient to avoid double jeopardy where it stated the time of offense and persons and amount of marijuana involved). In addition, the indictment was sufficiently clear to enable Lopez-Alvarez to prepare his defense. It alleged that Camarena was [597]*597“murdered” in the course of his kidnapping and stated that the crime was “wilfully perpetrated” by Lopez and others. It set forth the elements of the offense charged by stating that the count was brought under 18 U.S.C. § 1111(a), which defines mur-dér as “the unlawful killing of a human being with malice aforethought” and murder perpetrated during the commission of a kidnaping as murder in the first degree. Count Five of the indictment thus made it clear that Lopez-Alvarez was charged with committing the offense of first degree murder arising from his involvement in the Camarena affair. This appears sufficient to allow Lopez-Alvarez to prepare his defense, and he does not suggest additional information that should have been included in the indictment.
6. Proposed Jury Instructions
Lopez-Alvarez contends that the trial court incorrectly refused to instruct the jury on his theory of defense. The district judge rejected the following jury instruction:
If you believe that Defendant Raul Lopez-Alvarez was not present during the abduction, interrogation or murder of Agent Camarena, but merely made statements about those events based not on personal knowledge, but based on what he heard and what he read, then you must acquit him on Counts 1, 3, 4, and 5.
Also rejected was a proposed instruction essentially identical except for the substitution of Zavala for Camarena.
We believe that the district court did not commit reversible error in rejecting the proposed instructions. The jury was properly instructed in the elements of each offense and the prosecution’s burden of proof.13 These instructions made it obvious to the jury that if it found that Lopez-Alvarez’s admissions did not come from personal knowledge of the Camarena affair but were fabricated on the basis -of information received from other sources, it should find him innocent. In addition, under the facts of the case, it should have been clear to the jury even without the instruction, that Lopez-Alvarez should be acquitted if it found he was not present during any of the criminal occurrences. Thus, the defendant’s proposed instructions were not necessary to explain to the jury the legal effect of the theory of the defense. A defendant is not entitled to any particular form of instruction, nor is he entitled to an instruction that merely duplicates what the jury has already been told.14 Accordingly, the district judge did not err in refusing the proposed instructions. See United States v. Hall, 552 F.2d 273, 275 (9th Cir.1977).
7. Prosecutor’s Comments to the Jury
Lopez-Alvarez argues that the prosecutor’s comments to the jury contained impermissible references to his supposed involvement in drug trafficking, disparaged defense counsel, and vouched for the credibility of witnesses, thereby constituting misconduct sufficiently prejudicial to warrant a new trial. However, improprieties in counsel’s arguments to the jury do not constitute reversible error unless they prejudice the defendant and that prejudice has not been remedied by the trial judge. See United States v. Birges, 723 F.2d 666, 672 (9th Cir.), cert. denied, 466 U.S. 943, 104 S.Ct. 1926, 80 L.Ed.2d 472 (1984). In addition, the propriety of the prosecutor’s remarks must be judged in relation to what would constitute a fair response to the remarks of defense counsel. See United States v. Falsia, 724 F.2d 1339 (9th Cir.1983).
[598]*598Most of the comments challenged by Lopez-Alvarez were made in response to comments made by the defendant’s counsel. For example, the prosecutor’s contentions that the defense had mounted a personal attack upon him and his co-counsel and his insistence that the witnesses were trustworthy merely rebutted defense counsel’s repeated allegations that the prosecution had intimidated, coached, and bribed witnesses. Similarly, the prosecutor’s comments comparing defense counsel to both a magician and a squid were not likely to have prejudiced the jury against Lopez-Alvarez, particularly in light of defense counsel’s comparison of the prosecutor to the Wizard of Oz. Viewed in context, the prosecutor’s remarks were acceptable — though not highly desirable — advocacy. See United States v. Flake, 746 F.2d 535, 539-541 (9th Cir.1984) (holding that the prosecutor did not impermissibly vouch for the credibility of witness where his comments were “clearly invited” by the defense’s attack on the credibility of the government and its witnesses).
Lopez-Alvarez also contends that the prosecution prejudiced the jury by making remarks, which were unsupported by the evidence, about his supposed involvement in narcotics trafficking. The prosecutor told the jury:
Relative to those admissions that Lopez made to the undercover agent [Reynoso], the defense would have you believe that these were admissions that were being made to somehow impress this agent, to impress this agent that Lopez was involved in some narcotics deal, that he was interested in distributing some quantity of narcotics.
Whether or not the record supported the existence of narcotics dealing is irrelevant. The prosecutor did not assert that Lopez-Alvarez was involved in drug trafficking. Rather, he stated that the defense was trying to convince the jury that the defendant’s admissions had actually been lies told in order to convince Reynoso, whom he believed to be a criminal, that he (Lopez-Alvarez) was involved in narcotics trafficking. This was an accurate statement of the main theory of the defense as revealed in the record. Defense counsel established that Reynoso had represented himself to Lopez-Alvarez as a criminal. Reynoso testified that Lopez-Alvarez had claimed to work for reputed drug barons Caro-Quinte-ro and Ernesto Fonseca-Carillo. The jury could have reasonably inferred — indeed, the defense wanted it to infer — that Lopez-Alvarez had lied to Reynoso in order to make Reynoso believe that he was a drug trafficker. The defendant states in his opening brief that based on Garcia’s advice he decided to lie to Reynoso in order “to convince ... [him] that he [Lopez-Alvarez] was in fact a high-level drug trafficker....” Thus, the prosecutor’s statements were not prejudicial. In any event, any prejudice which might have resulted from the comments was “neutralized by the trial judge,” Birges, 723 F.2d at 672, when he instructed the jury that “[t]he lawyers’ statements are not evidence.”
8. Disclosure of Evidence
Finally, Lopez-Alvarez argues that the prosecution violated the rule of discovery established in Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by failing to disclose exculpatory evidence. Brady requires the government to produce exculpatory evidence which is “material to guilt or punishment.” 373 U.S. at 87, 83 S.Ct. at 1197.
Lopez-Alvarez contends that the government failed to produce information showing that Miguel Felix-Gallardo, rather than Rafael Caro-Quintero, was the originator of the plot to kidnap Camarena. That such information exists, however, is purely speculative. Contrary to the defendant’s suggestion, we do not find the inclusion of Gallardo in a later indictment of Caro-Quintero to be proof that the government withheld such evidence. In any event, Lopez-Alvarez fails to state how such information would exculpate him even if it were to exist.
Conclusion
The judgment of the district court on Counts One, Three, Four, and Five is AFFIRMED. The judgment of the District Court on Counts Two and Seven is REVERSED.
[599]*599. AFFIRMED IN PART AND REVERSED IN PART.