Sally-Anne Croft and Susan Hagan were convicted by a jury of conspiring to murder the United States Attorney for the District of Oregon, a violation of 18 U.S.C. §§ 1111, 1114, and 1117. Croft and Hagan now appeal their convictions, arguing on a variety of grounds that they were denied a fair trial and a full opportunity to confront the witnesses against them. We have jurisdiction pursuant to 28 U.S.C. § 1291, and we affirm the convictions.
BACKGROUND
Bhagwan Shree Rajneesh (“Rajneesh”) was an Indian mystic who developed a substantial following in Poona, India in the 1970s. In 1981, Rajneesh came to America with a number of his Western followers to found a spiritual community, known as Rajneeshpuram, in Central Oregon. From its inception, the community was highly controversial. The number of Rajneesh’s followers living at the community eventually grew to approximately four thousand, with as many as 10-15,000 followers attending annual celebrations there.
Rajneesh’s disciples were known as “san-nyasins,” and a small group of the most trusted among them oversaw the community’s business and spiritual operations. Ma Anend Sheela (“Sheela”), Rajneesh’s principal secretary and spokeswoman, was in charge of day-to-day operations, and was entrusted with transmitting and executing Rajneesh’s orders. Below Sheela were “department coordinators,” a group that included appellants Croft and Hagan. Croft was second-in-command of the community and the head of its financial department. Hagan was in charge of construction, heavy equipment, and the community’s security force. Four of the five government witnesses — all of whom were indicted or unindicted co-conspirators — also held important positions in the community: David Knapp was the community’s mayor; Richard Langford was the security force’s weapons expert; Ava Avalos managed Rajneesh’s correspondence and assisted Croft; and Alma Peralta was Sheela’s aide-de-camp. The fifth government witness, Phyllis Caldwell, was a member of the community. Two other members of the community, who did not appear as witnesses, figure in this appeal. One is Jane Stork, an indicted co-conspirator whom the government unsuccessfully tried to extradite from Germany. The other is Jorg Dauscher, who attended a few of the meetings. He was not indicted for the conspiracy to murder the United States Attorney, but was indicted for a wiretapping offense and remained out of the United States during the trial. The conspiracy to murder Charles Turner, then the United States Attorney for the District of Oregon, arose as a consequence of a series of legal difficulties that the Rajneesh-puram community encountered in 1984 and 1985. In 1984, the community learned that federal authorities were investigating numerous sham marriages by which members of the community had secured entry into the United States. At about the same time, a former member of the community, Helen Byron, sued the community to collect money she had lent it; a jury awarded $ 1.7 million in compensatory and punitive damages. Im*1114mediately after the verdict, Sheela told several of her department coordinators that the community would never obtain a fair trial in Oregon and that, if the community were to survive, its members would have to take the law into their own hands. Later, during a meeting attended by Croft, Hagan, Stork, Langford, and other members of the Rajneesh community, Sheela stated that it would be necessary for them to assassinate certain of the community’s enemies, including Turner.1 Hagan made a speech to the group at that meeting in which she told the others “we have to do something here. We have to support Sheela.” She said that she was going to run the meeting “so that everyone knows that Sheela isn’t forcing us to this, that everyone is taking responsibility on their own.”
Additional meetings involving Croft and Hagan, Sheela, and other key members of the commune followed. Although the testimony of the government’s witnesses was not wholly consistent, the witnesses generally agreed that the conspirators formed a “hit team” to kill Turner that included Stork and Hagan, and that Croft was designated to supply the hit team with money for guns and passports. Stork and Caldwell did, in fact, travel to Texas and New Mexico and purchased handguns. Other conspirators engaged in surveillance of Turner, and obtained a photograph of him. The conspiracy then began to unravel. No actual attempt was made on Turner’s life. One of the plotters, with approval of others, threw the handguns into a lake. Later several of the conspirators, including Sheela, departed from Rajneeshpuram.
The conspirators, including Croft and Ha-gan, were indicted in May 1990, after Avalos revealed the conspiracy to state and federal law-enforcement officials. Knapp, Avalos, Langford, Peralta, and Caldwell all made arrangements with the government to testify against Croft and Hagan in exchange for lenient treatment for their crimes. Their agreements required them to testify truthfully and provided that, if they did not keep their bargains, the agreements would be rescinded. Several of the agreements provided that the government retained the exclusive right to determine whether the agreement had been breached. Avalos received complete immunity from prosecution. Knapp was sentenced to two years in prison after pleading guilty to making false statements. Phyllis Caldwell was placed on probation for five years following a plea of guilty to wiretapping. Peralta and Langford served two and three years respectively following pleas of guilty to conspiracy to murder.
Croft’s and Hagan’s trial lasted nearly a month. The jury deliberated for four days. On the third day, the jury announced that it had reached a verdict as to one defendant, but had “deadlocked” as to the other. The district court then gave the jury a modified Allen charge, and on the afternoon of the following day the jury returned verdicts of guilty against both Croft and Hagan. Croft and Hagan were each sentenced to five years imprisonment. This appeal followed.
ANALYSIS
I. Sufficiency of the Indictment.
Croft and Hagan argue that the district court should have dismissed the indictment because it alleged objects of the conspiracy that did not constitute federal offenses. Count I of the indictment alleged a conspiracy to murder a federal official and was entitled “Conspiracy to Murder the United States Attorney.” Paragraph 14 of that Count, however, stated that “[ajmong the enemies of the commune targeted to be murdered were Mr. Turner and Swami Devaraj ... Bhagwan’s personal physician.” Devaraj is not a federal official; conspiring to kill him, therefore, is not a federal offense. Other non-federal criminal activities were also stated to be objects of the conspiracy.
The indictment does not fail to allege a federal offense. The inclusion of non-federal offenses as additional objects of a federal conspiracy is permissible as long as the in-
*1115dictment also includes an object that constitutes a federal offense. United States v. Giese, 597 F.2d 1170, 1179 (9th Cir.), cert. denied, 444 U.S. 979, 100 S.Ct. 480, 62 L.Ed.2d 405 (1979). There is no likelihood that the grand jury failed to understand that it was indicting for conspiracy to murder the United States Attorney, as the title to Count I states. The district court did not err, therefore, in refusing to dismiss the indictment on the ground that it contained non-federal offenses.
Croft and Hagan rely on United States v. Manarite, 44 F.3d 1407 (9th Cir.), cert. denied, 515 U.S. 1158, 115 S.Ct. 2610, 132 L.Ed.2d 854 (1995), and United States v. Pappadopoulos, 64 F.3d 522 (9th Cir.1995). Their reliance is misplaced. In both of those eases, we held that a federal conspiracy conviction could not be upheld when non-federal offenses as well as federal offenses were submitted to the jury as objects of the conspiracy, and it was impossible to determine on which basis the jury convicted. See Manarite, 44 F.3d at 1413-14; Pappadopoulos, 64 F.3d at 528. No such deficiency exists in this case. The district judge carefully confined the trial to the federal offense. He gave the jury a redacted indictment that deleted reference to Devaraj and other extraneous matters, excluded evidence relating to the Devaraj’s attempted murder, and made clear to the jury in his instructions that it could convict Croft and Hagan of conspiracy only if it found beyond a reasonable doubt that they had conspired “to help accomplish the murder of then United States Attorney Charles Turner.” There was no defect in the presentation of the charges to the jury.
II. Change of Yenue.
Croft and Hagan argue that, in light of the extensive prejudice against the Rajneesh community in Oregon, the district court erred in refusing to grant their motion for a change of venue.2 Croft and Hagan submitted evidence indicating that huge numbers of (largely negative) stories had appeared in local Oregon media since 1981 concerning Rajneesh and his followers, and introdueed opinion polls conducted in 1984, 1992, and 1994 indicating that 90% of Oregonians knew about Rajneeshpuram, over 60% had heard of their prosecution, and over 40% believed that the indicted conspirators were guilty of the conspiracy.
For Croft and Hagan to succeed on this point, the denial of a change of venue must have prejudiced their trial either presumptively or actually. United States v. Dischner, 974 F.2d 1502, 1523 (9th Cir.1992). Prejudice is presumed when the adverse publicity is so pervasive and inflammatory-that the jurors cannot be believed when they assert that they can be impartial. Id. at 1524. The presumption is “rarely applicable and is reserved for an ‘extreme situation.’ ” Harris v. Pulley, 885 F.2d 1354, 1361 (9th Cir.1988) (internal citations omitted). The district court did not abuse its discretion in concluding that Croft and Hagan had not made a showing of adverse publicity sufficient to raise a presumption of prejudice in the jury. Most of the news stories Croft and Hagan cite were over 10 years old by the time of their trial, a factor that weighs against a finding of presumed prejudice. See United States v. Rewald, 889 F.2d 836, 864 & n. 28 (9th Cir.1989), amended, 902 F.2d 18 (1990). Most of those stories were not directed at Croft and Hagan, but at Sheela, Rajneesh, and the Rajneesh community as a whole. The adverse opinions reported in the 1992 and 1994 polls were directed at all of the indicted co-conspirators, five of whom were government witnesses, and not specifically at Croft and Hagan. The most recent articles about the charges were factual and not inflammatory. The district court was not required to presume prejudice.
Croft and Hagan also have not shown actual prejudice. Of the approximately 42 veni-re-members who had heard about the Rajneesh community, only one stated that the media had given him “preconceived ideas” concerning the defendant’s guilt, and he was immediately excused for cause. Although most of the members of the venire who actually sat as jurors had heard of the Rajneesh community, none of those indicated *1116that he or she had formed an opinion of guilt, or could not put aside what he or she had read or heard and serve as an impartial juror. On that showing, the district court did not abuse its discretion in declining to find actual prejudice. See Mu’Min v. Virginia, 500 U.S. 415, 428, 111 S.Ct. 1899, 1906, 114 L.Ed.2d 498 (1991).
III. Yoir Dire.
In a related argument, Croft and Ha-gan contend that the district court abused its discretion by failing to conduct more extensive voir dire into the venire’s prejudice toward members of the Rajneesh community. We conclude that the court’s examination of prospective jurors was within “the wide discretion granted to the trial court in conducting voir dire in the area of pretrial publicity and in other areas of inquiry that might tend to show juror bias.” Mu’Min, 500 U.S. at 427, 111 S.Ct. at 1905.
Here, as in Mu’Min, “the voir dire examination conducted by the trial court ... was by no means perfunctory.” Id. at 431, 111 S.Ct. at 1908. The district court explored whether any members of the venire had heard of “this situation and of the commune in general,” and whether they had “come to an opinion about the merits of this case one way or the other.” It permitted defense counsel to formulate and ask some questions, and excused two additional members of the venire: one who stated that he might “be influenced by what I hear,” and one who was not certain that she could be impartial. Finally, when Hagan’s counsel expressed concern that the questioning had not covered everything “bad that the Rajneesh did,” the district court asked additional questions of the venire “to make sure that none of [them were] carrying around something out of the media.” There was no abuse of discretion.
IV. Immunity for Defense Witnesses.
Croft and Hagan contend that their convictions must be reversed because the government distorted the fact-finding process by failing to grant immunity to two defense witnesses, while providing immunity to prosecution witnesses. We reject their contention.
We begin with the proposition that “[i]m-munity is an executive, not a judicial, function, and ‘[t]his court has emphatically rejected the argument that the sixth amendment provides a defendant with a right to demand use immunity for defense witnesses who invoke their privilege against self-incrimination.’ ” United States v. Baker, 10 F.3d 1374, 1414 (9th Cir.1993) (quoting United States v. Brutzman, 731 F.2d 1449, 1451-52 (9th Cir. 1984)). We have recognized an exception, however, when the defense witness’s testimony would have been relevant, and the prosecutor’s denial of immunity intentionally distorted the fact-finding process. United States v. Lord, 711 F.2d 887, 891 (9th Cir. 1983). We further have held that intentional distortion does not require affirmative misconduct by the prosecutor:
For the government to grant immunity to a witness in order to obtain his testimony, while denying immunity to a defense witness whose testimony would directly contradict that of the government witness, is the type of fact-finding distortion we intended to prevent in Lord.
United States v. Westerdahl, 945 F.2d 1083, 1087 (9th Cir.1991). Croft and Hagan argue that this Westerdahl standard was met with regard to the denial of immunity to two prospective defense witnesses: Stork and Dauscher.
Jane Stork was a member of the community and a co-conspirator; she had journeyed to Texas and New Mexico to buy handguns, and had been part of the proposed “hit team” to assassinate Turner. Stork had pleaded guilty in state court to attempted murder of Devaraj and had been sentenced to ten years in prison, of which she served 20 months. She had subsequently moved to Germany. The prosecution attempted without success to extradite her to face charges on the Turner conspiracy.
Croft and Hagan wanted Stork to testify on their behalf, but she refused to come to the United States unless she was granted transactional immunity for her testimony. The government would grant no such immunity. Croft and Hagan moved the court to compel the government to grant such immu*1117nity (or, alternatively, to dismiss the indictment) on the ground that the denial of immunity distorted the fact-finding process. Along with the motion, they submitted a report of an interview with Stork in which she denied that Hagan or Croft were at the meeting where the Turner assassination plot was hatched, and stated that she did not recall their presence at other meetings where the matter came up. (In connection with a motion for reconsideration, Stork added a statement that Croft had not given her the money to purchase the guns.)
Also included in the motion was a request for similar immunity for Dauscher, a community member who had been indicted on a related wire-tapping charge and who was also overseas. His testimony was represented in eonclusory fashion primarily as controverting a government witness’s version of a meeting in which Turner’s name came up.
The district court stated that Stork’s testimony would be relevant and that it assumed for purposes of decision that Dauseher’s would be, but it denied the motion on the ground that there had been no improper distortion of the fact-finding process by the government. The court also noted that the purported testimony was not wholly exculpatory, because the conspiracy involved many meetings at different times, in which Croft and Hagan could have participated without Stork’s or Dauscher’s knowledge.
We conclude that the district court did not err. We are dealing here with one defense witness who was indicted as a co-conspirator, and another who was indicted on related wire-tapping charges. In the case of Stork, the government had gone to great lengths to attempt to extradite her from Germany. In opposing the motion to require grants of immunity, the government undertook to offer the two prospective defense witnesses the same arrangement it had made with the prosecution witnesses: the witness would have to submit to the jurisdiction of the court, plead guilty to some charges, and be granted immunity in connection with testimony in the present ease. These terms were not acceptable to Stork or Dauscher, who wanted a much broader transactional immunity or some form of safe passage, but the terms were even-handed. Moreover, as the district court observed, neither Stork nor Dauscher could provide testimony that would be wholly exculpatory because neither witnessed everything that took place in the conspiracy; their proffered testimony did not purport to cover all the charged activities. We decline to adopt a rule that would require the government to grant transactional immunity to an indicted co-conspirator, or to a more marginal witness indicted on related charges, under these circumstances.
Westerdahl is distinguishable. It did not involve a prospective witness against whom charges were pending, and certainly not one against whom charges were pending under the same or a related indictment. In Baker, where we denied on several grounds a defense request for witness immunity, we noted in passing that the government had not offered any “legitimate reason” for denying immunity: the prospective defense witnesses “were not charged with committing any crimes in the District of Nevada.” Baker, 10 F.3d at 1414. We reflected the same position in United States v. Young, 86 F.3d 944 (9th Cir.1996), when we required an evidentiary hearing to determine whether the government’s denial of immunity had intentionally distorted the fact-finding process. We pointed out that unrelated charges pending against the prospective defense witness would not be affected by use immunity: “the government never linked [the witness’s] charged firearms offenses or alleged, uncharged narcotics offenses with the instant case against defendants.” Id. at 948. Here, Stork and Dauscher were charged, in the same or related indictments, with crimes in the District of Oregon for which they would have been prosecuted but for the fact that they had succeeded in remaining beyond the reach of the government. The transactional immunity they sought would clearly affect the charges against them. The government did not improperly distort the fact-finding process in denying them that immunity.
V. Continuance for Deposition of Stork.
At about the same time that they moved for immunity for their defense witnesses (and five weeks before trial), Croft *1118and Hagan moved for leave to take Stork’s deposition in Germany. The government did not oppose that motion, but opposed the grant of immunity. When the district court denied the immunity motion a month later, it also denied the deposition motion because it was under the impression that Stork required immunity for the deposition. Croft and Hagan moved for reconsideration, and the district court granted the motion but stated that it would not stay proceedings for the deposition. The court authorized an informal method of taking the deposition, to reduce the delay that would have attended the usual process employing letters rogatory. Despite this concession, Croft and Hagan were unable to complete arrangements for the deposition prior to the end of trial, and they again moved for a continuance, which the court denied.
Croft and Hagan argue that denial of the continuance deprived them of a fair trial because Stork was their primary witness. We conclude, however, that the district court did not abuse its discretion. The factors we consider in determining whether a continuance was required are:
the extent of appellant’s diligence in his efforts to ready his defense prior to the date set for hearing .... [2] how likely it is that the need for a continuance could have been met if the continuance had been granted____[3] the extent to which granting the continuance would have inconvenienced the court and the opposing party, including its witnesses .... [4] the extent to which the appellant might have suffered harm as a result of the district court’s denial.
United States v. Flynt, 756 F.2d 1352, 1359, amended, 764 F.2d 675 (9th Cir.1985); see United States v. Mejia, 69 F.3d 309, 314 (9th Cir.1995). The first factor does not favor Croft and Hagan; they made their motion for deposition only five weeks before trial. It is true that the district court held the motion four weeks before denying and then reconsidering it, but it is not clear from the record that the deposition could have been arranged within five weeks. The second factor similarly supports the district court’s denial. Although counsel represented at the time of the request for continuance that the appropriate German ministry had “informally indicated that it [would] allow the deposition to go forward,” the necessary official signatures had not been obtained and there was no indication when they might be. Once they were, the paper had to be referred to our Department of State, transferred to the Department of Justice, and when all of those clearances were obtained, the paper could be returned to Germany and the deposition taken. As the district court observed in denying a new trial, “[t]here was simply no end in sight.” Thus, the third factor also supports the district court, because an open-ended continuance would have inconvenienced the court, the government, and its witnesses. The fourth factor does favor Croft and Ha-gan: they may have been harmed by the inability to have Stork’s deposed testimony. As the district court pointed out, however, if the deposition had been introduced in evidence, the court would have instructed the jury that it could consider the fact that the deposition testimony was given under an oath that the United States had no way of enforcing. When all of the factors are considered together, we conclude that the district court’s decision was within its discretion.
VI. Evidentiary Issues.
A. Evidence of other “bad acts.”
Croft and Hagan argue that they were denied a fair trial by the government’s introduction of evidence of other crimes. Prior to trial, the government filed notice of its intention to offer evidence of Croft’s and Hagan’s involvement in a variety of offenses other than the conspiracy to kill Turner, including violations of immigration laws, conspiracy to kill Devaraj, conspiracy to intercept wire and oral communications at Rajneeshpuram, and conspiracy to commit arson. Croft and Hagan objected that the evidence was impermissible character evidence under Fed.R.Evid. 404(b), and that the evidence was more unfairly prejudicial than probative. See Fed.R.Evid. 403. The district court agreed concerning all of the offenses other than the immigration violations, and forbade the government to introduce any *1119evidence linking Croft and Hagan to those other offenses.
The court’s ruling, however, did not prevent the government from introducing other “bad acts” committed by its own witnesses, as a means of minimizing the impeaching effect if such acts were brought out on cross-examination. Those acts were legion, and included such items as poisoning and wiretapping. The witnesses displayed an unfortunate tendency to relate that they had “participated” in such acts, implying the involvement of others. Croft and Hagan argue that the implication was clearly aimed at them. Portions of the government’s final argument support their contention:
These witnesses were bad on the bottom. We know that [Croft] and [Hagan] were in the middle in terms of the hierarchy.... You are going to trust the people that are closest to you. You are going to trust people who have committed crimes for you.
*1* -fc
[Langford] was asked ... a question that went to the effect, ‘What did you do of your own accord on the ranch? Did you do on your own? You remember his answer? He says, “I run everything past the moms.” And they don’t get any bigger than Mom [Croft] and Mom [Hagan].
Croft and Hagan, however, failed to object to this argument. In addition, the district court attempted to confine the government witnesses’ bad act testimony to their own actions. There was no testimony directly attributing the disputed bad acts to Croft or Hagan. The district court also instructed the jury after each witness and in final instructions that it could not consider the crimes confessed by the government’s witnesses in determining Croft’s and Hagan’s guilt. See United States v. Charmley, 764 F.2d 675, 677 (9th Cir.1985) (“cautionary instruction is ordinarily sufficient to cure any alleged prejudice to the defendant” from inadmissible evidence). In light of the indirectness of any imputation of bad acts to Croft or Hagan, and the district court’s efforts to preclude any prejudicial effect, we conclude that it is more probable than not that any improper implied attribution of bad acts to Croft or Hagan had no effect on the jury’s verdict. See United States v. Hill, 953 F.2d 452, 458 (9th Cir.1991).
B. Perjured testimony.
Croft and Hagan argue that the government presented perjured testimony at their trial. Their argument centers on the testimony of Avalos, Langford, and Peralta, all of whom testified that John Shelter had been present at one of the meetings in which the conspirators discussed killing Turner. As Croft and Hagan point out, Shelter could not have been at any of the meetings, because, as his passport indicated, he was out of the country during the relevant period. The government, however, conceded in its final argument that the witnesses were mistaken as to the date of the meeting Shelter attended, but contended that the meeting must have occurred at another time. Shelter testified that he had been at a meeting in which the murder of a different person was discussed, but he came to the meeting late and the murder of Turner could have been discussed earlier. The government did not mislead the jury.
Hagan also refers to Langford’s testimony that Caldwell was present at the conspiracy’s formative meetings in Sheela’s bedroom. She asserts that the government allowed Langford to testify even though it knew Caldwell was not present at those meetings. This argument, too, is unconvincing. Although the government may not convict on the basis of false testimony of one of its officers, even if the prosecution offered the evidence in good faith, United States v. Young, 17 F.3d 1201, 1203-04 (9th Cir.1994), Hagan has not shown such false testimony was used here. The fact that a witness may have made an earlier inconsistent statement, or that other witnesses have conflicting recollections of events, does not establish that the testimony offered at trial was false. In addition, the district court did not err in concluding that the inconsistencies related to collateral matters. See United States v. Saadeh, 61 F.3d 510, 523 (7th Cir.1995) (perjured testimony not cause for reversal if it was not “directly related to the defendant’s guilt or innocence”). The district court did *1120not abuse its discretion in denying a new trial.
C. Polygraph evidence.
Croft attempted to introduce the expert testimony of Robert Brisentine, a polygrapher. Brisentine would have testified that a polygraph examination indicated that Croft was truthful in her denial of having participated in the conspiracy to kill Turner, and of having furnished funds for that purpose. The district court refused to allow Brisentine to testify on two independent grounds: [1] Croft’s motion to present Brisentine’s testimony was untimely; and [2] this Circuit’s per se prohibition on polygraph testimony, announced in Brown v. Darcy, 783 F.2d 1389 (9th Cir.1986), survived the Supreme Court’s decision in Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). Croft argues that the court abused its discretion3 in refusing to allow Brisentine to testify.
We do not reach the substantive merits of Croft’s argument,4 because the district court clearly acted within its discretion when it denied Croft’s motion for untimeliness. The district court concluded that, although Croft knew from the early stages of the case that polygraph evidence would be proffered, she waited until trial was under way to notice that evidence. By that time, the district court found, the government did not have a “reasonable opportunity” to have its own expert administer a test covering “substantially the same questions” — the measure identified by the one circuit court that permits the limited introduction of polygraph evidence as “essential” to safeguarding the interests of the opposing party. See United States v. Piccinonna, 885 F.2d 1529, 1536 (11th Cir. 1989).
D. Bolstering of witnesses.
Croft argues that the government improperly bolstered the testimony of Avalos by calling an FBI agent to testify that Avalos had led him to Turner’s house and that he had verified that Avalos had rented an apartment and an automobile under abases. It is permissible, however, to bolster the testimony of a witness whose credibility has been attacked in an opening statement. United States v. Santiago, 46 F.3d 885, 891 (9th Cir.1995). In this case, Croft branded Avalos as a liar in her opening statement, rhetoric that clearly opened the door to rehabilitation through bolstering evidence.
Croft also argues that the district court improperly permitted one of the government’s witnesses to testify that his mother had committed suicide. That testimony, however, was merely an integral part of the witness’s explanation of why he joined the Rajneesh community and came to participate in its illegal activities. It is not improper for the government to elicit background information from a witness. See, e.g., State v. Hussey, 521 A.2d 278, 281 (Me.1987).
VII. Cross-Examination and Confrontation Issues.
A. The conditional plea agreements.
The government’s cooperating witnesses testified pursuant to conditional plea or immunity agreements. Those agreements each contained clauses stating that the witness was to testify truthfully, that if the witness breached the agreement it became void and the government could proceed as if the agreement never existed, and that the government retained the exclusive right to determine whether the agreement had been breached.5 Croft argues that the agree*1121ments violated her Sixth Amendment right of confrontation, because they forced the government’s witnesses to testify to the government’s approved version of the “truth.”
The district court properly condemned, and said that it would not enforce, the clause granting the government the exclusive right to determine whether the agreement had been breached insofar as that exclusive right encompasses the right to determine whether the witness had told the truth. We reject, however, Croft’s contention that these agreements so bound the witnesses to the government’s version of the “truth” that effective cross-examination was precluded. The witnesses themselves did not testify to an understanding that the government was the ultimate arbiter of the truthfulness of their testimony. Moreover, defense counsel made quite clear to the jury the nature of the agreements under which the prosecution witnesses were testifying, and exploited fully the possible effects of such agreements on the testimony. The district court instructed the jury to regard the testimony with caution for that reason. There was no infringement of Croft’s right of cross-examination.
B. Restrictions on witnesses’ communication.
Prior to trial, Croft sought an order sequestering the witnesses throughout the trial or, alternatively, prohibiting them from speaking to anyone. The district court excluded witnesses from the trial but declined to sequester them or to forbid them from speaking to anyone. Relying principally on Perry v. Leeke, 488 U.S. 272, 281 n. 4, 109 S.Ct. 594, 601 n. 4, 102 L.Ed.2d 624 (1989), Croft argues that the district court erred in denying her motion.
Croft’s reliance on Perry is misplaced. Perry merely endorses the principle that a prudent trial judge should remind witnesses not to discuss their testimony with one another during the trial — a principle that does not support the much broader order that Croft sought. Moreover, Croft was free to cross-examine each witness concerning his or her discussions with others. The district court, therefore, did not err in refusing to sequester witnesses or in refusing to order the witnesses to speak to anyone.
C. Re-cross examination of Peralta.
Hagan argues that the district court erred when it refused to allow her to question Peralta concerning a false sworn statement during re-cross examination. During cross-examination, Hagan impeached Peralta through numerous prior inconsistent statements, but did not use affidavits that the government had written for Peralta to sign in connection with extradition proceedings. After redirect, however, during which the government attempted to rehabilitate Peralta by eliciting from her that she had learned the value of honesty in prison, Hagan attempted on re-cross to use the affidavits to show that Peralta was simply tailoring her testimony to please the government. The district court refused to permit Hagan’s re-cross on the ground that the information was not responsive to any new matter brought out on redirect examination, but rather involved inconsistencies that could have been and were covered on cross-examination.
“Allowing re-cross is within the sound discretion of the trial court except where new matter is elicited on redirect examination.” United States v. Baker, 10 F.Bd 1374, 1404 (9th Cir.1993). The district court was correct in ruling that the government’s re-direct examination did not elicit “new matter.” The re-direct examination made no mention of the affidavits, and the subject of Peralta’s decision to confront the reality of her conduct and to tell the truth to government officials was first broached by the government on direct examination.
VIII. The Jury Instructions.
A. The intent instruction.
Croft and Hagan were charged with conspiracy to commit murder, in violation of 18 U.S.C. §§ 1111, 1114, and 1117. The government was required to prove both that they intended to enter into the conspiratorial agreement, and that they specifically intended to effectuate the commission of the con*1122spiracy’s underlying substantive offense. United States v. United States Gypsum Co., 438 U.S. 422, 443 n. 20, 98 S.Ct. 2864, 2877 n. 20, 57 L.Ed.2d 854 (1978). Croft and Hagan asked the district court to instruct the jury that, to be guilty of conspiracy, they had specifically to intend to kill Turner with both premeditation and malice aforethought. The district court rejected their proposed instruction, and instructed the jury on intent as follows:
[T]he United States Code provides in pertinent part that murder is the unlawful killing of a human being with malice aforethought ... In order to find that either defendant is guilty of [the offense of conspiring to murder the United States Attorney], the government must prove each of the following elements beyond a reasonable doubt:
First, ... there was an agreement between two or more persons to kill then United States Attorney Charles Turner with malice aforethought.
Second, the defendant willfully became a member of the conspiracy, knowing of its objectives and specifically intending to help accomplish the murder of ... Turner.
* * * *
A person only becomes a member of an unlawful conspiracy if she willingly participates in the unlawful agreement with the intent to advance the objective of the conspiracy, even though that person may not have knowledge of all of the details of the conspiracy.
* * * *
The term “willfully” ... means to act or participate voluntarily and intentionally and with specific intent to help accomplish the murder of ... Turner.
Croft and Hagan argue that these instructions were inadequate.
Hagan first argues that the required element of malice aforethought was diluted by the court to a requirement of “intending to help accomplish the murder” of Turner. There is no such dilution, however, when the instructions are taken as a whole. The district court defined murder as “the unlawful killing of a human being with malice aforethought.” The district court stated the first element of conspiracy to require “an agreement between two or more persons to kill then United States Attorney Charles Turner with malice aforethought.” The next element required the jury, for conviction, to find that the defendant “willfully became a member of the conspiracy knowing of its objectives and specifically intended to help accomplish the murder of then United States Attorney Charles Turner.” Under this combination of instructions, the jury, in finding that Croft and Hagan specifically intended to help accomplish the murder of Turner, necessarily had to find malice aforethought; murder had been defined to include that mental state.
We also reject Croft’s and Hagan’s related argument that the district court required only the intent to join the conspiracy and the intent to help accomplish the murder of Turner, but faded to require a specific intent to murder Turner. The distinction is not a realistic one. Taken as a whole, the instructions did not permit the jury to convict without finding that Croft and Hagan shared the specific intent to murder Turner. It is not reasonable to interpret a specific intent “to help accomplish the murder of ... Turner” as an intent to help someone murder Turner without sharing that someone’s intent. Particularly is this so when the court has instructed the jury that the conspiracy was one “to kill ... Turner” and that a person joins a conspiracy if “she willfully participates in the unlawful agreement with the intent to advance the objective of the conspiracy.”
Croft argues that the crime of murder as defined by 18 U.S.C. § 1111(a) requires an element of premeditation that was omitted from the court’s instructions. Section 1111(a), however, encompasses both first- and second-degree murder. The indictment in this case included no element of premeditation; it accordingly alleged only second-degree murder as the object of the conspiracy. See United States v. Harrelson, 754 F.2d 1153,1174 (5th Cir.1985). Although our circuit has not yet addressed the question, the Fifth Circuit has held that it is logically possible to conspire to commit sec*1123ond-degree murder. United States v. Chagra, 807 F.2d 398, 401-02 (5th Cir.1986). We accept that view, and conclude that the indictment here alleged that crime.6 As a consequence, it was not error for the district court to omit the element of premeditation in its instructions.
B. The multiple-conspiracy instruction.
Hagan contends that, because a defense witness testified that some participants in the conspiracy discussed killing a person other than Turner-namely, Devaraj-she was entitled to an instruction concerning multiple conspiracies.
The district court did not err. Although a multiple-conspiracy instruction must be given even if it is only “possible” to find that two conspiracies exist, United States v. Eubanks, 591 F.2d 513, 518 (9th Cir.1979), Hagan has not satisfied even that minimal requirement. The witness’s fleeting reference to a discussion involving killing Devaraj did not indicate a separate conspiracy, and could not have implicated either Croft or Hagan as a participant in any such conspiracy, because: (1) neither was mentioned by the witness as being involved in any discussion of, much less agreeing to participate in, the conspiracy; (2) the district court expressly forbade the government to refer to the agreement to kill Devaraj; (3) and the district court clearly instructed the jury that, to convict Croft and Hagan, it had to conclude beyond a reasonable doubt that they had conspired to kill Turner. There was no foundation for a multiple-conspiracy instruction.
C. The approval-of-a-conspiracy instruction.
The district court instructed the jury that “a person does not become a member [of a conspiracy] merely by associating with one or more persons who are conspirators, knowing of the existence of the conspiracy, being present where a crime takes place or is discussed, or having knowledge of criminal conduct.” Hagan argues that the district court erred in refusing also to instruct that “approval” of a conspiracy is insufficient to permit conviction. See United States v. Abayomi, 820 F.2d 902, 906 (7th Cir.1987) (evidence of mere approval of conspiracy would be insufficient for conviction).
The district court was under no obligation to accept Hagan’s proposed instruction because the given instructions, taken as a whole, correctly stated the law. See, e.g., Estelle v. McGuire, 502 U.S. 62, 72, 112 S.Ct. 475, 481, 116 L.Ed.2d 385 (1991). The court’s instruction quoted above was amplified by its instruction that “[a] person only becomes a member of an unlawful conspiracy if she willfully participates in the unlawful agreement with the intent to advance the objective of the conspiracy....” Under the instructions taken in their entirety, the jury was not permitted to convict Hagan on a theory that she merely “approved” of the conspiracy.
D.The modified Allen charge.
Hagan argues that the district court erred in giving the jury a modified Allen charge. We uphold a district court’s decision to give an Allen charge “unless it is clear from the record that the charge had an impermissibly coercive effect on the jury.” United States v. Easter, 66 F.3d 1018, 1023 (9th Cir.1995), cert. denied — U.S.-, 116 S.Ct. 1026, 134 L.Ed.2d 104 (1996). In the present case, we conclude that there was no coercive effect.
Late in its first day of deliberations, the jury submitted a note to the district court stating that “[a]t this point we are divided and worn out with discussion.” The district court declined to comment. Shortly after 2:00 p.m. the next day, the jury submitted a note stating that it had reached a verdict as to one defendant but was deadlocked as to the other. The district court then read to the jury the following instruction:
*1124[I]t is your duty as jurors to consult with one another and to deliberate with the view of reaching an agreement.... Now, in the course of those deliberations do not hesitate to reexamine your own views and change your opinion if you are convinced that it was erroneous. You need not of course surrender your honest conviction ... solely because of the opinion of fellow jurors or for the purpose of reaching a verdict. But keep in mind that you are here for the purpose of giving your best efforts to returning a verdict. And that in order to do so it may very well be necessary to carefully listen to the views of your fellow jurors.
The jury returned its verdict at 1:30 p.m. the following day.
This modified Allen charge was not imper-missibly coercive. The instruction was balanced, making clear that no juror should surrender his or her honest convictions solely in order to reach a verdict. See United States v. Ajiboye, 961 F.2d 892, 894 (9th Cir.1992). The trial court made no numerical inquiry concerning, the division among the jurors, and thus did not put undue pressure on holdout jurors or indicate disapproval or approval of any particular outcome in the trial. See id.. Finally, the jury did not immediately return a verdict but continued to deliberate for almost an entire day. See Id.. Thus, it is certainly not “clear from the record that the charge had an impermissibly coercive effect on the jury.” Easter, 66 F.3d at 1023.
IX. Discovery issues.
A.Witness interviews.
Croft and Hagan argue that the district court erred in refusing their request for the government’s notes concerning the dates and content of meetings between government agents and the government’s cooperating witnesses. Those notes, they argue, would have been useful to impeach the witnesses and to assist in an attack on the integrity of the investigation or “the process by which the [government] gathered evidence and assembled the case.” Kyles v. Whitley, 514 U.S. 419, 449 n. 19, 115 S.Ct. 1555,1573 n. 19, 131 L.Ed.2d 490 (1995).
Croft and Hagan’s arguments are speculative. They have not shown grounds for relief under Brady: that “there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 3383, 87 L.Ed.2d 481 (1985). The district court ordered broad discovery, exempting only information that was “obviously not Brady or Jencks material.” The government turned over 8,000 to 10,000 pages of Jencks materials to Hagan, and both Hagan and Croft impeached government witnesses with their prior inconsistent statements numerous times throughout the trial. “The mere possibility that an item of undisclosed information might have helped the defense, or might have affected the outcome of the trial, does not establish ‘materiality’ in the constitutional sense.” United States v. Agurs, 427 U.S. 97, 109-110, 96 S.Ct. 2392, 2400-01, 49 L.Ed.2d 342 (1976). We find no abuse of discretion.
B. Psychological and psychiatric records.
Croft argues that the district court erred in refusing her request for information regarding the psychological or psychiatric condition of the government’s witnesses. Croft has not shown, however, that “there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Bagley, 473 U.S. at 682,105 S.Ct. at 3383. Croft’s only mention of how such information would be helpful concerns witness Caldwell, who had suffered complete memory loss for three years prior to “remembering” that Croft had given Stork the money to purchase guns. Croft was able to elicit that fact on cross-examination. Caldwell’s testimony, moreover, was merely cumulative to the testimony of a number of the government’s other witnesses.
C. Interview with Turner.
[33] Hagan argues that the district court erred in refusing to allow her to interview Turner regarding a letter he sent to one of *1125the prosecutors in which he stated that he anticipated allegations would be made that he “gin[ned] up the case which, otherwise, would not have been prosecuted citing, inter alia, FBI efforts to Mil it.” Hagan has not shown, however, that “there is a reasonable likelihood that the testimony could have affected the judgment of the trier of fact,” United States v. Valenzuela-Bernal, 458 U.S. 858, 874, 102 S.Ct. 3440, 3449, 73 L.Ed.2d 1193 (1982). The district court allowed Hagan to interview Mr. Turner concerning any area other than “ongoing investigations.”
D. Request for investigative funds.
Croft argues that the district court abused its discretion7 in denying her ex parte motion for funds to investigate government witnesses. There was no abuse of discretion. Croft did not show that the lack of extra funds unduly hampered her defense or denied her effective assistance of counsel under the Sixth Amendment. See United States v. Smith, 893 F.2d 1573, 1580 (9th Cir.1990). The district court granted many of Croft’s requests for investigative funds, and, as Croft concedes, the government turned over “voluminous” Jencks materials to Croft and Hagan, enabling them fully to test the credibility of the government’s witnesses at trial.
E. Evidentiary hearing.
We reject Hagan’s assertion that she should have been granted an evidentiary hearing into alleged discovery abuses. She has not furnished reasonable ground to believe that any discoverable material has been withheld.
X. Sufficiency of the evidence.
Finally, we reject Hagan’s contention that the evidence against her was insufficient to support her conviction. On reviewing sufficiency of the evidence, “the relevant question is whether, after viewing the evi-denee in the light most favorable to the government, 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, 2788, 61 L.Ed.2d 560 (1979). Here, three government witnesses testified that, after Sheela proposed murdering Turner, Hagan made statements calculated to induce the other commune members to support the scheme. Moreover, witnesses testified that Hagan later took a count of who was “in or out” of the scheme, became a member of the “hit team,” and mediated a dispute concerning who would be the one to pull the trigger. None of that testimony is “so inconsistent or improbable on its face that no reasonable fact finder could accept it,” nor does that testimony violate the laws of nature. See United States v. Ramos-Rascon, 8 F.3d 704, 709 n. 3 (9th Cir.1993). Because we are powerless to question a jury’s assessment of witnesses’ credibility, Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942), that testimony is sufficient to sustain Ha-gan’s conviction.
CONCLUSION
We have reviewed all remaining contentions of Croft and Hagan and find them to be without merit. The judgment of the district court with regard to both Croft and Hagan is affirmed in its entirety.
AFFIRMED.
. Croft and Hagan dispute many of these facts, but we accept the prosecution’s version in light of the jury’s verdict. See Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2788, 61 L.Ed.2d 560 (1979).
. We review a district court’s denial of a change-of-venue motion only for "clear abuse of discretion.” United States v. Dischner, 974 F.2d 1502, 1523 (9th Cir.1992).
. We review for abuse of discretion a district court’s decision to exclude expert testimony under Fed.R.Evid. 403. See Daubert v. Merrell Dow Pharmaceuticals, Inc., 43 F.3d 1311, 1315 (9th Cir.), cert. denied, -U.S. -, 116 S.Ct. 189, 133 L.Ed.2d 126 (1995).
. We have recently held that the Supreme Court’s decision in Daubert did overrule Brown's per se prohibition against unstipulated polygraph evidence. United States v. Cordoba, 104 F.3d 225, 227-28 (9th Cir.1997). We left admission of such evidence to the discretion of the trial judge under Fed.R.Evid. §§ 702 and 403, after observing that such evidence "has grave potential for interfering with the deliberative process.” Id. at 228.
.The agreements of Avalos and Knapp stated that the government retained the exclusive right to make the “initial ” determination whether the agreement had been breached. The remainder *1121of the agreements, however, did not contain the word "initial.”
. By stating that it is possible to commit the crime of conspiracy to commit second-degree murder, we do not mean to imply that a grand jury is without power to allege a lesser offense than the facts logically support. The latter proposition has not been argued to us, and we do not decide the issue.
. We review for abuse of discretion a district court’s decision to deny funds for an investigator. United States v. Smith, 893 F.2d 1573, 1580 (9th Cir.1990).