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PER CURIAM: Following a lengthy jury trial in the United States District Court for the Southern District of New York (Duffy, /.), defendants were convicted of various crimes related to the bombing of the World Trade Center Complex in New York City. Defendants now appeal, asserting a congeries of arguments. For the reasons that follow, we affirm the judgment of the district court but remand for re-sentencing and decline to exercise jurisdiction over certain post-trial motions pending before the district court. TABLE OF CONTENTS Background.■.107 I. Suppression Motions.108 A. Motions to Suppress Materials Seized From Ajaj .108 (1) Ajaj’s Motion.108 (2) Abouhalima s Motion. r — 4 i — 4 (a) Rule 403 . i — 4 t — 4 (b) First Amendment. i — 4 i — 4 (3) Ayyad’s Motion. i — 4 i — 4 B. Motion to Suppress Contents of the Storage Shed i — l r — 4 (1) Probablese. r-4 r — t (2) Franks Hearing. r — t i — 4 (3) Good Faith Reliance... i — 4 i — I II. Procedural Motions.114 A. Abouhalima — Severance.114 (1) Ajaj’s Holy War Materials.115 (2) Salameh’s Summation.116 B. Abouhalima — Involuntariness of Statement .117 C. Ayyad — Failure to Grant Funds for Experts.118 D. Ajaj — Eastern District Plea Agreement .118 III. Jury Selection.120 IV. Evidentiary Rulings.122 A. Admission of Evidence Regarding Bombing Victims.122 (1) Probative Value.122 (2) Danger of Unfair Prejudice.123 B. Admission of Evidence Regarding Nosair.123 (1) Photographs of Salameh and Nosair.123 (2) Admission of Abouhalima’s Contacts with Nosair.124 C. Admission of Identification.124 (1) Use of Photo Array.125 (2) Subsequent In-Court Identifications.126 D. Examination of Storage Facility Employee.127 (1) Leading Questions.127 (2) Comments Regarding Meeting.128 E. Testimony of the Government’s Fingerprint Expert.128 F. Admission of DNA Evidence.129 G. Confrontation Clause.130 (1) Moneeb.131 (2) Butler.131 (3) Moharam.132 H. Requested Read-back of Testimony.132 V. Jury Arguments.133 A. Prosecutorial Misconduct as to Abouhalima.134 (1) Government Misrepresentations.134 (a) Witnesses.134 (b) Affiliation With Yousef.134 (c) Inexplicable Nervousness.134 (2) Jury Fear.134 (3) Government Vouching .135 (4) Burden of Proof.136 B. Prosecutorial Misconduct as to Ajaj.137 (1) Government’s Improper Arguments .137 (2) Attacks on the Defense .138 (3) Change in Summation Theory.139 VI. Jury Charge .140 A. The Bully Hypothetical.140 B. Abouhalima — Terrorist Materials.144 C. Elements of the Charged Conspiracy.145 D. Ajaj’s Objection to the Jury Charge.147 (1) Essential Nature of Plan.147 (2) Inclusion of the Pinkerton Charge.148 (3) Failure to Charge on Withdrawal Sua Sponte o VII. Sufficiency of the Evidence. 1 — 1 LO i — t A. Standard of Review ... 1 — 1 LO tH B. Ajaj. T — 1 LO r — ( C. Abouhalima. hQ LO i — 1 VIII. Unfair Trial — Due Process Cn -3 IX. Post-Trial Motions. H-L Cn OO A. New Trial (Ajaj). I — l Cn OO B. Ineffective Assistance of Counsel I — l Oí o X. Sentencing. Conclusion BACKGROUND On April 24,1992, Ahmad Mohammad Ajaj departed from his home in Houston, Texas, and traveled to the Middle East to attend a terrorist training camp, known as “Camp Khaldan,” on the Afghanistan-Pakistan border. There he learned how to construct homemade explosive devices. During his time in Pakistan, Ajaj met Ramzi Ahmed Yousef. Together the two plotted to use their newly acquired skills to bomb targets in the United States. In the fall of 1992, after formulating a terrorist plan, Ajaj and Yousef traveled to New York under assumed names. Ajaj carried with him a “terrorist kit” that he and Yousef had assembled in Pakistan. The Mt included, among other things, handwritten notes Ajaj had taken while attending explosives courses, manuals containing formulae and instructions for manufacturing bombs, materials describing how to carry-off a successful terrorist operation, videotapes advocating terrorist action against the United States, and fraudulent identification documents. On September 1, 1992, Ajaj and Yousef, using false names and passports, arrived at John F. Kennedy International Airport in New York. At customs, INS inspectors discovered that Ajaj’s passport had been altered and, consequently, they searched his belongings. Upon discovery of the “terrorist kit,” Ajaj became belligerent. The INS seized Ajaj’s “terrorist kit” and placed him under arrest. Ajaj was later indicted in the United States District Court for the Eastern District of New York for passport fraud. He pled guilty and was sentenced to six months’ imprisonment. During Ajaj’s encounter with the INS inspectors, he denied that he was traveling with Yousef, who proceeded unmolested to the secondary inspection area where he presented an Iraqi passport and claimed political asylum. Yousef was arrested for entering the United States without a visa. Eventually he was released on his own recognizance. Once in New York, Yousef assembled a team of trusted criminal associates, including Mohammed Salameh, Nidal Ayyad, Mah-moud Abouhalima and Abdul Rahman Yasin. Together, the conspirators implemented the bombing plot that Ajaj and Yousef had hatched overseas. Ayyad and Salameh opened a joint bank account into which they deposited funds to finance the bombing plot. Some of that money was later used by Sala-meh to rent a storage shed in Jersey City, New Jersey, where the conspirators stored chemicals for making explosives. Yousef also drew on that account to pay for materials described in Ajaj’s manuals as ingredients for bomb making. The first target of the conspirators’ plot was the World Trade Center. Ayyad used his position as an engineer at Allied Signal, a large New Jersey chemical company, to order the necessary chemical ingredients for bomb making, and to order hydrogen tanks from ALG Welding Company that would enhance the bomb’s destructive force. Abouha-lima obtained “smokeless powder,” which the conspirators used to make explosives. Smokeless powder, and all the other chemicals procured by the conspirators for the bomb, were stored in the shed rented by Salameh. Abouhalima helped Salameh and Yousef find a ground floor apartment at 40 Pamrapo Avenue in Jersey City. The apartment fit the specifications in Ajaj’s manuals for an ideal base of operations. In the 40 Pamrapo apartment, Abouhalima, Salameh, Yousef and Yasin mixed the chemicals for the World Trade Center bomb, following Ajaj’s formu-lae. Abouhalima also obtained a telephone calling card, which the conspirators used to contact each other and to call various chemical companies for bomb ingredients. During this entire period, although Ajaj remained incarcerated, he kept in telephone contact with Yousef. By doing so, Ajaj stayed abreast of the conspirators’ progress in carrying out the terrorist plot and attempted to get his “terrorist kit” into You-sefs hands. Because Ajaj was in jail and his telephone calls were monitored, Ajaj and Yousef spoke in code when discussing the bomb plot. On February 23, 1993, Salameh rented a yellow van at DIB Leasing, a Ryder dealership in Jersey City. The conspirators loaded their homemade bomb into that van. On February 26, 1993, the conspirators drove the bomb-laden van into a below-ground parking lot on the B-2 level of the World Trade Center Complex and, using a timer, set the bomb to detonate. At 12:18 p.m., the bomb exploded, killing six people, injuring over a thousand others, and causing hundreds of millions of dollars in damage. After the explosion, Ayyad took credit for the bombing on behalf of the conspirators by, among other things, writing an anonymous letter to the New York Times explaining that the attack was undertaken in retaliation for American support of Israel. The letter threatened future terrorist “missions.” Immediately after the bombing, Yousef, Abouhalima and Yasin fled the country. Abouhalima was apprehended in Egypt prior to the trial and turned over to federal agents by Egyptian authorities, but Yousef and Ya-sin remained fugitives. Salameh arranged to flee as well, but was arrested the day before he planned to depart when he made the ludicrous mistake of going back to the Ryder truck rental office to get his rental deposit back. On March 1, 1993, Ajaj completed his term of imprisonment on the passport fraud conviction and was released. Approximately one week later, on March 9, Ajaj was taken into government custody on an INS detainer. In September 1993, Ayyad, Abouhalima, Ajaj, Salameh, Yousef and Yasin were indicted in the United States District Court for the Southern District of New York (Duffy, /.), on various charges relating to their participation in the plot to bomb the World Trade Center. Yousef and Yasin were still fugitives at the time of trial. The trial lasted six months and involved over 1000 exhibits and the testimony of more than 200 witnesses. The defendants were convicted on all counts and each was sentenced to 240 years’ imprisonment. Defendants now appeal their convictions and sentences, raising a variety of issues. I. SUPPRESSION MOTIONS A. Motions to Suppress Materials Seized from Ajaj 1. Ajaj’s Motion Ajaj claims that Judge Duffy should have suppressed the terrorist materials seized from him at Kennedy Airport. He maintains that the materials were obtained and then held pursuant to an illegal grand jury subpoena. Ajaj’s argument has no merit. On October 6, 1992, Ajaj pled guilty in the United States District Court for the Eastern District of New York (Raggi, J.) to one count of passport fraud. After the guilty plea, Judge Raggi ordered the government to return Ajaj’s belongings or to come forward with a reason for failing to do so. On December 22, 1992, an Assistant United States Attorney for the Eastern District of New York served a grand jury subpoena on Ajaj calling for production of many of the terrorist materials seized at Kennedy Airport. Although the subpoena purported to be a subpoena ad testificandum, it was accompanied by a duces tecum rider that specified the materials Ajaj was ordered to produce. When Ajaj’s counsel in the passport fraud case inquired whether the subpoena really sought Ajaj’s testimony as well as the evidence listed in the rider, the government explained that the subpoena sought only the specified evidence. Ajaj did not move to quash the subpoena. After Ajaj learned that the government was planning to introduce the terrorist materials in the World Trade Center bombing trial, he moved to suppress the materials held pursuant to the grand jury subpoena. Ajaj argued that the subpoena was illegal since: (1) Ajaj could not have been under investigation when the subpoena was issued because it was issued after the completion of the passport fraud case but before the World Trade Center was bombed; and (2) the subpoena was a subpoena ad testificandum, not a subpoena duces tecum. Judge Duffy denied Ajaj’s motion to suppress, finding that the use of the subpoena was proper. Ajaj renews his claim on appeal, It is “improper for the government to use a grand jury subpoena ‘for the sole or dominant purpose of preparing for trial.’” United States v. Sasso, 59 F.3d 341, 351 (2d Cir.1995) (quoting United States v. Leung, 40 F.3d 577, 581 (2d. Cir.1994)). However, “[w]here there [is] some proper dominant purpose for the postindictment subpoena ... the government is not barred from introducing evidence obtained thereby.” Id. at 351-52. A grand jury subpoena is presumed to have a proper purpose, and the defendant bears the burden of showing that the grand jury has exceeded its legal powers. See United States v. R. Enterprises, Inc., 498 U.S. 292, 300-01, 111 S.Ct. 722, 112 L.Ed.2d 795 (1991). A defendant must present “particularized proof’ of an improper purpose to overcome the presumption of propriety of the grand jury subpoena. See United States v. Mechanik, 475 U.S. 66, 75, 106 S.Ct. 938, 89 L.Ed.2d 50 (1986). Ajaj failed to present any proof that the government misused the grand jury subpoena. He maintains that the subpoena had no legitimate purpose because in December 1992, when the subpoena was issued, his passport fraud prosecution was over and the World Trade Center had not yet been bombed. He therefore posits that he could not have been under investigation when the subpoena was issued and therefore that the sole purpose of the subpoena was to circumvent Judge Raggi’s order for the return of the materials. The government presented evidence that demonstrated a proper purpose for the grand jury subpoena. It consisted primarily of an affidavit from the Assistant United States Attorney who prepared the subpoena, explaining that the materials seized from Ajaj were used in a joint FBI-NYPD investigation of terrorism. The affidavit further noted that the subpoena was not connected to the Eastern District passport fraud case. This evidence established that the subpoena had a proper purpose. See Sasso, 59 F.3d at 352. While the government should not have ignored Judge Raggi’s' order to return Ajaj’s belongings or to explain its reasons for failing to do so, any relief that Ajaj was entitled to seek would have been some sort of remedial order directed to the entity that violated Judge Raggi’s order — the United States Attorney’s Office for the Eastern District of New York. Ajaj did not seek such an order. The subsequent grand jury proceeding in the Southern District of New York was a wholly independent investigation into terrorist activity. Such an investigation was clearly within the province of the Southern District grand jury. See, e.g, Branzburg v. Hayes, 408 U.S. 665, 668, 92 S.Ct. 2646, 33 L.Ed.2d 626 (1972) (grand jury can investigate “ ‘merely on sus-pieion that the law is being violated, or even because it wants to assure that is not’ ” (citation omitted)). With respect to the Southern District investigation, Ajaj has not met his burden of showing that the government’s use of the grand jury was improper. Accordingly, he has not overcome the presumption of regularity applicable to grand jury proceedings. See Leung, 40 F.3d at 581. Ajaj also argues that the subpoena was somehow illegal because it purported to be a subpoena ad testificandum when it actually was a subpoena duces tecum. Ajaj fails to explain why the subpoena was invalid because of this technical error. A subpoena ad testificandum may order a person to bring objects with him for the use of the grand jury. See 2 Charles Alan Wright, Federal Practice and Procedure § 274, at 150 (2d ed.1982). On its face, the subpoena issued to Ajaj appeared to request both his presence and the production of physical evidence. Although it turned out that Ajaj’s testimony was superfluous, the subpoena was not improper because the grand jury requested production of Ajaj personally in addition to the terrorist materials. See id. at 151. Moreover, Ajaj suffered no prejudice as a result of the mischaracterization of the subpoena. The rider made it clear that the subpoena sought the terrorist materials Ajaj brought into the United States. Moreover, when Ajaj’s counsel inquired whether the subpoena sought testimony from Ajaj, the government explained that it did not. Thus, the government’s inadvertence did not prejudice Ajaj, and was not grounds to suppress the evidence held pursuant to the subpoena. 2. Abouhalima’s Motion Judge Duffy admitted some of the materials seized from Ajaj into evidence against all the defendants. Abouhalima argues that the admission of Ajaj’s terrorist materials violated Federal Rule of Evidence 403, and his rights under the First Amendment of the Constitution. a. Rule 403 The trial judge admitted the following terrorist materials seized from Ajaj into evidence against all the defendants: (1) a videotape of the bombing of an American embassy which also provided instruction on how to make explosives and timing devices; (2) Ajaj’s handwritten notebooks on how to make explosives (including urea nitrate) and improvised weapons; (3) a videotape containing a chemistry lesson on manufacturing explosives; (4) manuals on catalysts, detonators and other bomb ingredients; (5) a document entitled “Facing the enemies of God terrorism is a religious duty and force is necessary,” which urged acts of terrorism against the enemies of Islam; and (6) a book entitled “Rapid Destruction and Demolition,” which described the destruction of buildings and contained a formula for using explosives to accomplish this end. In addition, Judge Duffy admitted copies of: (1) “Facing the enemies of God”; and (2) “Rapid Destruction and Demolition” that were recovered from Abouhalima’s residence. The copy of “Rapid Destruction and Demolition” found in Abouhalima’s residence bore his fingerprint on the page containing the formula for destroying buildings with explosives. Abouhalima argues that Judge Duffy should not have admitted these terrorist materials because they were highly prejudicial and lacked probative value. He is incorrect. Under Rule 403, relevant evidence may be excluded when its probative value is “substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence.” Fed. R.Evid. 403. A district court is obviously in the best position to do the balancing mandated by Rule 403. See, e.g., United States v. Birney, 686 F.2d 102, 106 (2d Cir.1982). We will second-guess a district court “only if there is a clear showing that the court abused its discretion or acted arbitrarily or irrationally.” United States v. Valdez, 16 F.3d 1324, 1332 (2d Cir.1994). To avoid acting arbitrarily, the district court must make a “conscientious assessment” of whether unfair prejudice substantially outweighs probative value. Birney, 686 F.2d at 106. Although it does not bear directly on the charged elements of a crime, evidence offered to prove motive is commonly admitted. See id. at 106-07. In addition, evidence that provides background information necessary to the jury’s understanding of the nature of the conspiratorial agreement properly is admitted “to furnish an explanation of the understanding or intent with which certain acts were performed.” United States v. Daly, 842 F.2d 1380, 1388 (2d Cir.1988). Where a defendant is a member of a conspiracy, all the evidence admitted to prove that conspiracy, even evidence relating to acts committed by co-defendants, is admissible against the defendant. See, e.g., United States v. Cunningham, 723 F.2d 217, 230 (2d Cir.1983). The record amply demonstrates that Judge Duffy made a “conscientious assessment” of the proffered evidence and properly determined that unfair prejudice did not substantially outweigh the probative value of these materials. See Birney, 686 F.2d at 106. Before admitting any materials, Judge Duffy scrupulously reviewed each item and heard extensive argument from counsel. Having heard both sides, Judge Duffy excluded a number of the materials seized from Ajaj as unduly prejudicial. The materials that were admitted established the existence of the conspiracy to bomb American targets and demonstrated the defendants’ intent and motivation to use violence to protest American foreign policy in the Middle East. For example, the documents seized from Ajaj provided instruction on: (1) constructing bombs; (2) mixing explosives; and (3) using bombs to destroy buildings. Specific pages of these materials contained formulae for the same explosives that were used to construct the World Trade Center bomb, and Ajaj’s and Yousefs fingerprints were found on those pages. Moreover, traces of those same explosives were found in the homes of, and on objects linked to, Yousef, Abouhalima, Salameh and Ayyad. Thus, the terrorist materials provided circumstantial proof of a connection among the conspirators and then-familiarity with bomb' making and the use of explosives. In addition, the copies of “Facing the enemies of God,” and “Rapid Destruction and Demolition,” that were recovered from Abo-uhalima’s residence linked the conspirators. The copy of “Rapid Destruction and Demolition” seized from Abouhalima bore his fingerprint on the page containing the formula for destroying buildings with explosives. Under the circumstances, the fact that Ajaj and Abouhalima both possessed the same documents was probative of their relationship as co-conspirators. The materials possessed by both Ajaj and Abouhalima bristled with strong anti-American sentiment and advocated violence against targets in the United States. These same themes were expressed in a letter attributed to another co-conspirator, Ayyad, that was sent to the New York Times in the aftermath of the bombing. The materials, in addition to establishing a link between the co-conspirators, evidenced the conspiracy’s motive and intent to bomb targets in the United States. In addition, the materials provided the jury with background and “an explanation of the understanding or intent with which certain acts were performed.” Daly, 842 F.2d at 1388. Furthermore, the materials had probative value in light of their similarity to the actual bombing. As Judge Duffy recognized, one videotape admitted in evidence showed a man driving a truck into a building that was flying an American flag. The building was then demolished in an explosion. The videotape thus closely resembled the actual events at the World Trade Center and provided further evidence of motive and intent. The sulphurous anti-American sentiments expressed in the terrorist materials no doubt threatened to prejudice the jury against the defendants. However, Judge Duffy did not abuse his discretion by concluding that the significant probative value of this evidence was not substantially outweighed by the danger of unfair prejudice. b. First Amendment Abouhalima argues also that the admission of Ajaj’s terrorist materials violated Abouhalima’s First Amendment rights. Ajaj’s possession of the terrorist materials, Abouhalima contends, was used as the basis for an inference that Abouhalima and the other conspirators engaged in criminal acts. It is difficult to comprehend this argument since it is beyond cavil that “[t]he First Amendment ■... does not prohibit the evi-dentiary use of speech to establish the elements of a crime or to prove motive or intent.” Wisconsin v. Mitchell, 508 U.S. 476, 489, 113 S.Ct. 2194, 124 L.Ed.2d 436 (1993). Neither Ajaj nor Abouhalima was prosecuted for possessing or reading terrorist materials. The materials seized from Ajaj were used appropriately to prove the existence of the bombing conspiracy and its motive. Moreover, any prejudicial effect they might have had was ameliorated by the trial court’s instruction that mere possession of the literature is not illegal and that the defendants’ political beliefs were not on trial. 3. Ayyad’s Motion Ayyad argues that admission of Ajaj’s terrorist materials violated Federal Rule of Evidence 801(d)(2)(E). This claim is meritless because the materials were admissible for a non-hearsay purpose. Federal Rule of Evidence 801(c) defines hearsay as “a statement, other than one made by the declarant while testifying at the trial or hearing, offered in evidence to prove the truth of the matter asserted.” Rule 801(d)(2)(E) provides that, notwithstanding the definition in Rule 801(e), “a statement by a coconspirator of a party during the course and in furtherance of the conspiracy,” is equally not hearsay. Obviously, if the proffered evidence is not hearsay in the first place, under Rule 801(c), the various requirements of Rule 801(d)(2)(E) need not be met. See Anderson v. United States, 417 U.S. 211, 219, 94 S.Ct. 2253, 41 L.Ed.2d 20 (1974). The terrorist materials seized from Ajaj discussed two issues: (1) the desirability of attacking enemies of Islam; and (2) how to produce and use explosives. However, the government introduced this evidence to prove the state of mind of those who harbored these materials, relevant to prove: (1) the existence of the bombing conspiracy; and (2) the conspirator’s intent and motives. See Tr. 7320-21. “Where, as here, the statement is offered as circumstantial evidence of [a defendant’s] state of mind, it does not fall within the definition given by Rule 801(c); because it was- not offered to prove the truth of the matter asserted.” United States v. Detrich, 865 F.2d 17, 21 (2d Cir.1988); see United States v. Pedroza, 750 F.2d 187, 200 (2d Cir.1984). As proof of defendants’ state of mind, Ajaj’s terrorist materials were not hearsay under Rule 801(c), and their failure to come within Rule 801(d)(2)(E) is of no consequence. See Anderson, 417 U.S. at 219, 94 S.Ct. 2253. B. Motion to Suppress Contents of the Storage Shed At trial, the government introduced homemade nitroglycerine and large quantities of bomb making ingredients seized from a storage shed (the “Shed”), at the Space Station storage facility in Jersey City (the “Space Station”). Salameh argues that Judge Duffy should have suppressed this evidence. Sala-meh is wrong. On March 5, 1993, a Magistrate Judge in the District of New Jersey issued a search warrant for the Shed. Probable cause for the warrant was based upon an affidavit of FBI Special Agent Eric Pilker. Before trial, Salameh moved to suppress the evidence from the Shed on the ground that Pilker’s affidavit did not establish probable cause for the search. Salameh also requested a hearing to test alleged misstatements in Pilker’s affidavit. Judge Duffy denied the motion to suppress as well as the requested hearing, finding that: (1) Salameh. lacked standing to contest the search; (2) there was probable cause for the search warrant; and (3) even if the warrant was not supported by probable cause, the search was proper because it was conducted in good faith reliance on the search warrant. Because we agree that there was both probable cause and good faith, we need not and do not address the standing argument. 1. Probable Cause. In deciding whether probable cause exists for a search warrant, a judge must determine whether “there is a fair probability that contraband or evidence of a crime will be found in a particular place.” Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983). “[0]nly the probability, and not the prima facie showing, of criminal activity is the standard of probable cause.” Id. at 235, 103 S.Ct. 2317 (internal quotation marks and citation omitted). In assessing the proof of probable cause, the government’s affidavit in support of the search warrant must be read as a whole, and construed realistically. See id. at 230-31, 103 S.Ct. 2317. We accord “great deference” to a judge’s determination that probable cause exists, and we resolve any doubt about the existence of probable cause in favor of upholding the warrant. See United States v. Jakobetz, 955 F.2d 786, 803 (2d Cir.1992). Our duty is “simply to ensure that the magistrate had a ‘substantial basis for ... concluding]’ that probable cause existed.” Gates, 462 U.S. at 238-39, 103 S.Ct. 2317 (citation omitted; alterations in original). Pilker’s affidavit in support of the search warrant stated that an explosion had occurred at the World Trade Center, and that an FBI explosives expert had determined that it was caused by a bomb. The affidavit also related that the expert knew from examining an auto part recovered at the crime scene that the part belonged to whatever vehicle carried the bomb. Using the part’s vehicle identification number, investigators traced it to a yellow Ford Econoline 350 van registered in Alabama to the Ryder Truck Rental Company and leased by Mohammad Salameh from a rental office in Jersey City for a one-week period beginning three days before the explosion. Elsewhere in the affidavit, Pilker related that a Space Station employee informed the FBI that storage shed number 4344 was under lease to “Kamil Ibrahim.” The employee told the FBI that on February 25, 1993, one day before the bombing, he observed “Kamil Ibrahim,” along with other males, making numerous trips to the Shed using a yellow Ryder van. Moreover, the same Space Station employee stated that on March 4, 1993, less than one week after the bombing, he entered the Shed and observed containers marked “sulfuric acid,” “nitric acid” and “urea.” A forensic chemist at the Bureau of Alcohol, Tobacco and Firearms informed the FBI that those three substances could be combined to produce a powerful bomb. Finally, the affidavit described that, when renting the Ryder van, Salameh had given a telephone number that belonged to someone named Jodie Hadas at 34 Kensington Avenue, Apt. 4, in Jersey City. When investigators searched that apartment on March 4, 1993, they found tools, wiring and manuals concerning antennae, circuitry and electromagnetic devices. A law enforcement bomb technician advised the FBI that these items indicated that a bomb maker lived in that apartment. Cumulatively, this evidence provided ample probable cause to believe that the Shed contained evidence of the World Trade Center bombing. 2. Franks Hearing Salameh argues that Pilker’s affidavit contained recklessly false statements regarding the alleged evidence of bomb making discovered at the Kensington Avenue apartment. Salameh asserts that Judge Duffy should have granted him a hearing under Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), to test the accuracy of Pilker’s claims. To be entitled to a Franks hearing, a defendant must make a “substantial preliminary showing” that: (1) the claimed inaccuracies or omissions are the result of the affiant’s deliberate falsehood or reckless disregard for the truth; and (2) the alleged falsehoods or omissions were necessary to the judge’s probable cause finding. See United States v. Levasseur, 816 F.2d 37, 43 (2d Cir.1987). If, after setting aside the allegedly misleading statements or omissions, the affidavit, nonetheless, presents sufficient information to support a finding of probable cause, the district court need not conduct a Franks hearing. See id. In his affidavit, Pilker related that the Kensington Avenue apartment contained evidence of a bomb maker. Salameh maintains that this statement was false, and that Pilker was reckless in including it in his affidavit. In support of his claim of recklessness, Salameh proffered the affidavit of Musab Yasin, an electrical engineering professor who claimed to reside in the Kensington Avenue apartment. Yasin averred that the materials discovered by the government were used in his electrical engineering studies. He also said that he informed Pilker of this fact on two separate occasions, but Pilker failed to include Yasin’s benign explanation of the materials in the affidavit in support of the search warrant. The district judge did not err in denying Salameh a Franks hearing because the allegedly false statements in Pilker’s affidavit were not necessary for a finding of probable cause. See United States v. Trzaska, 111 F.3d 1019, 1027-28 (2d Cir.1997). As detailed above, there was a wealth of evidence presented in Pilker’s affidavit which raised a reasonable probability that the Shed contained evidence of the World Trade Center bombing. Disregarding the allegedly false statements in Pilker’s affidavit, the other evidence presented by the government amply supported a finding of probable cause. See United States v. Marin-Buitrago, 734 F.2d 889, 895 (2d Cir.1984). 3. Good Faith Reliance Even assuming, ' arguendo, that probable cause was lacking for the issuance of the search warrant, Judge Duffy properly declined to suppress the evidence discovered in the Shed because the search of the Shed was conducted in good faith reliance on the search warrant. If a reviewing court determines that a search warrant was not supported by probable cause, a motion to suppress will still be denied if the court finds that the officers Who conducted the search acted in good faith reliance'' on a facially valid warrant. See United States v. Leon, 468 U.S. 897, 918-23, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984). An officer’s reliance on a warrant is not in good faith when the application supporting the warrant is “ ‘so lacking in indicia of probable cause as to render official belief in [the existence of probable cause] entirely unreasonable.’ ” Id. at 923, 104 S.Ct. 3405 (quoting Brown v. Illinois, 422 U.S. 590, 610-11, 95 S.Ct. 2254, 45 L.Ed.2d 416 (1975) (Powell, J., concurring in part)). For the reasons explained above, the application for the warrant presented ample indi-cia of probable cause. Thus, the agents’ reliance on the warrant in conducting the search of the Shed was reasonable and in good faith. II. PROCEDURAL MOTIONS A. Abouhalima—Severance Abouhalima argues that the district court deprived him of a constitutionally fair trial by denying his pretrial motion for a severance. Specifically, Abouhalima first claims that absent severance, he was harmed by the admission and the subsequent “spillover” effect of “holy war” literature and video tapes that were seized from Ajaj at Kennedy Airport in September 1992. These materials included (1) a videotape of the bombing of the American Embassy, which contained instructions regarding how to make explosives and timing devices and how to construct a bomb; (2) Ajaj’s manuals, detailing how to prepare explosives, including urea nitrate, and improvised weapons; (3) a videotape containing a chemistry lesson on manufacturing explosives; (4) additional manuals on catalysts, detonators and other bomb ingredients; (5) a document entitled “Facing the enemies of God—[Terrorism is a[R]eligious [D]uty and [F]oree is [N]ecessary,” which urged acts of terrorism against the enemies of Islam; and (6) a book entitled “Rapid Destruction and Demolition,” which described the destruction of buildings and contained a formula for using explosives to accomplish this end. Copies of publications (5) and (6) above were recovered from Abouhalima’s residence and admitted into evidence. Although identical, Abouhalima does not dispute the admissibility of these items, but only those items seized from Ajaj. Next, Abouhalima argues that through the joinder, he was prejudiced by Salameh’s closing argument, where Salameh purportedly asserted a defense antagonistic to his own. In this regard, as part of his defense, Abo-uhalima refused to concede either that a bomb had caused the World Trade Center explosion, or that he had any association with Yousef. Salameh, on the other hand, conceded not only the existence of a bomb, but argued that he was an unwitting dupe of Yousef, who had masterminded the bombing. Because the government had characterized Yousef as Abouhalima’s close associate, Abo-uhalima avers that Salameh’s summation undermined his defense of not knowingly participating in the conspiracy. We find no basis for reversal. “There is a preference in the federal system for joint trials of defendants who are indicted together.” Zafiro v. United States, 506 U.S. 534, 537, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993); United States v. Hernandez, 85 F.3d 1023, 1029 (2d Cir.1996). This preference is particularly strong where, as here, the defendants are alleged to have participated in a common plan or scheme. See Fed.R.Crim.P. 8(b); United States v. Cardascia, 951 F.2d 474, 482 (2d Cir.1991); United States v. Turoff, 853 F.2d 1037, 1042 (2d Cir.1988). “It would impair both the efficiency and the fairness of the criminal justice system to require ... that prosecutors bring separate proceedings, presenting the same evidence again and again, requiring victims and witnesses to repeat the inconvenience (and sometimes trauma) of testifying, and randomly favoring the last-tried defendants who have the advantage of knowing the prosecution’s case beforehand.” Richardson v. Marsh, 481 U.S. 200, 210, 107 S.Ct. 1702, 95 L.Ed.2d 176 (1987). Whether to grant or deny a severance motion is “committed to the sound discretion of the trial judge.” United States v. Casamento, 887 F.2d 1141, 1149 (2d Cir.1989); see United States v. Torres, 901 F.2d 205, 230 (2d Cir.1990). The district court’s exercise of that discretion is “virtually unre-viewable.” United States v. Lasanta, 978 F.2d 1300, 1306 (2d Cir.1992) (citation and internal quotation marks omitted). Accordingly, a district court’s denial of a severance motion under Federal Rule of Criminal Procedure 14 will be reversed “only if a defendant can ‘show prejudice so severe that his conviction constituted a miscarriage of justice, and that the denial of his motion constituted an abuse of discretion.’ ” Hernandez, 85 F.3d at 1029 (quoting United States v. Rosa, 11 F.3d 315, 341 (2d Cir.1993)). To satisfy this “extremely difficult burden, of showing an abuse of discretion, an appellant must demonstrate that the denial of the motion caused substantial prejudice,” Casamento, 887 F.2d at 1149-50 (internal quotation marks and citations omitted), that is, “prejudice so great as to deny him a fair trial,” Cardascia, 951 F.2d at 482. “If the denial of the motion causes some prejudice, but less than substantial prejudice, we are not apt to reverse, since, by and large, joinder promotes judicial efficiency.” Casamento, 887 F.2d at 1150. 1. Ajaj’s Holy War Materials The admission of Ajaj’s “holy war” materials did not result in prejudicial spillover as to Abouhalima. Therefore, the district court did not err in denying severance. A defendant’s claim that he was prejudiced by the admission of evidence at a joint conspiracy trial is insupportable when the evidence would have been admissible against him in a separate trial alone as a member of the conspiracy. See Rosa, 11 F.3d at 341 (such evidence “is neither spillover nor prejudicial”); United States v. Cunningham, 723 F.2d 217, 230 (2d Cir.1983). “Prejudice” occurs in joint trials when proof inadmissible against a defendant becomes a part of his trial solely due to the presence of co-defendants as to whom its admission is proper. See, e.g., United States v. Cervone, 907 F.2d 332, 341-42 (2d Cir.1990). This is an unlikely occurrence when all the defendants are charged under the same conspiracy count. See United States v. DiNome, 954 F.2d 839, 843-44 (2d Cir.1992). In the present case, Ajaj and Abouhalima were alleged to have participated in a common plan or scheme and were tried under the same conspiracy count. As we have already discussed in connection with co-appellant Ayyad, the materials seized from Ajaj at Kennedy Airport were properly admitted as background evidence to establish the nature and scope of the conspiracy and to establish the motive and intent of the conspirators, namely, a desire to use violence to effect change in American foreign policy in the Middle East. See United States v. Daly, 842 F.2d 1380, 1387 (2d Cir.1988) (“Background evidence may be admitted to show, for example, the circumstances surrounding the events or to furnish an explanation of the understanding or intent with which certain acts were performed.”). Additionally, the materials were admissible to link Abouhalima to the conspiracy, as two of the terrorist publications seized from Ajaj were identical to the publications found in Abouhalima’s apartment. Because each of the items would have been admitted against Abouhalima had he been tried alone, they were properly admitted against Abouhalima in the joint trial and there is no prejudicial “spillover.” Consequently, Abouhalima has not shown that the district court erred in denying his pretrial motion for a severance, let alone an abuse of discretion and a miscarriage of justice. 2. Salameh’s Summation We find no prejudice to Abouha-lima arising from Salameh’s summation. “‘[MJutually antagonistic’ or ‘irreconcilable’ defenses may be so prejudicial in some circumstances as to mandate severance.” Zafiro, 506 U.S. at 538, 113 S.Ct. 933. In order to make a showing of “mutually antagonistic” or “irreconcilable defenses,” the defendant must make a factual demonstration that “acceptance of one party’s defense would tend to preclude the acquittal of [the] other.” United States v. Smith, 788 F.2d 663, 668 (10th Cir.1986) (internal quotation marks and citation omitted); United States v. Keck, 773 F.2d 759, 765 (7th Cir.1985). However, “[m]utually antagonistic defenses are not prejudicial per se. Moreover, Rule 14 does not require severance even if prejudice is shown; rather, it leaves the tailoring of the relief to be granted, if any, to the district court’s sound discretion.” Zafiro, 506 U.S. at 538-39, 113 S.Ct. 933; see, e.g., id. at 540-41, 113 S.Ct. 933 (where two co-defendants both claim they are innocent and each accuses the other of the crime, district court did not err in denying motion for severance). “The risk of prejudice will vary with the facts in each case ... [and w]hen the risk of prejudice is high, a district court is more likely to determine that separate trials are necessary, but, as [the Supreme Court] indicated in Richardson v. Marsh, less drastic measures, such as limiting instructions, often will suffice to cure any risk of prejudice.” Id. at 539, 113 S.Ct. 933. “ ‘[J]uries are presumed to follow their instructions.’ ” Id. at 540, 113 S.Ct. 933 (citation omitted). Throughout the trial in this case, all four defendants challenged the government’s case without attempting to accuse one another. Unlike Abouhalima, during summation Sala-meh abandoned his trial strategy of disputing that a bomb had caused the explosion and argued that he was nothing more that an unwitting dupe of Yousef, who had masterminded the bombing. While the defense asserted by Salameh was, in the end, inconsistent with Abouhalima’s defense, at no time did Salameh argue or suggest that Abouhali-ma was involved in the bombing, or directly contradict Abouhalima’s defense strategy. Salameh and Abouhalima both claimed to be innocent of the charges and neither’s claim of innocence required the jury to find the other guilty. ■ Consequently, because there was nothing directly antagonistic between the two defense theories so as to create mutually antagonistic or irreconcilable defenses, we perceive no ground for reversal based on the court’s denial of severance. Furthermore, any possible prejudice was eliminated by the district court’s repeated admonitions to the jury that each defendant’s guilt had to be separately and individually considered. See, e.g., Her nandez, 85 F.3d at 1029-30 (rejecting claim of prejudicial spillover where “the district court instructed the jury that it was required to consider the evidence against each defendant individually for each count”); United States v. Losada, 674 F.2d 167, 171 (2d Cir.1982) (same). Moreover, to the extent that Salameh’s summation may have undermined Abouhali-ma’s defense by indirectly linking him to Yousef, any possible prejudice was cured by the district court’s jury instruction that “[m]ere association with other people that you found are members of the conspiracy is not enough for you to find a person to be a member ... [even] a person who has knowledge of a conspiracy and all of its ramifications and does nothing about it is not a co-conspirator- [It’s] got to be an intentional joining of the conspiracy.” In light of this instruction, we find no error. B. Abouhalima—Involuntariness of Statement Abouhalima made two incriminating remarks during his post-arrest interview. Specifically, shortly after being taken into United States’ custody, Abouhalima was informed that he was under arrest for his participation in the World Trade Center bombing. Once FBI agents advised him of his constitutional rights, they interviewed him about the apartment at 40 Pamrapo. During the interview, Abouhalima asked an officer whether he knew an individual by the name of “Rashid.” Yousefs nickname was “Rashed.” Abouhalima also corrected an FBI agent’s pronunciation of “Pamrapo.” At trial, Abouhalima requested a suppression hearing directly before these remarks were admitted into evidence. The court, however, found that such a hearing was unnecessary. After introducing these statements into evidence, the government used these statements to assert that Abouhalima had linked the questioning about 40 Pamrapo to the World Trade Center bombing and to Yousef. Abouhalima now argues that we should direct the district court on remand to reconsider Abouhalima’s motion to suppress his post-arrest remarks. Specifically, Abouhali-ma asserts that his comments were given involuntarily and without a valid Miranda waiver because they followed ten days of incarceration and torture in Egypt. Accordingly, Abouhalima argues that the court’s failure to hold a suppression hearing violated his Fifth and Sixth Amendment rights. Under the circumstances, we find no basis for a suppression hearing. “[Courts are not required to] divine a defendant’s motivation for speaking or acting as he did [when] there [is] no claim that governmental conduct coerced his decision.” Colorado v. Connelly, 479 U.S. 157, 165-66, 107 S.Ct. 515, 93 L.Ed.2d 473 (1986). “A diminished mental state is only relevant to the voluntariness inquiry if it made mental or physical coercion by the police more effective.” United States v. Chrismon, 965 F.2d 1465, 1469 (7th Cir.1992). In the present case, while it is reasonable that Egyptian incarceration and torture, if true, would likely weaken one’s mental state, one’s mental state does not become part of the calculus for the suppression of evidence unless there is an allegation that agents of the United States engaged in some type of coercion. Because Abouhalima does not contend that federal agents either mentally or physically coerced his remarks during that interrogation, there is no basis for inquiry into a possible constitutional violation. “Only if we were to establish a brand new constitutional right—the right of a criminal defendant to confess to his crime only when totally rational and properly motivated—could respondent’s present claim be sustained.” Connelly, 479 U.S. at 166, 107 S.Ct. 515. C. Ayyad—Failure to Grant Funds for Experts • • Ayyad argues that the district court unreasonably interfered with his efforts to secure expert testimony and consultation by authorizing only a portion of the Criminal Justice Act (CJA) funds that he requested. Specifically, on January 28, 1994, during the fourth month of the trial, Ayyad, who was represented by «retained counsel, applied for $35,000 in CJA funds for five expert witnesses concerning DNA evidence, explosives, computers, linguistics and culture. The district court initially responded by authorizing $1,000 for the DNA expert and $1,000 for the explosives expert, but denied Ayyad’s request to retain the computer expert, linguist and an expert on culture (sociologist). Ayyad asserts that the district court’s response “left him unprepared and unable to test the government’s direct case ... requiring] reversal.” The government responds that just three days after its initial ruling, the court reconsidered and granted Ayyad’s application in full. Accordingly, the government avers that Ayyad’s argument is factually incorrect and does not support a reversal. We agree. The Criminal Justice Act of 1964 provides in pertinent part: “Counsel for a person who is financially unable to obtain investigative, expert, or other services necessary for adequate representation may request them in an ex parte application.” 18 U.S.C. § 3006A(e)(l). The statute requires the district court to authorize these funds when a defense attorney “makes a reasonable request in circumstances in which he would independently engage such services [if his client was able to pay for them].” United States v. Durant, 545 F.2d 823, 827 (2d Cir.1976) (citing United States v. Theriault, 440 F.2d 713, 717 (5th Cir.1971) (Wisdom, J., concurring)); see United States v. Oliver, 626 F.2d 254, 259 (2d Cir.1980). While the district judge should entertain such requests with a liberal attitude, he is nevertheless “obligated to exercise his discretion in .determining whether such services áre necessary.” Oliver, 626 F.2d at 260. Services “necessary for an adequate defense” include “preparation for cross-examination of a government expert as well as presentation of an expert defense witness.” Id.; see id. at 828 (district court commits reversible error when it denies CJA funds for fingerprint expert, where fingerprint evidence was likely to be “pivotal”). In this case, we need not decide whether the district court erred in initially declining to grant Ayyad’s application in full. Because the district court timely reconsidered that order and granted Ayyad the full $35,000 in. CJA funds, we perceive no prejudice. Moreover, we observe that during the three-week interval between the district court’s authorization of the funds and the time that Ayyad rested before the jury, he called no witnesses and never requested a continuance to consult with his experts. Consequently, there is no basis for reversal. D. Ajaj—Eastern District Plea Agreement Ajaj argues that his prosecution under the instant indictment is barred by the express terms of his plea agreement regarding the passport fraud charges in the Eastern District of New York (“Eastern District plea agreement”). He claims that the United States Attorney’s Office for the Eastern District of New York (“Eastern District prosecutor’s office”) improperly passed along work to the United States Attorney’s Office for the Southern District of New York (“Southern District prosecutor’s office”) to circumvent a restriction on its own ability to prosecute Ajaj on charges stemming from Ajaj’s role in the World Trade Center bombing. For the reasons that follow, we conclude that Ajaj’s arguments are meritless. Following his arrest and detention at Kennedy Airport, Ajaj was charged in the Eastern District of New York with knowingly using a false passport, 18 U.S.C. § 1543 (Count One), and using the passport of another person, 18 U.S.C. § 1544 (Count Two) (“Eastern District indictment”). On October 6,1992, Ajaj, with the assistance of his then-counsel, Douglas Morris, executed a written plea agreement with the Eastern District prosecutor’s office. Ajaj agreed to plead guilty to Count Two in return for the Eastern District prosecutor’s promise to move to dismiss Count One at sentencing and not oppose a two-level reduction under the Sentencing Guidelines for Ajaj’s acceptance of responsibility. Paragraph 4 of that plea agreement provided that “[tjhis agreement is limited to the United States Attorney’s Office for the Eastern District of New York and cannot bind other federal, state or local prosecuting authorities.” On October 6, 1992, Ajaj pled guilty to Count Two of the Eastern District indictment before United States District -Judge Raggi. During the course of the allocution, Judge Raggi asked the parties whether they had agreed to any additional terms to supplement the written plea agreement. Attorney Morris, counsel for Ajaj, responded: There’s also an agreement that the Government will not bring any charges arising out of Mr. Ajaj’s entry into the United States on September 1st, including any false statement charge, and it will not bring any charges arising from any thing or document that Mr. Ajaj was carrying with him on that date. (emphasis added). Following Attorney Morris’ articulation of this supplementary oral agreement, the Eastern District prosecutor agreed, stating “[tjhat’s correct, your Hon- or.” Judge Raggi, to ascertain whether Ajaj understood the agreement in its entirety, questioned Ajaj and paraphrased Attorney Moms’ articulation of the oral agreement. Judge Raggi stated: THE COURT: Now, the lawyers tell me that the agreement represents all of the promises and agreements between you and the Government, except that the Government also promises that it’s not going to bring any other charges against you relating to your conduct on September 1st. The question I want to put to you, now, is do you know of any other promises [or] agreements made by you or the Government as a part of this decision to plead guilty? Is there anything else? THE DEFENDANT: No. (emphasis added). Prior to trial under the instant indictment filed in the Southern District of New York (“Southern District indictment”), Ajaj moved to dismiss the indictment, arguing that the prosecution was barred by the terms of the Eastern District plea agreement. Specifically, Ajaj argued that under the terms of the oral supplement to that agreement, “the Government,” which included the Southern District prosecutor’s office, was barred from prosecuting Ajaj on charges “arising from” and “relating to” his September 1 entry into the United States and the terrorist materials in his possession. Ajaj argued that in contravention of that agreement, two overt acts charged in Count One of the Southern District indictment stated: a. On or about September 1, 1992, AHMAD MOHAMMAD AJAJ, using an airline ticket issued in the name of “Khurram Khan,” and RAMZI AHMED YOUSEF, using an airline ticket issued in the name of “Azan Muhammad,” traveled together from Pakistan to John F. Kennedy International Airport, in Queens County, New York (“Kennedy Airport”). b. On or about September 1, 1992, AHMAD MOHAMMAD AJAJ transported from Pakistan to Kennedy Airport, manuals and other materials containing, among other things, instructions on the construction and use of explosive devices, including improvised explosive devices using urea and nitric acid and nitroglycerine. The government, in opposition to Ajaj’s motion, argued that the parties to the Eastern District plea agreement never contemplated that the plea agreement would bar the prosecution of Ajaj for terrorist-related activities. According to the government, the parties had entered into the supplementary oral agreement to address Ajaj’s concern that (1) he had made false statements to INS officials on September 1, 1992; (2) the government would bring additional fraud-related charges against Ajaj based on his possession of false identification documents; and (3) the possession of terrorist materials themselves might constitute a crime. On September 13, 1993, the district court denied Ajaj’s motion, concluding that “the written portion of the plea bargain specifically limited the [plea agreement] to the United States Attorney’s Office for the Eastern District of New York. -It is unreasonable to believe that anyone, including Ajaj, believed that the addendum announced in open court by his own attorney could bind all levels of government within the United States.... Under the circumstances leading up to Ajaj’s guilty plea, the only reasonable expectation Ajaj could have" was that he would not be further prosecuted by the United States Attorney in the Eastern District of New York.” We agree. It is well settled that a prosecutor’s promises made in return for a defendant’s guilty plea must be fulfilled. See Mabry v. Johnson, 467 U.S. 504, 509, 104 S.Ct. 2543, 81 L.Ed.2d 437 (1984) (“[W]hen the prosecution breaches its promise "with respect to an executed plea agreement, the defendant pleads guilty on a false premise, and hence his conviction cannot stand.”); Santobello v. New York, 404 U.S. 257, 262, 92 S.Ct. 495, 30 L.Ed.2d 427 (1971). When the express terms of a plea agreement set forth promises by “the Government,” we have held that the “plea agreement binds only the office of the United States Attorney for the district in which the plea is entered unless it affirmatively appears that the agreement contemplates a broader restriction,” United States v. Annabi, 771 F.2d 670, 672 (2d Cir.1985) (per curiam), or unless “there [is] evidence to show that [a prosecutor] [i]s attempting to evade its own obligations [under the plea agreement] by transferring a prosecution” to another office, United States v. Alessi, 544 F.2d 1139, 1154 (2d Cir.1976); see also United States v. DiNapoli, 817 F.2d 978, 979 (2d Cir.1987) (per curiam); United States v. Papa, 533 F.2d 815, 825 (2d Cir.1976). The mere use of the term “ ‘government’ in the plea agreement , does not create an affirmative appearance that the agreement contemplated barring districts” other than the particular district entering into the agreement. United States v. Laskow, 688 F.Supp. 851, 853 (E.D.N.Y.1988), aff'd, 867 F.2d 1425 (2d Cir.1988). Here, Ajaj presents no evidence that the parties to the Eastern District plea agreement contemplated that it would bar the prosecution of Ajaj in any district other than the Eastern District. Indeed, the explicit terms of the Eastern District plea agreement expressly limited the plea agreement to the Eastern District of New York. Moreover, assuming that the plea agreement would bar the Eastern District prosecutor’s office from prosecuting Ajaj for crimes arising from the World Trade Center bombing, Ajaj presents no evidence that the Eastern District prosecutor’s office attempted to circumvent a restriction op its authority to prosecute by transferring its work to the Southern District prosecutor’s office. The Southern District prosecutor’s office independently investigated criminal offenses arising from the World Trade Center bombing and filed an indictment in the Southern District charging Ajaj with crimes that were distinct from the passport fraud charges in the Eastern District. We therefore affirm the district court’s denial of Ajaj’s motion. HI JURY SELECTION Abouhalima maintains that he was denied a fair trial because Judge Duffy, during voir 'dire, failed to ask sufficiently probing questions regarding the jury panel’s bias against Muslims, Arabs and Islamic Fundamentalism. Abouhalima argues that, aside from uncovering bias, a more extensive voir dire would have helped the defendants exercise their peremptory challenges more effectively. Abouhalima adds that the judge should have asked questions about Ajaj’s terrorist materials during voir dire. Because the record shows that Judge Duffy conducted a proper and searching voir dire, we disagree. Before trial, the parties submitted proposed voir dire questions. Abouhalima’s counsel submitted a proposed written questionnaire with 79 questions soliciting the prospective jurors’ views about “Islam, Muslims and Arabs.” However, Judge Duffy declined to use a written questionnaire and instead conducted jury selection in three stages. In the first stage, potential jurors were sent to the courtroom in groups of 50. The judge explained the charges in the Indictment, read a list of names and places that might be mentioned during the trial and entertained petitions from those who sought to be excused from jury service. Judge Duffy eliminated anyone who expressed bias against the defendants or hesitancy about serving on the jury. After this stage, approximately 60 out of 150 possible jurors remained. In the second stage of jury selection, Judge Duffy randomly placed jurors in five groups of twelve. Each group was brought separately into open court where Judge Duffy asked a series of questions, including: (1) “If you had to describe your religious views, how would you do it?”; (2) “Have you ever had an incident in your life that would make it difficult to judge another person because of their race or creed or color or national origin or anything like that?”; (3) “Have you ever moved out of an area because you were disturbed that the area was changing?”; and (4) “Do you think that you could be fair and impartial in a case like this?” Again, jurors who expressed bias or difficulty assessing the case impartially were excused. In the third stage of jury selection, the judge questioned each remaining venire person privately in the jury room, with all counsel present. Before beginning the individual questioning, Judge Duffy emphasized that jurors had to be “totally fair and impartial” and base their decisions solely on the evidence. Judge Duffy asked each venire person whether he or she: (1) had ever traveled to the Middle East; (2) had any feelings abou