
545 F.3d 139 (2008)
UNITED STATES of America, Appellee,
v.
Mohammed Ali AL-MOAYAD, Mohammed Mohsen Zayed, Defendants-Appellants.
Docket Nos. 05-4186-cr (L), 05-4838-cr (CON).
United States Court of Appeals, Second Circuit.
Argued: November 26, 2007.
Decided: October 2, 2008.
*145 Robert J. Boyle, New York, NY, for Defendant-Appellant Mohammed Ali Al-Moayad.
Steven A. Feldman, Feldman & Feldman, Uniondale, NY, for Defendant-Appellant Mohammed Mohsen Zayed.
Pamela K. Chen, Jeffrey H. Knox, Assistant United States Attorneys (David C. James, Assistant United States Attorney, on the brief), for Roslynn R. Mauskopf, United States Attorney for the Eastern District of New York, for Appellee.
Before: McLAUGHLIN, B.D. PARKER, and WESLEY, Circuit Judges.
B.D. PARKER, JR., Circuit Judge:
Defendants Mohammed Ali Al-Moayad ("Al-Moayad") and Mohammed Mohsen Zayed ("Zayed") appeal from judgments of conviction in the United States District Court for the Eastern District of New York (Johnson, J.). Both were convicted of conspiring to provide material support to designated terrorist organizations Hamas and Al-Qaeda, and attempting to provide material support to Hamas. See 18 U.S.C. § 2339B(a)(1). Al-Moayad was also convicted of attempting to provide material support to Al-Qaeda and providing material support to Hamas. Id. Al-Moayad was sentenced to the statutory maximum of 180 months' imprisonment on each count, which the district court directed would run consecutively for a total period of incarceration of 900 months. The district court also sentenced Zayed to the statutory maximum of 180 months on each count to run consecutively, for a total of 540 months' imprisonment. We conclude that the district court committed evidentiary errors that were sufficiently prejudicial as to deprive the defendants of a fair trial. We therefore vacate the convictions and remand for further proceedings.

I. BACKGROUND

A. Government's Evidence Against the Defendants

1. FBI investigation
The convictions arose from an investigation and sting operation conducted principally by the Federal Bureau of Investigation. At trial, the jury heard testimony from various witnesses describing the operation and the events that led to the prosecution, and viewed video tapes of FBI-orchestrated meetings between the defendants and government informants that took place in Frankfurt, Germany in January 2003.
In investigating the defendants, the government relied heavily on the assistance of a confidential informant named Mohammed Al-Anssi,[1] a Yemeni national who later played a central role in the sting operation. The government did not call Al-Anssi as a witness, but the defendants did, as the main thrust of their defense *146 was that they were entrapped by Al-Anssi. Al-Anssi testified that in November 2001, prompted by the events of September 11, 2001, he approached the FBI to offer information relating to terrorism. He described meeting with FBI Special Agent Brian Murphy in Washington, D.C. and giving him a list of individuals about whom he claimed to have information, including defendant Al-Moayad.
Al-Anssi testified that he first met Al-Moayad in Yemen in 1995. According to Al-Anssi, they were neighbors in Yemen, and Al-Moayad was the imam of a mosque. Al-Anssi stated that Al-Moayad also ran a bakery and a school.[2] Al-Anssi further testified that in 1996 or 1997, he learned from Al-Moayad that he was involved in supplying money, arms, and recruits to terrorist groups. After Al-Anssi relayed this information to Murphy, Murphy enlisted Al-Anssi as his principal informant and used him to help develop the government's case against Al-Moayad, and later Zayed.
Al-Anssi did not offer his assistance for free. Rather, he admitted that he was in difficult financial circumstances when he approached the FBI and that he sought compensation in exchange for information. Al-Anssi testified that in 2001, he was in the United States on a tourist visa. He was heavily in debt, looking for work, and in need of assistance for himself and his family. Al-Anssi initially asked the FBI for 5 million dollars in exchange for his assistance, "hoping that it will go up, no problem." He also requested United States citizenship and that his family be brought to the United States from Yemen. In describing his motive for seeking compensation, Al-Anssi testified, "the issue was the truth, the whole issue, and after I chase the terrorists and to bring him here to America, I deserve even 10 million dollars."
Al-Anssi stated that he was paid $100,000 by the FBI for his assistance. However, he believed that he deserved millions, "[a]nd I expect more than that." Al-Anssi admitted that, because he was upset about his small payment from the FBI, he falsely told the Washington Post that the FBI promised to pay him 5 million dollars. He also testified that in November 2004, in an attempt to coerce the FBI into paying him more money, he set himself on fire in front of the White House. With regard to this incident, Al-Anssi testified that he did not intend to commit suicide, but that he "wanted to put the government and the world on notice," and that "[i]t is my right to get as much as I can from the FBI."
As part of its investigation of Al-Moayad, the FBI sent Al-Anssi to Yemen three times in 2002. In January 2002, Murphy sent Al-Anssi to re-establish contact with Al-Moayad, who was then serving as head of an organization called the Al-Aqsa foundation.[3] Al-Anssi took a second trip to Yemen in May 2002 to gather information about people in the United States who might be involved in funding terrorist organizations, and to introduce the idea of a wealthy American named "Saeed" (actually *147 another government informant) who wanted to donate money to support militant Islamic jihad[4] and the mujahidin (i.e., armed fighters). Al-Anssi testified that during that trip, Al-Moayad told him that he had met with Osama bin Laden at some point in Afghanistan. Al-Moayad also gave Al-Anssi a list of contacts in the United States who could send money, introduced Al-Anssi to defendant Zayed, who was his assistant, and gave Al-Anssi a tour of his bakery. Al-Anssi testified that during both of these trips, he took notes of his conversations with Al-Moayad and delivered them to Murphy when he returned to the United States. As discussed below, the admissibility of these notes was a central, hotly contested issue at trial.
Al-Anssi took a third trip to Yemen in August 2002. During that trip, he attended a group wedding hosted by Al-Moayad on September 19, 2002. At the FBI's behest, Al-Anssi videotaped and photographed the wedding. According to Al-Anssi, Al-Moayad asked him to show Saeed the pictures "to prove that this a part of the effort to prepare the youth for El Jihad." During the wedding, Mohammed Siyam, who was identified at trial as the representative of Hamas in Yemen, gave a speech that Al-Anssi videotaped. Among other things, Siyam said the following:
Thanks be to God ... The Father, the Mujahid Sheikh Abdullah bin Hussein al-Ahmar, benefactor of this honorable celebration, the Honorable Sheikh Mohammed bin Ali Ali al-Moayad, president of the high committee of group weddings. May God join us to him, meaning, may we be joined to him in helping others get married and not to get married ourselves, God willing.... I greet you with Islam's [traditional] greeting: peace be with you and God's mercy and blessings. Either those who organized the celebration found out about the timing of Hamas's operation in Tel Aviv, that it will be todayand this is leaking the newsso they held the wedding here to coincide with the wedding there. An organized operation, God willing, you will hear about it, you will read about it tomorrow in the newspapers and hear about it in the media. It brought down many of the invading occupiers, and thanks be to God, Lord of the universe.
At trial, the government established through the testimony of a witness, a young Scottish law student named Gideon Black, that a suicide bombing occurred on a bus in Tel Aviv that same day. Black was a passenger on the bus along with his cousin Yoni, who was killed in the attack. As discussed below, Black testified at length and in considerable detail about the bombing, and his testimony was a prominent feature of the government's case. The testimony was admitted over the defendants' objections that it was unrelated to the charges against them and enormously prejudicial; the admissibility of the testimony is a central issue in this appeal.
During the August 2002 trip, Al-Moayad gave four paper receipts to Al-Anssi, documenting donations to various organizations. Al-Anssi testified that Al-Moayad told him these groups were fronts for Hamas. Al-Anssi further claimed that Al-Moayad admitted having delivered more than $20 million to Bin Laden and $3.5 million to Hamas in the past. Whether these donations occurred, and when, was a *148 significant issue at trial, especially with regard to the alleged contributions to Bin Laden and Al-Qaeda.[5]
During his third trip to Yemen, Al-Anssi again took notes purportedly memorializing his conversations with Al-Moayad. These notes did not specify when Al-Moayad's alleged donations to Hamas occurred, but suggested that the donations to Al-Qaeda were relatively recent. The notes recorded that the Al-Qaeda donations occurred "during last few years and before the Sept. 11th 2001." However, during his trial testimony Al-Anssi could not, in contrast to his notes, specify when Al-Moayad allegedly provided money to either Al-Qaeda or Hamas. As to Hamas, Al-Anssi stated that Al-Moayad "did not give me specific dates." Similarly, with regard to the Al-Qaeda donations, Al-Anssi said that Al-Moayad "did not give me dates" and conceded that it could have been delivered "[p]ossibly in the 80s," and that "I don't know what year or over what years. He did not decide." When asked to explain what he meant in his notes by "a few years," Al-Anssi stated, "I cannot be specific. It could be few years, could be less than five years or less than ten years, or ten years.... I would say it is before 20 years." As discussed below, other evidence presented at trial suggested that any support that Al-Moayad may have provided to Al-Qaeda lasted only through the Afghan conflict in the 1980s.

2. Sting operation in Germanyvideo tapes
In collaboration with German law enforcement agencies, the FBI arranged for Al-Moayad and Zayed to meet with Al-Anssi and the second informant, "Saeed," in Frankfurt, Germany in January 2003. Many of the conversations that occurred among the defendants and the two informants over the next few days were captured by audio and video recorders hidden in the defendants' hotel rooms.
The tapes showed the following. On the morning of January 7, Al-Anssi met Al-Moayad and Zayed at the Frankfurt airport and brought them to their hotel. When they arrived, Al-Moayad expressed his desire to secure money for his charity projects, including the bakery. During this conversation, no one explicitly mentioned funding terrorist activity. The government repeatedly argued at trial, however, that the defendants' references to Al-Moayad's charitable endeavors were actually code for various forms of support for terrorism. (The government also argued that Al-Moayad's references to going to Germany for medical treatment were similarly coded allusions to conspiring to support terror.) The defendants maintain on appeal that throughout the Germany meetings, they were referring to actual charitable endeavors.
The tapes showed that the next day, January 8, Al-Moayad and Zayed met with Al-Anssi and Saeed. Saeed invoked verses *149 of the Qu'ran referring to jihad, in order to establish that jihad is "basically our business." He also said, "I believe, we're working in the same field." Al-Moayad responded, "[t]he same field. But... the most important thing for the Muslims is to know and learn their religion." At Saeed's request, Al-Moayad discussed his prior relationship with Bin Laden, whom he said he financially supported and instructed in Islamic law. Al-Moayad did not, however, state that he had given $20 million to Bin Laden, nor did he provide any other figure. Al-Moayad and Zayed both clarified verbally that this relationship dated back to the 1980s, "before all these crises happened. A long time ago.... [b]ack in the days of Afghanistan.... [w]ith the Russians." Al-Moayad also mentioned his ties to Khaled Meshal, who was identified at trial as the head of Hamas's political and military bureau.
When Saeed asked what he could do for Al-Moayad, Al-Moayad described five goals: (1) teaching people their religion; (2) uniting Muslims; (3) raising young men in a manner of which God approves; (4) helping young people in need; and (5) doing everything for God's sake. Al-Moayad also discussed more specific projects, including the charitable bakery, educating Muslim women, and aiding the families of people who have been jailed or martyred. Saeed said that he was willing to support these projects, but that he primarily wanted to fund mujahidin. Al-Moayad replied, "[l]et me tell you that I want to be honest with you.... We can't say `yes, yes' to what you're asking then lie to you. It's not right. And it is also not right to say `no, no' which may cause him to be discouraged, and that is a sin." He then added that he would work "in these fields, as they are my fields with God's permission." The rest of the meeting revolved mainly around how Al-Moayad and Zayed would meet with their Hamas contacts and arrange for Saeed's money to be used according to his wishes.
That night, Al-Anssi and the defendants discussed, again on tape, how Saeed's money would be sent. They talked about the various projects for which the money could be designated, including the bakery, educating women, helping orphans and the elderly, and others. Al-Anssi referred a few times to these projects as codes, but it is not clear from the tapes whether the defendants were also referring to the charities as codes.[6] The three men also discussed the need to transfer Saeed's money in several people's names.
Al-Moayad and Zayed met again with Al-Anssi and Saeed on January 9. Saeed asked for clarification as to how his money would be spent, and Al-Moayad once again described his charitable projects. Al-Moayad also explained, at Saeed's request, that although he had delivered money to Bin Laden during the "Afghani Jihad," he distanced himself from Al-Qaeda once that conflict was over. In response to Saeed's questions about the Al-Aqsa foundation, Al-Moayad described it as a charitable organization that aids needy Palestinian Muslims. Saeed then asked whether his money would go to Hamas, Al-Qaeda, or other groups. Al-Moayad replied, "Hamas, Al-Qaeda, Massajins [prisoners], Mujahidins, *150 and such. Anyone who we know of, who is in the Jihad field."
The men also discussed the four receipts that Al-Moayad gave to Al-Anssi during his third trip to Yemen. The government argued at trial that the receipts documented contributions to groups that were fronts for Hamas and its terrorist activities. The transcript of the conversation, however, does not clearly reflect that conclusion. At one point, Al-Moayad did say of one of the receipts, "this one we deliver it to Hamas." About another contribution, however, he said, "it supports everyone who needs it in Palestine, for example, someone's house in Palestine was ruined, a check is issued to him immediately to help him in rebuilding his house." In addition, Al-Moayad never stated during the Frankfurt meetings that he had given $3.5 million to Hamas.
Al-Anssi told Al-Moayad and Zayed that Saeed had $2.5 million to donate. Saeed offered to give five percent for Al-Moayad's charitable projects, which he raised to ten percent at Al-Moayad's insistence.[7] They discussed how best to send the money, including the possibility that Saeed could transmit it directly to Hamas without Al-Moayad's and Zayed's involvement. Al-Anssi explained that Saeed would provide Al-Moayad and Zayed with a book of pre-signed checks so that they could withdraw money directly from his account. Near the end of the meeting, the informants raised the topic of the September 2002 group wedding in Yemen. Al-Anssi explained that Saeed had enjoyed Siyam's speech and his reference to the suicide bombing, at which point the defendants and the informants laughed and clapped. At trial, Al-Anssi admitted the possibility that he had started laughing before the defendants, and stated that "I want to make them believe that I'm happy because of the that [sic] suicide."
Later that evening, the tapes showed Al-Moayad and Zayed privately expressing reservations about the arrangement with Saeed. Al-Moayad stated that "[t]he problem is Hamas ... this guy ... I don't know." They agreed, however, to keep their word, and discussed further how to make arrangements with Hamas. Al-Moayad and Zayed continued the conversation with Al-Anssi the next morning, January 10. They also contemplated asking for more money for their charitable work. Al-Moayad said, "[w]e'll tell him to loosen it up a bit, let us [unintelligible] for our efforts .... we'll tell him let us do jihad ... we want to do jihad, but let us do jihad our way." He also said, "[o]ur work is clear: charity, the charitable bakery, and education."
The defendants' last meeting with Saeed took place later that morning. In response to a query from Saeed, Al-Moayad and Zayed disavowed any knowledge as to a future terrorist attack being planned in New York. They also reviewed how they should use the checks that Saeed would provide. At the conclusion of the meeting, the informants gave the checkbook to Al-Moayad and left the defendants' room. German law enforcement agents arrested Al-Moayad and Zayed shortly thereafter.

3. Post-arrest statements
After their arrests, Al-Moayad and Zayed were questioned by law enforcement officers and gave statements. Agent *151 Murphy interviewed Al-Moayad in November 2003. According to Murphy, Al-Moayad denied ever having given money directly to Hamas, but also said that he might possibly have done so as head of the Al-Aqsa foundation. Al-Moayad confirmed having met with and given money to Osama bin Laden during the conflict with the Soviets in Afghanistan. However, he said that the relationship ended sometime after that conflict ended, that he had since spoken publicly against Bin Laden, and that Bin Laden issued a fatwah, or religious ruling, calling for his death. During the interview, Al-Moayad did not state how much 10 money he had given to either Al-Qaeda or Hamas. With regard to the Frankfurt meetings, Al-Moayad asserted that his intention was to take his portion of Saeed's money for his charities and that it would be up to Al-Anssi to get the rest of the money to Hamas.
Speaking to German police in January 2003, Zayed described himself as Al-Moayad's escort and the person in charge of the charitable bakery. He also described the Al-Aqsa foundation as a charitable organization that "supports people in Palestine who have suffered from the war." Zayed stated that he first learned about the true purpose of the Frankfurt meetings during the defendants' first face-to-face conversation with Saeed, not while he was in Yemen. When he was interviewed by Murphy in November 2003, Zayed told him that while he was still in Yemen, Al-Moayad told him only that one of Al-Anssi's contacts wanted to donate money to Al-Moayad's causes.

B. Prosecution Case
Al-Moayad and Zayed were indicted on charges of conspiring to provide material support to Hamas and Al-Qaeda and attempting to provide material support to Hamas and Al-Qaeda, in violation of 18 U.S.C. § 2339B(a)(1).[8] In addition, Al-Moayad was charged with providing material support to Hamas and Al-Qaeda. Trial commenced in the Eastern District of New York on January 28, 2005 and ended on March 11, 2005. The government's principal evidence during its case-in-chief consisted of tapes and translations of the Frankfurt meetings in January 2003.

1. Al-Moayad's Crawford objection to Zayed's post-arrest statement
During the government's case-in-chief, Agent Murphy testified about, among other things, his post-arrest interview of Zayed. According to Murphy, before the trip to Germany, "Al-Moayad advised Zayed that one of [Al-Anssi's], one his [sic] associates, had a significant amount of money looking to donate that money to Al-Moayad's causes."
*152 During his cross-examination of Murphy, Zayed's counsel attempted to demonstrate that before arriving in Germany, Zayed thought that the meetings would revolve entirely around possible donations for Al-Moayad's charities, not merely his "causes." Defense counsel asked, "[n]ow, in fact, what Mr. Zayed told you was that Al-Moayad had told him that an individual wanted to provide a lot of money to Al-Moayad [sic] charity; isn't that what he told you?" Murphy responded, "I remember there were two answers he gave, one in the beginning and then he completely contradicted this statement you are referring to." Murphy then said that "Zayed stated Al-Moayad at the interview that [sic] an individual wanted to provide lots of money to Al-Moayad's charity," but later in the interview, Zayed "advised that once they had reached the hotel room in Germany, he knew from discussions about [sic] Al-Moayad that Al-Moayad told him they were there to collect money for Hamas." Al-Moayad's attorney objected under Crawford v. Washington, 541 U.S. 36, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004).[9] The court asked Al-Moayad's counsel to suggest a remedy, but he never followed up. When Zayed's counsel resumed his cross-examination of Murphy, he clarified "that there was no contradiction whatsoever in what Mr. Zayed told you about what he knew the reason for going to Germany was when he was in Yemen." Murphy agreed that "there was no contradiction."

2. Testimony of Gideon Black
The government's final witness in its case-in-chief was Gideon Black. Black was on a bus in Tel Aviv on September 19, 2002the same day as the group wedding in Yemenwhen a Hamas suicide bomber detonated his explosives, killing Black's cousin. Black testified at considerable length about the attack. Furthermore, the government highlighted his testimony during its opening and closing arguments.[10]
Early on in the trial, Zayed's counsel moved in limine to exclude Black's upcoming testimony. He argued in essence that because the defendants conceded that they knew Hamas and Al-Qaeda had engaged in terrorist activity and offered to stipulate to that fact,[11] Black's testimony about the bombingwith which the defendants were not charged or shown to be connected would be far more prejudicial than probative. The government contended that it was entitled to put on evidence proving the defendants' knowledge that Hamas and Al-Qaeda were terrorist groups. The court ruled, without further explanation, that the testimony was more probative *153 than prejudicial, and that it would allow the testimony with "[n]o gory stuff."
Just before Black's testimony, the court viewed photographs of the destroyed bus and viewed a DVD of a news story about the bombing, which the government also sought to introduce. The defendants objected to the graphic nature of the images. The court concluded, "[t]here are splatterings of blood in all of them and if you object to places where there is blood, and I don't think it is that gory, then the only thing you'd be able to show is the outside, I'm going to admit it." The court also stated that it would allow all three photographs of the bus to be admitted over defense counsel's objection that they were cumulative.
On the stand, Black described his background and his studies in Israel in the early 2000s. He recounted the events of September 19, 2002, on which he and his cousin Yoni planned to travel from Jerusalem to Tel Aviv to celebrate a Jewish holiday with Black's family. Black stated that when they arrived in Tel Aviv, they almost took a cab, but decided instead to take a bus. While they were aboard, the bus stopped to pick up passengers. As the bus pulled away, a suicide bomber detonated an explosive device at the front of the vehicle.
After Black stated that there was an explosion, defense counsel objected "to any further questions." The court allowed the government to proceed. Black testified that he saw, "[a]mongst other things, glass, metal and shrapnel flying in all directions particularly towards the back of the bus from the center of the bus." He also described the scene immediately after the explosion, testifying that "there was an eerie silence for a few moments and then sirens, screaming, panic." He turned around and saw Yoni crouched on the floor, unconscious. Black also testified that as he absorbed what had happened, he cried. At this point, defense counsel again objected to further questioning, arguing that "[t]his terrible tragedy has now been described, we know what happened and I think that to further dwell on these events is only to reinforce the prejudice which is being attempted to be injected into the record by this testimony." However, the court allowed the government to proceed. The government asked Black to view the photographs of the scene and describe them to the jury, during which Black again described the events immediately before the attack and its aftermath. The government also played the DVD containing the newscast about the bombing.
After Black's testimony, Al-Moayad's counsel asked the court to instruct the jury that there was no evidence or allegation that either defendant was involved in the bombing. The court refused to give the instruction and proposed alternative language instead. Al-Moayad's counsel withdrew his request for a jury instruction, and the jury received none.

C. Defense Case
The defendants' case-in-chief revolved mainly around their view that they had been entrapped by the government through its informants Al-Anssi and Saeed. To make out a defense of entrapment, "a defendant must first prove government inducement by a preponderance of the evidence. The burden then shifts to the government to show that the defendant was predisposed to commit the crime beyond a reasonable doubt." United States v. Gagliardi, 506 F.3d 140, 149 (2d Cir.2007). At trial, the government never seriously disputed the proposition that Al-Moayad was induced to participate in the *154 Germany meetings by Al-Anssi.[12] Therefore, the defense and the prosecution both focused on the issue of the defendants' predisposition. "A defendant is predisposed to commit a crime if he is `ready and willing without persuasion to commit the crime charged and awaiting any propitious opportunity' to do so." United States v. Salerno, 66 F.3d 544, 547 (2d Cir.1995) (quoting United States v. Harvey, 991 F.2d 981, 992 (2d Cir.1993)). The government may show that a defendant was predisposed to commit the crime charged by demonstrating: "(1) an existing course of criminal conduct similar to the crime for which [the defendant] is charged, (2) an already formed design on the part of the accused to commit the crime for which he is charged, or (3) a willingness to commit the crime for which he is charged as evidenced by the accused's ready response to the inducement." Id. (quoting United States v. Valencia, 645 F.2d 1158, 1167 (2d Cir.1980)).
The defendants began their presentation with two character witnesses from Yemen, Abdeh Al Zahr and Karim Ahmed Al Faisal. Both men testified about Al-Moayad's and Zayed's numerous charitable projects, including the bakery and other endeavors, and confirmed Al-Moayad's reputation in Yemen as the "father of the poor." They also stated that neither Al-Moayad nor Zayed condoned violence and that both had spoken out against terrorist acts. The witnesses denied any knowledge that Al-Moayad or Zayed had ever given money to or solicited money for Hamas or Al-Qaeda.

1. Al-Anssi's notes
The defendants called Al-Anssi during their case-in-chief and elicited significant impeachment testimony from him, including admissions of his heavy indebtedness, financial difficulties, and his attempts to obtain large sums of money from the FBI in exchange for information. Al-Anssi also conceded that he had a prior felony conviction, having pled guilty in the Eastern District of New York to bank fraud (specifically, writing bad checks). Al-Anssi further testified that he had purchased a dry cleaning business with a portion of the $100,000 he received from the FBI, but the business failed and he returned it to the seller in June 2004. Al-Anssi admitted that, after this failure, he had run out of money, leading to his attempt in November 2004 to get more money from the FBI by setting himself on fire at the White House.
Impeaching Al-Anssi's credibility was important to the defendants' entrapment defense. Defense counsel examined Al-Anssi extensively about his meetings with Al-Moayad in Yemen, during which he had gathered, at the behest of the FBI, much of the government's background evidence against the defendants. Al-Moayad's attorney queried Al-Anssi about whether he had made notes of his conversations with Al-Moayad, and Al-Anssi indicated that he had. Defense counsel then asked about the list of American contacts that Al-Moayad gave to Al-Anssi. Al-Moayad's counsel pressed Al-Anssi to admit that he did not know whether those contacts sent money to Al-Moayad for armed jihad or for his charities, but Al-Anssi repeatedly insisted that Al-Moayad was funneling money into jihad. Defense counsel asked, "[i]s there one recording or one piece of paper that's prior to Frankfurt that says that?" In response, Al-Anssi pointed to the four receipts that Al-Moayad gave him. Defense counsel followed up, "[i]s there any other document aside from these four documents that shows that Mr. Al-Moayad *155 donated money to Hamas, Al-Qaeda or any other organization involved in the Jihad organization?", and then, "I ask you before you went to Frankfurt, was there anything, any document or any recording supporting what you've told this jury today?" After Al-Anssi answered that the Frankfurt videos supported his testimony, Al-Moayad's attorney asked once more, "[b]etween the first time you met with the FBI and the time you went to Frankfurt, is there any document or any recording supporting the truthful testimony that you've given today?"
During its examination of Al-Anssi, the government moved to introduce Al-Anssi's handwritten notes into evidence, arguing that defense counsel had opened the door to their admission with his questioning. The notes memorialized, among other things, the following information that Al-Anssi purportedly gathered while he was still living in Yemen, and during the FBI investigation: Al-Moayad was "the right hand" to Sheikh Abdul Majid Al-Zindani[13]; at some point in the past, Al-Moayad was "the main person choosing the volunteers" to send to fight in the conflicts in Chechnya, Afghanistan, and Bosnia; during Al-Anssi's first trip to Yemen, Al-Moayad provided him with information about foreign arms dealers; Al-Moayad asked Al-Anssi not to call him on the phone, and to refer only to medical treatment if he did so; Al-Moayad was aware while still in Yemen that Saeed intended to give a substantial sum of money ($2 million) specifically to support the armed mujahidin; Al-Moayad visited and supported Bin Laden in Afghanistan; he knew young volunteers who were ready for training in jihad; and he gave $3.5 million to Palestine and $20 million to Al-Qaeda "during last few years and before the Sept. 11th 2001."
Defense counsel objected to admission of the notes on hearsay grounds. The government contended that the notes constituted a prior consistent statement after impeachment and that the jury had been left with the false impression that no documents supported Al-Anssi's testimony. The court admitted the notes without limitation and, therefore, as substantive evidence and without specifying the ground for their admission.

2. Siyam wedding speech
At the same time that the court admitted Al-Anssi's notes, it also admitted Al-Anssi's video of the September 2002 group wedding in Yemen, which included Mohammed Siyam's speech. Before trial, the court had granted a defense motion to suppress the video. Prior to cross-examining Al-Anssi, the government signaled its intent to re-offer the video "to corroborate [Al-Anssi's] version of events as disputed by the defense through his direction [sic] examination." Zayed's counsel objected on the grounds that he did not open the door to introduction of the video, and that it would be more prejudicial than probative. The government contended that the video was relevant to predisposition and the entrapment defense, and that it was admissible to counteract the impression that no document or recording supported Al-Anssi's testimony about Al-Moayad's previous support for terrorism. The court permitted the government to play the video for the jury and to provide an English translation of its contents. Again, the *156 court admitted this evidence without limitation.

D. Prosecution Rebuttal Case
The government's rebuttal case focused largely on countering the defendants' entrapment defense by showing that Al-Moayad and Zayed were predisposed to support terrorist activities.

1. Mujahidin form
Against Al-Moayad only, the court admitted without limitationover hearsay, relevance, and authenticity objections, and without explaining the grounds for its ruling a document that appeared to be an application form for a mujahidin training camp (the "mujahidin form"). It had been partially filled out in 1999 by an individual who called himself "Abu Jihad," and who listed "Sheikh Mohammed Al Moayad" next to the question, "[w]ho recommended you, and how do you know him." The government did not present any evidence about who Abu Jihad was, and he was not available at trial. Instead, the government authenticated the form through the testimony of FBI Special Agent Jennifer Hale Keenan, who stated that she was stationed in Islamabad, Pakistan on September 11, 2001 and during the ensuing United States invasion of Afghanistan. Hale Keenan recounted that in December 2001, she received a number of items collected by American personnel in Afghanistan, including materials seized from an Al-Qaeda training facility. The mujahidin form was among these documents. Hale Keenan then described the process of receiving, inventorying, and shipping the documents to Washington D.C.

2. Goba testimony
The government also called Yahya Goba, an American citizen of Yemeni heritage who attended an Al-Qaeda training camp in Afghanistan in 2001, to testify about the form. Goba had pled guilty to providing material support to Al-Qaeda in September 2002 pursuant to a cooperation agreement. In response to concerns expressed by defense counsel about his testimony, the government proffered that he would explain the significance of the form from personal experience without directly implicating Al-Moayad. Al-Moayad's counsel objected on the grounds that his testimony would be irrelevant and highly prejudicial, and would constitute inadmissible hearsay. The court allowed the testimony to proceed, but again did not explain the basis for its ruling.
Goba's testimony went far beyond the scope of the government's proffer. He testified that in 1998, he met an individual who later arranged for him to attend an Al-Qaeda training camp in Afghanistan in 2001. Goba described flying to Pakistan and journeying across the border to an Al-Qaeda guest house in Kandahar, Afghanistan. At the guest house, Goba was given a form to fill out that he testified was identical to the mujahidin form. The government asked Goba about the importance of indicating who had recommended him for the camp. He stated, among other things, that without the assistance of the recommender, he would not have been able to attend the camp.
Goba then went on to testify about traveling to the Al-Qaeda camp, the camp layout, and the type of training (weapons, tactics, explosives, topography) that he received there. Al-Moayad's counsel objected periodically to the relevance of Goba's continued testimony, but the court allowed the government to continue. Goba was permitted to testify, for example, that Bin Laden had visited the camp on two occasions. He was also allowed to describe what occurred at the camp during Bin Laden's first visit and to summarize for the jury a speech that Bin Laden gave, in which he talked about the "importance of *157 unifying and performing jihad." The government also played an Al Jazeera news video documenting Bin Laden's visit, which included images of Bin Laden standing with his bodyguards and various associates, including Ayman Al-Zawahiri,[14] and asked Goba to provide commentary. As discussed further below, Al-Moayad's counsel objected to the video on a variety of grounds going to its prejudicial nature, but the court allowed the video to be shown. The court also permitted Goba, over objection, to describe photographs of the Al-Qaeda guest houses and the camp.
At the beginning of the second day of Goba's testimony, Al-Moayad's counsel moved for a mistrial based on Goba's accounts of the training camp and the references to and images of Bin Laden, arguing that "the court very carefully instructed each juror during voir dire that this case was not about 9[/]11, not about Osama bin Laden ... I think the line was crossed yesterday with this testimony." The court responded, "[y]ou made the application. The application is denied. I will instruct the jury that the defendant will have to be judged guilty or not guilty based upon what is charged in the indictment."
During the remainder of his testimony, Goba stated, among other things, that he had attended a rally in 1995 co-hosted by the Al-Aqsa foundation. Goba testified that he had volunteered to guard a picture gallery, which featured photos "of the Al Aqsa mosque, leaders of Hamas and pictures of suicide bombers." Videos were shown at the rally, which Goba described as "contributes [sic] of suicide bombers." In addition, Mohammed Siyam gave a speech. According to Goba, money was collected at the rally for Al-Aqsa.

3. Croatian documents
Through a Croatian intelligence officer, the government offered various documents seized from two Yemeni men who were detained in 1995 by Croatian authorities as they were crossing into Croatia from Bosnia. The officer testified that the men were mujahidin fighters leaving the armed conflict in Bosnia. The government introduced these documents to demonstrate a connection between Al-Moayad and Al-Qaeda continuing into the 1990s (i.e., after the end of the conflict with the Soviets in Afghanistan), which was relevant to the charge of providing material support to Al-Qaeda and to the government's case on predisposition.
Among the documents are photographs of the two Yemeni individuals, copies of their passports, a last will and testament belonging to one of the men, and both men's address books. The intelligence officer affirmed that both address books included Al-Moayad's name and phone number. Al-Moayad's counsel objected to the documents on hearsay, relevance, and authenticity grounds. The government argued that the evidence was relevant to entrapment and was admissible either as non-hearsay or as co-conspirator statements. The court admitted the documents against Al-Moayad as substantive evidence, without limitation and without specifying the basis for their admission.

E. Summations, Jury Charge, Verdict, and Sentencing

1. Derivative entrapment charge
At trial, the government argued that Zayed was induced to commit the *158 crimes charged not by a government agent, but by Al-Moayad, and he was therefore entitled only to a "derivative" entrapment (as opposed to a direct entrapment) defense.[15] Zayed's counsel contended that Zayed could assert a direct entrapment defense as no evidence suggested that he was induced by Al-Moayad, rather than directly entrapped by Al-Anssi. Zayed's counsel objected to the court's proposed entrapment charge, which incorporated the government's requested instruction and read as follows (with the portion to which he objected in italics):
The government inducement must be direct, unless the government used an unwitting middleman to induce another person. For example, if the government induces defendant A to commit a crime, and defendant A takes it upon himself to induce defendant B to participate in the crime, then there can be no entrapment with respect to defendant B.

The court denied defense counsel's application to remove the challenged language.
Defense counsel submitted letter briefing in which he argued again that the instruction did not apply, and also that the proposed language did not correctly state the law. The court deferred revisiting its ruling until after closing arguments. Zayed's attorney discussed derivative entrapment in his summation, as did the government. After summations, the court denied Zayed's attorney's motion for reconsideration of the derivative entrapment instruction. The court then began to charge the jury.
During the charge, the government requested a sidebar and asked the court not to include the derivative entrapment language, "to avoid any possibility of an appellate issue." Zayed's counsel then asked the court to instruct the jury to disregard the attorneys' closing arguments as to derivative entrapment. The court gave the rest of the charge, instructing only on normal entrapment, but did not instruct the jury with regard to the attorneys' closing arguments. Zayed's counsel indicated that he had "[n]o objections or exceptions" to the charge. However, after jury deliberations had begun, another of Zayed's attorneys asked to revisit the derivative entrapment issue. He requested "a curative charge that [Zayed's counsel] was required to close under an incorrect charge," that "closing arguments be reopened for the purposes of [Zayed's counsel] to correctly address the standard of law," and moved for a mistrial. The court denied the applications.

2. Verdict and sentencing
The jury found Al-Moayad guilty of conspiring to provide and attempting to provide material support to Al-Qaeda and Hamas, and of providing material support to Hamas. Al-Moayad was acquitted of providing material support to Al-Qaeda. The jury convicted Zayed of conspiring to provide material support to Al-Qaeda and Hamas and attempting to provide material support to Hamas, but acquitted him of attempting to provide material support to Al-Qaeda.
*159 The district court sentenced Al-Moayad to the statutory maximum of 180 months' imprisonment on each count to run consecutively, for a total of 900 months or seventy-five years, and imposed a fine of $1,250,000.00. Zayed also received the statutory maximum sentence of 180 months on each count to run consecutively, for a total of 540 months' or forty-five years' imprisonment, as well as a fine of $750,000. This appeal followed.

II. DISCUSSION
The defendants raise a number of issues on appeal. They contend that: (1) the district court erred in admitting Al-Anssi's notes as substantive evidence; (2) the court erred in admitting the mujahidin form, the video of Mohammed Siyam's wedding speech, and the Croatian documents; (3) the court abused its discretion in admitting the testimony of Gideon Black and Yahya Goba; (4) the court erred with respect to the derivative entrapment instruction issue; and (5) Al-Moayad's Confrontation Clause rights were violated by admission of an incriminating portion of Zayed's post-arrest statement. For the reasons that follow, we find that the district court committed prejudicial error with respect to the Black and Goba testimony and Al-Anssi's notes. Further, the cumulative effect of the district court's errors deprived the defendants of a fair trial.[16]

A. Testimony of Gideon Black and Yahya Goba
The defendants contend that the testimony of Gideon Black about the Tel Aviv bus bombing and of Yahya Goba about the Al-Qaeda training camp was irrelevant, prejudicial, and highly inflammatory. They also contend that the district court permitted the government to elicit testimony from both witnesses that strayed far beyond the government's proffered purpose in offering the evidenceas to Black, establishing the defendants' knowledge that Hamas engaged in terrorist acts, and as to Goba, authenticating the mujahidin form. We agree that the district court should have excluded the challenged testimony under Rule 403, and that its failure to do so deprived the defendants of a fair trial.

1. Gideon Black testimony
Federal Rule of Evidence 403 provides that "[a]lthough relevant, evidence may be excluded if 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." When we are confronted with a Rule 403 issue, "so long as the district court has conscientiously balanced the proffered evidence's probative value with the risk for prejudice, its conclusion will be *160 disturbed only if it is arbitrary or irrational." United States v. Awadallah, 436 F.3d 125, 131 (2d Cir.2006). "To avoid acting arbitrarily, the district court must make a `conscientious assessment' of whether unfair prejudice substantially outweighs probative value." United States v. Salameh, 152 F.3d 88, 110 (2d Cir.1998) (per curiam) (quoting United States v. Birney, 686 F.2d 102, 106 (2d Cir.1982)).
With regard to Black's testimony, the record reflects that the district court did consider the balance between its probative value and probable prejudicial effect before allowing Black to take the stand.[17] However, we must conclude that, given the highly charged and emotional nature of the testimony and its minimal evidentiary value, the court's decision was arbitrary. The court also refused to give a limiting instruction proposed by the defense, which could have cabined the prejudicial effect of Black's testimony.
The defendants were not charged with planning or carrying out the Tel Aviv bus bombing. Indeed, the government did not introduce any evidence connecting Al-Moayad or Zayed to that or any other terrorist act, other than the fact that Siyam mentioned the Tel Aviv incident during his speech at the group wedding. Nevertheless, Black was permitted to testify at length about the suicide bombing. Black spoke about his cousin Yoni, their shared experience studying in Jerusalem, their plans to visit family on the day of the bombing, the catastrophic explosion and subsequent chaotic scene aboard the bus, and Yoni's death. Black also repeated certain parts of his narrative multiple times, such as when he viewed photos of the destroyed bus and described them for the jury, and when he commented on a video of a news story about the bombing.
The government argued that the testimony was necessary to establish the defendants' knowledge that Hamas engaged in terrorist activity, and was relevant to the issue of predisposition. However, neither Al-Moayad nor Zayed ever denied knowing about Hamas's involvement in violent acts and they both offered to stipulate as to that knowledge, essentially eliminating the government's burden of proof on that element. In light of these concessions, as well as the considerable testimony during other parts of the trial about notorious terrorist attacks carried out by Hamas, any probative value to be gained from Black's testimony was significantly diminished.
The Supreme Court has stated, in a case upon which the government heavily relied at trial, that "what counts as the Rule 403 `probative value' of an item of evidence ... may be calculated by comparing evidentiary alternatives." Old Chief v. United States, 519 U.S. 172, 184, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997); see also United States v. Pepin, 514 F.3d 193, 206-07 (2d Cir.2008) (stating that Rule 403 "permits a judge to consider both the defendant's willingness to stipulate and the potential for prejudice [in later phases] in conducting the requisite [Rule 403] balancing."). The defendants offered an adequate evidentiary alternative at trialto stipulate to their *161 knowledge of Hamas's terrorist activities. Therefore, the already questionable probative value of Black's testimony was diluted even further in comparison with its considerable prejudicial effect.
The government cited Old Chief at trial for the well-established proposition that "the prosecution is entitled to prove its case by evidence of its own choice." Old Chief, 519 U.S. at 186, 117 S.Ct. 644. However, in explaining this general rule, Old Chief emphasizes the importance of allowing the prosecution to maintain "the natural sequence of narrative evidence" in presenting its case, to ameliorate the concern that "[p]eople who hear a story interrupted by gaps of abstraction may be puzzled at the missing chapters." Id. at 189, 117 S.Ct. 644. The Court's concern in Old Chief has little to no application in this instance.
The September 2002 bus bombing was almost entirely unrelated to the elements of the charges  and, therefore, the government's "narrative evidence"  against Al-Moayad and Zayed, especially considering that the defendants never denied their knowledge of Hamas's terrorist activities. In fact, Black's testimony, during which he never referred to either defendant or to any aspect of the investigation or charges against them, constituted a significant break from the substance of the rest of the government's case-in-chief. Black's extended account of the tragedy could not reasonably be considered part of "the res gestae, the narrative" of the government's case against the defendants. Pepin, 514 F.3d at 208. Therefore, omitting Black's testimony would not have disrupted the narrative flow of the government's trial evidence.[18] Furthermore, an eyewitness account of a violent, destructive, and fatal suicide bombing seems quite clearly to "involve conduct more inflammatory than the charged crime[s]." United States v. Paulino, 445 F.3d 211, 223 (2d Cir.2006) (quoting United States v. Livoti, 196 F.3d 322, 326 (2d Cir.1999)). Indeed, the government's extended presentation of Black's testimony, supplemented by photos and video, amounted to a blatant appeal to the jury's emotions and prejudices.[19]
*162 Even if the district court properly admitted Black's testimony for the proffered purpose  to show that a bombing actually occurred, just as Siyam said it had  the court erred in allowing the testimony to continue after that fact was established. After Black stated that a "huge explosion" occurred at the front of the bus, defense counsel repeatedly objected to any further testimony. The subsequent details about and images of the wreckage and the death of Black's cousin were even less probative as to the issues at trial, and much more prejudicial. Nor can we find, as we typically have done in rejecting Rule 403 challenges to the admission of evidence, that a limiting instruction mitigated the prejudicial effect of the testimony. See, e.g., United States v. Elfgeeh, 515 F.3d 100, 127 (2d Cir.2008); Paulino, 445 F.3d at 223; United States v. Downing, 297 F.3d 52, 59 (2d Cir.2002); Livoti, 196 F.3d at 326. The district court rejected the instruction proposed by Al-Moayad's counsel, which would have informed the jury that "there is no evidence nor allegation that either defendant had anything to do with the bus bombing [of] which Mr. Black and his cousin were victims." Instead, the district court proposed the following vague, tendentious instruction: "You have heard the testimony of a bus bombing, you will determine based on the evidence or lack of evidence who was responsible for that incident. You will also determine what that incident has to do or not to do with the allegations in the indictment." Because neither the bombing nor any other terrorist attack was part of the charges against the defendants, it would have been inappropriate for the jury to determine "based on the evidence or lack of evidence" who was responsible for the attack, and it was reasonable at that point for Al-Moayad's counsel to withdraw his request for a limiting instruction. Therefore, the district court ultimately provided no guidance to the jury that might have mitigated the self-evident prejudicial effect of Black's testimony.

2. Yahya Goba testimony
The district court also erred in allowing Yahya Goba to testify about his experiences at the Al-Qaeda training camp in Afghanistan. With regard to Goba, the district court seems simply to have failed to make the required "conscientious assessment" of the testimony's prejudicial effect in comparison with its probative value, without which we have no adequate basis for deferring to the district court's judgment. This omission stemmed, at least in part, from the government's misleading proffer as to what Goba would say. In addition, the court repeatedly and over objection allowed Goba to continue testifying far beyond the proffer, without providing any indication of how (or whether) it had performed the Rule 403 assessment.
In theory, the government offered Goba's testimony to provide additional authentication of the mujahidin form, although the form had already been authenticated and admitted into evidence during Agent Hale Keenan's testimony. Before Goba took the stand, Al-Moayad's counsel raised a concern that "they intend to ask this gentleman what the business practices of this Al-Qaeda training camp was, what *163 it means if your name is in a certain slot on one of these forms ... it seems to me this is beyond the scope of his ability to be able to testify. ..." Counsel for the government then assured the court that "we're not going to ask him about the business practices of the Al-Qaeda training camp. ... What he will specifically say is that in order to get into that camp, he knew he had to put down the name of somebody known to the camp leaders." Goba did testify about filling out a form identical to the mujahidin form, and about listing as his reference the individual who sent him to the camp.
However, as described above, Goba's testimony continued well beyond the government's proffer. Al-Moayad's counsel interposed numerous objections throughout. While several of these were sustained, the court never appears to have assessed the probative value of the continuing narrative, or required the government to constrain the testimony to the scope of its proffer. For example, early in the examination but well after Goba discussed the application form, defense counsel stated, "we're learning about this gentleman's experience in the camp that is unrelated to anything involving the defendant in this case." The court received that objection without comment, and the testimony continued. As to the Al Jazeera video of Bin Laden's visit, defense counsel objected, "[t]his is further evidence offered in support of testimony which was irrelevant to start with and much of which was already excluded." The court responded that "[i]t's only three minutes. I am going to allow it." The court also summarily and without comment denied defense counsel's Rule 403 objection.
Goba's testimony about the camp, and particularly the government's presentation of images of Bin Laden and Al-Zawahiri, was highly inflammatory and irrelevant, and should not have been permitted by the district court. The government presented no evidence linking Goba to Al-Moayad, and yet his extensive testimony was admitted against Al-Moayad as part of the government's rebuttal case. Even if Goba's testimony had some value in authenticating the mujahidin form, we have no assurance that the court conscientiously balanced the probative value of the testimony against its prejudicial effect, given the court's failure to explain. Nor do we think that, had the court performed that weighing analysis, it could have rationally concluded that the account of the events occurring at the training camp, including testimony about visits by Bin Laden and his associates, was admissible. Finally, as with Black's testimony, the prejudicial effect of Goba's statements was not mitigated by any limiting instruction to the jury.

3. Harmless error
In sum, we conclude that the probative value of the Black and Goba testimony was far outweighed by its unfair prejudice, which the Supreme Court has described as "an undue tendency to suggest decision on an improper basis, commonly, though not necessarily, an emotional one." Old Chief, 519 U.S. at 180, 117 S.Ct. 644 (quoting Fed.R.Evid. 403 advisory committee's note). Further, the district court's error in admitting the testimony was not harmless as to the issue of the defendants' predisposition and, therefore, their entrapment defense.[20]See Arlio v. Lively, 474 F.3d 46, 51 (2d Cir.2007) (holding that even when an evidentiary ruling constitutes *164 an abuse of discretion, "a new trial should be granted only if a substantial right of a party is affected  as when a jury's judgment would be swayed in a material fashion by the error."). Consequently, we must vacate the defendants' convictions on the conspiracy and attempt counts.
A district court's erroneous admission of evidence is harmless "if the appellate court can conclude with fair assurance that the evidence did not substantially influence the jury." United States v. Garcia, 291 F.3d 127, 143 (2d Cir.2002) (quoting United States v. Rea, 958 F.2d 1206, 1220 (2d Cir.1992)). In conducting a harmless error review of inadmissible evidence, we consider the following factors: "(1) the overall strength of the prosecution's case; (2) the prosecutor's conduct with respect to the improperly admitted evidence; (3) the importance of the wrongly admitted [evidence]; and (4) whether such evidence was cumulative of other properly admitted evidence." United States v. Kaplan, 490 F.3d 110, 123 (2d Cir.2007) (quoting Zappulla v. New York, 391 F.3d 462, 468 (2d Cir.2004)); see also United States v. Garcia, 413 F.3d 201, 217 (2d Cir.2005). All four harmless error factors tilt strongly in the defendants' favor.
First, the government's evidence on predisposition was not overwhelming, and significant parts of it were inadmissible. See United States v. Jean-Baptiste, 166 F.3d 102, 110 (2d Cir.1999) (stating that a district court's improper admission of evidence constituted harmful error where "the government's properly admitted evidence, though sufficient, was not overwhelming."). Much of the evidence that the government presented during its rebuttal case, which was expressly intended to counter the entrapment defense by demonstrating predisposition, was improperly admitted (including, of course, the Goba testimony, which was the centerpiece of the government's rebuttal case). For example, we conclude below that the district court should not have admitted the mujahidin form, and the court's error in admitting the Croatian will, while harmless when considered in isolation, nevertheless contributed to the cumulative unfairness of the trial. We also determine below that the district court erroneously admitted  during the government's examination of Al-Anssi, when it was attempting to rehabilitate his crucial testimony as to the defendants' predisposition  the Siyam wedding speech and Al-Anssi's notes. The notes in particular were highly probative as to Al-Moayad's and, by extension, Zayed's predisposition to support terrorism.[21]
As further evidence of predisposition, the government cited the portion of the Frankfurt tapes showing the defendants laughing after the informants brought up Siyam's reference to the suicide bombing, arguing to the jury during its rebuttal summation that "[t]hey laugh because they support that type of activity. ... You think for a moment prior to Frankfurt they weren't inclined to support terrorist activities? Watch that video. Talk about a ready response, they're all over it." In our view, the fact that the defendants laughed with the informants constituted only equivocal evidence of predisposition, especially given Al-Anssi's admission at trial that he might *165 have laughed first to encourage the defendants to believe that he was happy about the suicide bombing. The government also points to Al-Moayad's list of money sources in the United States as evidence of predisposition. However, no evidence at trial demonstrated that any money sent to Al-Moayad through these sources was funneled into supporting terrorism. Further, although Al-Moayad stated during the Frankfurt meetings that he and Saeed were working in the same "field," on balance Al-Moayad's repeated statements regarding his desire to use Saeed's money for charitable purposes, as well as the defendants' privately expressed reservations about Saeed, do not convincingly demonstrate their predisposition to commit the crimes charged.
The defendants' admitted ties to Hamas figures, the appearance in Al-Moayad's address book of names connected with Hamas, and the four charity receipts that Al-Moayad gave to Al-Anssi (which we discuss further below) are, to be sure, some evidence of predisposition. However, this showing is not overwhelming, especially in comparison with the likely impact of Black's and Goba's extensive testimony suggesting that the defendants were linked with a deadly Hamas bombing and with Bin Laden and Al-Qaeda training camps. Overall, we conclude that the prosecution's predisposition case was not strong enough to assure us that the jury was not substantially influenced by the court's improper admission of the Black and Goba testimony.
The remaining three harmless error factors also tilt in the defendants' favor. As to the second factor, we find that the government's conduct with respect to the Black and Goba testimony likely increased the prejudicial effect of that evidence. During both examinations, the government continuously attempted (with a great deal of success) to elicit testimony well beyond the scope of its proffer for each witness. The government also referred repeatedly to Black and Goba in its arguments to the jury. For example, in her opening, counsel for the government was apparently openly emotional as she described how Black "knelt beside his best friend and watched the life begin to pour out of him from a head wound ... When you see them clapping and cheering and reminiscing about the announcement of that attack at their group wedding, think of Gideon Black and the testimony you'll be hearing from him."
With regard to the third factor, the government treated the Black and Goba testimony as important evidence, although it was only tangentially related to the charges against the defendants. Both witnesses testified at considerable length. In addition, the government prominently positioned their testimony: Black was the last witness in the government's case-in-chief, and Goba was the second-to-last witness on rebuttal. We have further indication that the testimony played an important role in the trial because, after the jury began deliberations, one of its first requests was for Goba's testimony and "testimony of all Al-Qaeda training camps." Finally, Black's account of the bus bombing and Goba's description of the Al-Qaeda training camp constituted unique evidence not duplicated elsewhere in the government's trial presentation.
We have stated that "[o]nly rarely-and in extraordinarily compelling circumstances  will we, from the vista of a cold appellate record, reverse a district court's on-the-spot judgment concerning the relative weighing of probative value and unfair effect." Awadallah, 436 F.3d at 134 (quoting United States v. Conley, 186 F.3d 7, 16 (1st Cir.1999)). This case presents such circumstances. As we observed in Elfgeeh, *166 "[t]here can be little doubt that in the wake of the events of September 11, 2001, evidence linking a defendant to terrorism in a trial in which he is not charged with terrorism is likely to cause undue prejudice." Elfgeeh, 515 F.3d at 127. In this case, the defendants were charged with conspiring to, attempting to, and providing material support to Hamas and Al-Qaeda, but not with violent terrorist acts like the deadly bus bombing about which Black testified. Given the inflammatory, highly charged, and extensive nature of Black's and Goba's testimony, we believe there was a significant danger that it caused undue prejudice, and "lure[d] the fact finder into declaring guilt on a ground different from proof specific to the offense charged." Awadallah, 436 F.3d at 133 (quoting Old Chief, 519 U.S. at 180, 117 S.Ct. 644).
As was the case in United States v. Harvey, 991 F.2d 981 (2d Cir.1993), "[t]hough the evidence of predisposition was not insubstantial, the jury faced a fair issue as to whether predisposition was proven beyond a reasonable doubt, and we are unwilling to conclude that the jury would have convicted in the absence of the prejudicial evidence gratuitously presented by the prosecutor." Id. at 996-97. The district court's error in admitting the testimony was not harmless, and we must therefore vacate the defendants' convictions on the conspiracy and attempt charges.[22]

B. Al-Anssi's notes
Al-Anssi's handwritten notes purportedly memorialize the content of his initial meeting with Agent Murphy in Washington and his conversations with Al-Moayad in Yemen. See supra Part I.C.1. The government argued, over the defendants' objections, that the notes were admissible as prior consistent statements and to rebut a misleading impression created during Al-Anssi's testimony that no document supported his claims about the defendants' predisposition. The district court admitted the notes without limitation as substantive evidence.[23] Because the court did not explain the basis for its ruling, we *167 cannot be sure whether it admitted the notes as prior consistent statements or to rebut a false impression. In either case, the court clearly erred. See, e.g., United States v. Padilla, 203 F.3d 156, 161 (2d Cir.2000) ("We review a district court's admission of alleged hearsay evidence only for `clear error.'"). Further, this error was not harmless.

1. Inadmissibility as prior consistent statements
At trial, the government did not argue that the notes were not hearsay, but invoked Federal Rule of Evidence 801(d)(1)(B), which provides that an out-of-court statement may be admitted for its substance if "[t]he declarant testifies at the trial or hearing and is subject to cross-examination concerning the statement, and the statement is ... consistent with the declarant's testimony and is offered to rebut an express or implied charge against the declarant of recent fabrication or improper influence or motive." Rule 801(d)(1)(B) also includes a fundamental temporal requirement: "The statement must have been made before the declarant developed [an] alleged motive to fabricate." United States v. Forrester, 60 F.3d 52, 64 (2d Cir.1995) (citing Tome v. United States, 513 U.S. 150, 156, 115 S.Ct. 696, 130 L.Ed.2d 574 (1995)); see also United States v. Wilkerson, 361 F.3d 717, 725 n. 3 (2d Cir.2004). A prior consistent statement made after an improper motive exists is simply "not within the scope" of Rule 801(d)(1)(B). Forrester, 60 F.3d at 64.
If the district court admitted Al-Anssi's notes for their substance as prior consistent statements, it erred in doing so, as the notes do not satisfy the temporal requirement of the Rule. Al-Anssi created the notes after a significant motive to fabricate arose, namely the large amount of money he expected and was paid to furnish information to the FBI. The government does not challenge the proposition that Al-Anssi had a motive to fabricate the notes when he created them. However, the government asserts that the notes were nonetheless admissible to rehabilitate Al-Moayad's credibility.
Our case law makes clear that prior consistent statements that do not meet the requirements of Rule 801(d)(1)(B) can indeed be admitted for rehabilitation if appropriately limited, but are inadmissible as substantive evidence.[24]See Phoenix Assocs. *168 III v. Stone, 60 F.3d 95, 103 (2d Cir.1995) (distinguishing the use of prior consistent statements to rehabilitate the credibility of a witness from admission of the statements for their substance); see also 5 Jack B. Weinstein & Margaret A. Berger, Weinstein's Federal Evidence § 801.22[1][a], 801.22[2] (Joseph M. McLaughlin, ed., 2d ed.2008) (outlining the requirements for admission of a prior statement as substantive evidence under Rule 801(d)(1)(B), and noting that "[s]ome courts hold that the requirements of Rule 801(d)(1)(B) do not apply if a prior consistent statement is admitted for the limited purpose of rehabilitation."). For example, in United States v. Castillo, 14 F.3d 802 (2d Cir.1994), we held that the admission of hearsay as a prior consistent statement was permissible where it "was admitted for the limited purpose of clarifying the apparent contradiction brought out during cross-examination." Id. at 806 (emphasis added). In that case, we also noted that both the court and the government informed the jury that the statement was not being introduced and should not be considered for its truth. Id.
In this case, it is undisputed that Al-Anssi's notes were admitted without limitation as substantive evidence. Under our precedents, the district court erred in doing so, given Al-Anssi's preexisting motive to fabricate.

2. Inadmissibility to rebut a false impression
The government also argues that the notes were admissible to correct a false impression created during the defendants' examinations of Al-Anssi, namely that no document supported Al-Anssi's testimony about his meetings with Al-Moayad in Yemen and about Al-Moayad's predisposition to support terrorism. If the court intended to admit the notes on this ground (which is not at all obvious), our precedents are clear that it was required to admit them for a limited purpose only.
In arguing that the notes were properly admitted, the government relies on cases stating that "[r]edirect examination may be used to rebut false impressions that arise from cross examination, and the scope of such an examination is a matter confided to the district court's discretion." United States v. Wiley, 846 F.2d 150, 156 (2d Cir.1988) (internal citations omitted); see also United States v. Vasquez, 267 F.3d 79, 85 (2d Cir.2001); United States v. Naiman, 211 F.3d 40, 51 (2d Cir.2000); United States v. Bilzerian, 926 F.2d 1285, 1296 (2d Cir.1991); cf. United States v. Martinez, 775 F.2d 31, 37 (2d Cir.1985). These cases involve challenges to a redirect examination when a court has admitted evidence that exceeds the scope of the preceding cross-examination, because the evidence was relevant to correct a false impression created during that cross-examination.
These cases also demonstrate, however, that otherwise inadmissible evidence may be used to rebut a false impression only if the evidence is carefully limited. For example, in Martinez, we held that guilty pleas introduced during a redirect examination *169 were admissible to rebut a false impression because they were not admitted for their truth but rather to shed light on whether a witness's testimony was credible. Martinez, 775 F.2d at 37. Therefore, Al-Anssi's notes could potentially have been admissible to correct a false impression only if the notes were admitted not for their truth but for the limited purpose of rebuttal, and the jury was appropriately instructed. Here, the district court admitted the notes without limitation and in their entirety as substantive evidence. It was error to do so.[25]
The distinction between admitting Al-Anssi's notes for their substance or truth and admitting them for a specified limited purpose is by no means a technical one. When erroneously admitted for their truth, the notes assumed essentially the same status as Al-Anssi's trial testimony, but were not subject to the same "devices for ensuring [the] accuracy" of in-court testimony: the witness oath, the opportunity to be observed by the adverse party, and cross-examination. 5 Weinstein's Federal Evidence § 802.02[3]. Even if the notes were potentially admissible for limited, non-substantive purposes, which we do not concede, the jury should have been admonished not to consider them for their truth, and received guidance as to the properly circumscribed use and value of the evidence. The jury received no such guidance, and was therefore free to consider the notes  which were hearsay  as the equivalent of any of the other properly admitted trial evidence. Indeed, the government used the notes basically as a substitute for Al-Anssi's testimony, repeatedly supporting its arguments with assertions from the notes rather than with Al-Anssi's statements on the stand. See supra note 23. The admission of the notes without limitation constituted clear error.

3. Admission of the notes was not harmless as to Al-Moayad's conviction on providing material support to Hamas
The district court's erroneous admission of Al-Anssi's notes as substantive evidence was not harmless. Given the importance of the notes to the government's case, the fact that they buttressed the testimony of a witness whose credibility had otherwise been severely damaged, and their direct relevance to Al-Moayad's conviction on providing material support to Hamas, we cannot "conclude with fair assurance that the [notes] did not substantially influence the jury" on that count. Garcia, 291 F.3d at 143 (quoting United States v. Rea, 958 F.2d 1206, 1220 (2d. Cir.1992)); see also Kotteakos v. United States, 328 U.S. 750, 765, 66 S.Ct. 1239, 90 *170 L.Ed. 1557 (1946) (holding that "if one cannot say, with fair assurance, after pondering all that happened without stripping the erroneous action from the whole, that the judgment was not substantially swayed by the error, it is impossible to conclude that substantial rights were not affected.").
Most of the harmless error factors tilt against the government. We first review the government's evidence with regard to Al-Moayad's conviction for providing material support. In its main summation, the government pointed to only two sources of proof on that charge: Al-Moayad's statements in Frankfurt, including his descriptions of his ties to individuals in Hamas, and Al-Anssi's claim that Al-Moayad told him he gave $3.5 million to Hamas (a figure that came not from the Frankfurt tapes but only from Al-Anssi's own notes and testimony). On rebuttal, the government again highlighted Al-Anssi's claim that Al-Moayad admitted to donating $3.5 million to Hamas. The government then cited the four charity receipts, the appearance in Al-Moayad's address book of phone numbers for Hamas leaders, Mohammed Siyam's wedding speech, Al-Moayad's relationship with Hamas figure Khaled Meshal, and Al-Moayad's position as president of the Al-Aqsa foundation, which the government described as "another front for Hamas."
This evidence is not overwhelming. The information regarding Al-Moayad's connections to individuals in Hamas and Mohammed Siyam's wedding speech constituted only inconclusive proof that Al-Moayad actually provided material support to that organization. As to Al-Moayad's position as the president of the Al-Aqsa foundation, the government produced no direct evidence at trial that Al-Aqsa really was merely a front for Hamas, or that it ever funneled money to support Hamas's terrorist activities. With regard to the four charity receipts, as Al-Moayad points out, these receipts make no mention of Hamas, the government's evidence did not directly establish that the contributions listed in the receipts actually went towards providing material support to Hamas's terrorist activities (rather than to charitable groups), and the significance of the receipts was contested at trial. See Jean-Baptiste, 166 F.3d at 109 (in finding that the erroneous admission of evidence was not harmless, noting that although the government's properly admitted evidence on a particular issue was "legally sufficient on its face ... the import of that evidence was disputed.") Overall, when reviewing the government's evidence on the charge of providing material support to Hamas, we cannot say with reasonable assurance that without the notes, the jury would have decided that Al-Moayad was guilty on this count beyond a reasonable doubt.
The remaining three factors also compel us to find that the error was not harmless. As discussed above, the government relied heavily on the notes in its summations and twice highlighted Al-Moayad's alleged $3.5 million donation to the jury as proof that he provided material support to that organization. See id. at 110 (listing the government's reliance on the improperly admitted evidence in its summation as a factor in finding harmful error). The notes were important, as they buttressed Al-Anssi's testimony on key points that were unquestionably central to the charge of providing material support to Hamas. See United States v. Grinage, 390 F.3d 746, 751 (2d Cir.2004) ("Where the erroneously admitted evidence goes to the heart of the case against the defendant, and the other evidence against the defendant is weak, we cannot conclude that the evidence was unimportant or was not a substantial factor in the jury's verdict."); Forrester, 60 F.3d at 64-65 ("Error going `to the heart' of a critical issue is less likely to be harmless." (quoting United States v. Tussa, 816 F.2d 58, 67 (2d Cir. *171 1987))). For example, the notes constituted the only support for Al-Anssi's claim that Al-Moayad gave $3.5 million to Hamas, and the notes reinforced Al-Anssi's claim that the four charity receipts actually represented donations to Hamas, a point that was not clearly established elsewhere in the government's evidence. Finally, the notes cannot be viewed as simply cumulative of Al-Anssi's testimony, given that Al-Anssi's credibility was subjected to significant attacks by the defendants, which the government attempted to remedy by introducing the notes.
In sum, we cannot conclude that the jury may not have been significantly affected by the admission of Al-Anssi's notes. Despite the probative force that the charity receipts, the tapes, or other evidence may have had, it is apparent to us that Al-Anssi's notes were of considerable significance "in relation to everything else the jury considered on the issue in question, as is revealed in the record." Garcia, 291 F.3d at 144 (quoting United States v. Rea, 958 F.2d 1206, 1220 (2d Cir.1992)); see also Kaplan, 490 F.3d at 123. As in Garcia, "[t]he evidence [on the charge of providing material support to Hamas] was largely circumstantial and not so overwhelming to allow us to conclude that the jury would have found [Al-Moayad] guilty" without considering his notes. Garcia, 291 F.3d at 145; see also Grinage, 390 F.3d at 752 (in finding harmful error, noting that the evidence against a defendant was "thin" and "weak"). Because the introduction of Al-Anssi's notes as substantive evidence was not harmless as to the charge that Al-Moayad provided material support to Hamas, we vacate Al-Moayad's conviction on that count.

4. Admission of the notes was not harmless as to the defendants' entrapment defense
The defendants also contend that the erroneous admission of the notes requires that we vacate their convictions on the conspiracy and attempt counts. We have already concluded above that the improper admission of the Black and Goba testimony compels us to vacate those convictions. Similarly, we find that the district court's error in admitting the notes was not harmless as to predisposition and therefore the entrapment defense, and constitutes an additional ground for vacating the defendants' convictions on the conspiracy and attempt counts.
We have already determined that the government's other evidence on predisposition was largely inadmissible and not overwhelming. See supra Part II.A.3. The substance of Al-Anssi's notes, by contrast, was highly probative as to the defendants' predisposition, and enabled the government to bolster its otherwise problematic evidence on that issue. Several assertions in the notes that were critical to the government's predisposition case were not duplicated anywhere else in the government's evidence except for Al-Anssi's testimony. As stated earlier, these assertions include, inter alia, Al-Moayad's purported ties to Sheikh Abdul Majid Al-Zindani, his past responsibility for choosing volunteers to fight abroad (a claim that Al-Moayad himself did not make either during the taped conversations in Frankfurt or in his post-arrest statement), his knowledge while still in Yemen that "Saeed" specifically wanted to support the armed mujahidin, an assertion that Al-Moayad's counsel contested in marshaling his entrapment defense, and Al-Moaayd's alleged statements that he gave millions to Hamas and Al-Qaeda.
The notes were also critically important on the issue of Al-Moayad's relationship with Bin Laden, as they were the government's only source suggesting that Al-Moayad maintained close ties with Bin *172 Laden and financially supported Al-Qaeda in the few years before the events of September 11, 2001. During his testimony at trial, Al-Anssi himself was unable to identify the time frame during which Al-Moayad professed to have supported Bin Laden, and as we have already noted, Al-Moayad and Zayed both clarified during the Germany meetings (and Al-Moayad strongly suggested in his post-arrest statement) that Al-Moayad's relationship with Bin Laden did not extend past the 1980s.[26] Such a distinction could undoubtedly color a jury's view of the charges against Al-Moayad, and of his predisposition to support terrorist activities.
We have found that "[e]ven if an appellate court is without doubt that a defendant is guilty, there must be a reversal if the error is sufficiently serious." Forrester, 60 F.3d at 65 (quoting Tussa, 816 F.2d at 67). Like the admission of the Black and Goba testimony, the admission of Al-Anssi's notes as substantive evidence was a serious error. The notes contained much of the government's strongest, most direct evidence regarding Al-Moayad's predisposition and significantly buttressed Al-Anssi's trial testimony, which had been impeached by the defendants. As we have already noted, the government cited the notes repeatedly in its main and rebuttal summations, both as corroboration and as independent evidence of Al-Moayad's guilt. See supra note 23. For these reasons, we cannot be "sure that the [erroneous admission of the notes as substantive evidence] did not influence the jury, or had but very slight effect." Kaplan, 490 F.3d at 122 (quoting Kotteakos, 328 U.S. at 764, 66 S.Ct. 1239). Therefore, we conclude that the improper admission of the notes was not harmless, and constitutes an additional ground upon which to vacate the defendants' conspiracy and attempt convictions. See infra Part II.E.

C. Mujahidin Form, Wedding Speech, and Croatian Documents
The defendants assert that the district court erroneously admitted the mujahidin form, Siyam wedding speech, and Croatian documents. We agree that the district court erred in admitting these items without limitation as substantive evidence.

1. Mujahidin form
During the government's rebuttal case, the district court admitted the mujahidin form, which purported to link Al-Moayad to Al-Qaeda by showing that Al-Moayad had sponsored a mujahidin fighter to attend an Al-Qaeda training camp. The court admitted the form (against Al-Moayad only) without limitation as substantive evidence and without explaining its ruling, over Al-Moayad's hearsay, relevance, and authenticity objections.

a. Authenticity
The government argues that the form was properly authenticated. We agree. Under Federal Rule of Evidence 901(a), "[t]he requirement of authentication or identification as a condition precedent to admissibility is satisfied by evidence sufficient to support a finding that the matter in question is what its proponent claims." We have often commented that "[t]he bar for authentication of evidence is not particularly high," Gagliardi, 506 F.3d at 151, and proof of authentication may be direct or circumstantial. See, e.g., United States v. Tin Yat Chin, 371 *173 F.3d 31, 37 (2d Cir.2004); United States v. Maldonado-Rivera, 922 F.2d 934, 957 (2d Cir.1990). Rule 901 is satisfied "if sufficient proof has been introduced so that a reasonable juror could find in favor of authenticity or identification." SCS Commc'ns, Inc. v. Herrick Co., 360 F.3d 329, 344 (2d Cir.2004) (quoting United States v. Dhinsa, 243 F.3d 635, 658 (2d Cir.2001)).
Agent Hale Keenan described how the documents she received from Afghanistan, including the mujahidin form, were collected, received, sorted, analyzed, and sent to the United States. This testimony was sufficient to demonstrate that the form was likely what the government claimed it to be-an application form for admittance to a mujahidin training camp, which had been seized in an area of Afghanistan where Al-Qaeda maintained training facilities. The district court correctly concluded that the mujahidin form was properly authenticated.

b. Co-conspirator exception to hearsay rule
The government argues that even though the mujahidin form was hearsay, it was nevertheless admissible as "a statement by a coconspirator of a party during the course and in furtherance of the conspiracy." Fed.R.Evid. 801(d)(2)(E). According to the government, "there existed an Al-Qaeda conspiracy to recruit and train Mujahidin and ... Al-Moayad directly participated in that conspiracy by, among other things, sponsoring Mujahidin for training with Al-Qaeda." We disagree that the form could be admitted as a co-conspirator statement.
We review a district court's finding that hearsay is admissible under the co-conspirator exception for clear error. Maldonado-Rivera, 922 F.2d at 959. To admit hearsay testimony under Rule 801(d)(2)(E), the district court "must find (a) that there was a conspiracy, (b) that its members included the declarant and the party against whom the statement is offered, and (c) that the statement was made during the course of and in furtherance of the conspiracy." United States v. Alameh, 341 F.3d 167, 176 (2d Cir.2003) (quoting Maldonado-Rivera, 922 F.2d at 958); see also 5 Weinstein's Federal Evidence § 801.34[6][c][i] ("The existence and membership of a conspiracy are preliminary questions of fact that must be resolved by the district court before a challenged statement may be admitted under Rule 801(d)(2)(E)."). The court must find these preliminary facts by a preponderance of the evidence. Bourjaily v. United States, 483 U.S. 171, 176, 107 S.Ct. 2775, 97 L.Ed.2d 144 (1987). "[W]hile the hearsay statement itself may be considered in establishing the existence of the conspiracy, `there must be some independent corroborating evidence of the defendant's participation in the conspiracy.'" United States v. Gigante, 166 F.3d 75, 82 (2d Cir.1999) (quoting United States v. Tellier, 83 F.3d 578, 580 (2d Cir.1996)); see also United States v. Desena, 260 F.3d 150, 158 (2d Cir.2001).
In this case, the district court did not satisfy the requirements of Rule 801(d)(2)(E). The court made no findings, by a preponderance of the evidence or otherwise, about the existence of a conspiracy including Al-Moayad and the individual who filled out the mujahidin form ("Abu Jihad"), nor do we think the court could have done so based on the record before us. Contrary to the government's contention, the record fails to demonstrate Al-Moayad's "longstanding participation in a conspiracy to provide material support to Al-Qaeda," other than some indication that Al-Moayad had a relationship with Bin Laden sometime in the past. The form *174 itself, given that it provides no information about Abu Jihad's relationship with Al-Moayad other than the fact that he wrote Al-Moayad's name as his recommender, is not competent proof of their joint involvement in a conspiracy. Indeed, we do not know if Al-Moayad even knew Abu Jihad, or was aware that Abu Jihad listed him on the form. The district court had virtually no basis for admitting the mujahidin form for its substance as a co-conspirator statement.

c. Admissibility to rebut false impression
Alternatively, the government, citing Vasquez, Bilzerian, and Martinez, argues that the mujahidin form was properly admitted to rebut the false impression that no evidence corroborated Al-Anssi's testimony regarding Al-Moayad's predisposition and previous support for terrorist activity. We have already explained that these cases do not permit a district court to admit otherwise inadmissible hearsay as substantive evidence. See supra Section II.B.2. Therefore, even if the mujahidin form were proper rebuttal evidence, the district court would still have clearly erred in admitting the form without limitation for its substance.
More to the point, the government misinterprets these cases. They concern the scope of the evidence that may be introduced on redirect examination to rebut a specific false impression that was created during cross-examination. Nothing in those cases would permit the government, as it attempts to do here, to introduce hearsay evidence in its rebuttal case to counter a purportedly false impression created during the defendants' case-in-chief. Neither is the form admissible as substantive evidence to rebut Al-Moayad's entrapment defense.
"[A]ny improper admission of co-conspirator testimony is subject to harmless error analysis." United States v. Monteleone, 257 F.3d 210, 221 (2d Cir. 2001). Although the district court's admission of the mujahidin form was in error, we must conclude after applying the Kaplan factors that the error if considered in isolation was harmless. The second Kaplan factor, the prosecutor's conduct with respect to the improperly admitted evidence, weighs in favor of Al-Moayad; the government repeatedly mentioned the mujahidin form in its rebuttal summation and pointed to the form as evidence not only of Al-Moayad's alleged provision of support to Al-Qaeda, but also of his predisposition. However, the form was only one among several pieces of evidence that the government put forth as to Al-Moayad's predisposition, suggesting that the form was at least somewhat cumulative. Additionally, the government points with some persuasive force to the fact that Al-Moayad was acquitted on the charge of providing material support to Al-Qaeda.
Overall, the factors lead us to conclude that although erroneous, the district court's admission of the mujahidin form was ultimately harmless. We determine below, however, that in combination with other serious trial errors, the improper admission of the form cast sufficient 10 doubt on the fairness of the trial as to warrant new proceedings. See infra Section II.E.

2. Mohammed Siyam wedding speech
Prior to its cross-examination of Al-Anssi, the government re-offered the video of the group wedding and Mohammed Siyam's speech. The court admitted the video without limitation over Al-Moayad's objections on hearsay and Rule 403 grounds. The government asserts that the video was admissible as a co-conspirator *175 statement, to rebut the false impression that no document or recording supported Al-Anssi's testimony about Al-Moayad's previous involvement in terrorist activities, and as evidence of the defendants' knowledge that Hamas engages in terrorist acts.
For many of the same reasons we discussed with regard to the mujahidin form, the wedding video was not properly admitted under the co-conspirator statement exception to the hearsay rule. No independent evidence showed that either defendant was involved in a joint conspiracy with Mohammed Siyam, other than their general ties to Hamas.[27] The video itself was some evidence of a connection between the defendants and Siyam, showing that the defendants helped to organize a wedding at which Siyam spoke and referred to a suicide bombing. However, these facts standing alone fall well short of meeting the criteria discussed above for the admission of evidence under Rule 801(d)(2)(E).[28]
As to the government's professed non-hearsay uses of the wedding video-to rebut a false impression created during the defendants' examinations of Al-Anssi, and to demonstrate the defendants' knowledge of Hamas's terrorist activities and their predisposition to commit the charged crimes none of these uses justifies the district court's admission of the video for its substance, without limitation. Nevertheless, if admission of the video were the court's only evidentiary error, we would find no cause for reversal of the defendants' convictions, as the video was largely cumulative of other properly admitted evidence and the jury had already been exposed to much of the substance of the video even before it was introduced into evidence.[29] However, we have already found that the erroneous admission of the Black and Goba testimony and Al-Anssi's notes were sufficiently prejudicial as to warrant reversal. We conclude further that against the backdrop of the district court's other evidentiary errors, the improper admission of the wedding video as substantive evidence contributed to the overall unfairness of the trial. See infra Part II.E.

3. Croatian documents
During the government's rebuttal case, the court admitted the Croatian documents, including two address books containing *176 Al-Moayad's phone number and a last will and testament. The court admitted the documents without limitation against Al-Moayad, over his counsel's hearsay, relevance, and authenticity objections. On appeal, Al-Moayad maintains that the documents were irrelevant and, with respect to the last will and testament, inadmissible hearsay. The government maintains that the documents were offered for non-hearsay purposes.[30]
The address books were not hearsay. The government did not rely on them to establish that the phone number listed next to Al-Moayad's name was, in fact, his phone number. We also conclude that, under the very low standard for relevance, evidence that Al-Moayad's name and contact information appeared in the address books of two men identified as mujahidin fighters was at least marginally relevant to the allegations in this case. See United States v. Quattrone, 441 F.3d 153, 188 (2d Cir.2006) ("[S]o long as a chain of inferences leads the trier of fact to conclude that the proffered submission affects the mix of material information, the evidence cannot be excluded at the threshold relevance inquiry."). Relevancy determinations lie within the "broad discretion" of the district court, and "we will not reverse its ruling absent abuse of discretion indicative of arbitrariness or irrationality." United States v. Quinones, 511 F.3d 289, n. 311 (2d Cir.2007). Under this standard, the district court did not act arbitrarily or irrationally in admitting the address books.
The last will and testament is another matter. The document was hearsay, and the government used the will for its substance. During its rebuttal summation, the government argued, "[I]f you look through the translations of these materials, one of these men has a will. In his will he basically says he's going to die as a martyr. That's what he's there for. These guys are Mujahidin. ..." The will would not have been admissible for its truth as a co-conspirator statement. The government's evidence, including the will itself, was insufficient to establish that Al-Moayad and the individual from whom the will was seized were engaged in a shared criminal activity, even a general conspiracy to support Al-Qaeda. The district court therefore clearly erred in admitting the will as substantive evidence.
As with the mujahidin form and wedding video, however, were we considering the admission of the will in isolation, we would be inclined to conclude that it was not especially detrimental to the overall fairness of the trial. Although the will was relevant to Al-Moayad's predisposition, we think it was significantly less prejudicial and important than Al-Anssi's notes, the mujahidin form, and the wedding video. Second, the testimony of the Croatian intelligence officer sufficiently established without reference to the will-that the will was seized from a mujahidin fighter. Therefore, the will was cumulative evidence of its author's identity as mujahidin. We have, however, already identified several other serious evidentiary errors that tainted the trial and the defendants' convictions. In conjunction with these, the admission of the will added to the unfairness of the proceedings to which the defendants were subjected.

D. Derivative Entrapment Issue
Zayed contends that the district court erroneously denied his motions for a curative instruction and for reopening of closing *177 arguments, after the government and Zayed's counsel both discussed derivative entrapment in their summations but the court omitted the derivative entrapment instruction from the jury charge. We conclude that the district court did not commit reversible error.
We review Zayed's claims for plain error, as Zayed did not preserve his objections to the jury charge. See, e.g., Jones v. United States, 527 U.S. 373, 388, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999); Fed.R.Crim.P. 52(b). Zayed's requests for a supplemental charge and to reopen summations, articulated after the jury had begun deliberations, did not preserve his arguments for full appellate review, because "[a] party who objects to any portion of the instructions or to a failure to give a requested instruction must inform the court of the specific objection and the grounds for the objection before the jury retires to deliberate." Fed.R.Crim.P. 30(d) (emphasis added).
Zayed's counsel did ask the court, while it was still giving the charge, to instruct the jury to disregard the attorneys' closing arguments as to derivative entrapment. However, this request did not constitute a proper objection to the jury charge, particularly because Zayed's counsel indicated after the charge was completed that he had "[n]o objections or exceptions." We have held that "[a] party who has requested an instruction that has not been given is not relieved of the requirement [under Rule 30] that he state distinctly his objection to the instruction that is given." United States v. Crowley, 318 F.3d 401, 412 (2d Cir.2003) (quoting United States v. Friedman, 854 F.2d 535, 556 (2d Cir.1988)); see also Jones, 527 U.S. at 388, 119 S.Ct. 2090 ("Nor does a request for an instruction before the jury retires preserve an objection to the instruction actually given by the court."). Therefore, Zayed did not properly preserve his objection to the district court's failure to give a curative instruction.
Under plain error review, "relief is not warranted unless there has been (1) error, (2) that is plain, and (3) affects substantial rights." Jones, 527 U.S. at 389, 119 S.Ct. 2090. "Even when an error is plain and affects substantial rights, a reviewing court should only exercise its remedial discretion under Rule 52(b) if the error `seriously affect[s] the fairness, integrity or public reputation of [the] judicial proceedings.'" Crowley, 318 F.3d at 415 (quoting United States v. Olano, 507 U.S. 725, 736, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)). Were we able to engage in a more full-bodied review, we would likely conclude that the district court abused its discretion in failing to give a curative instruction as to derivative entrapment. We recognize the not-insignificant possibility that, after both sides explicitly discussed derivative entrapment in their summations, the jury was confused as to Zayed's direct entrapment defense, which constituted his primary defense to the charges against him.
However, the district court instructed the jury during the government's main summation that "I will give you what the law is. If there is any conflict between what lawyers say is the law and what I say is the law, it is my word that is controlling." The court repeated this admonition during the jury charge, stating that "[i]f any attorney has stated a legal principle different from any that I state to you in my instructions, it is my instructions that you must follow." When viewing the jury charge as a whole, see, e.g., Jones, 527 U.S. at 391, 119 S.Ct. 2090, and given the narrow confines of plain error review, we are unable to conclude that the district court's failure to give a curative instruction as to *178 derivative entrapment sufficiently affected "the fairness, integrity or public reputation" of the trial as to warrant reversal.

E. Cumulative Error
Finally, the defendants argue that the district court's errors, even if they do not warrant relief when considered individually, "when considered collectively denied [the defendants] due process of law and fundamental fairness." We agree.[31]
The Supreme Court has repeatedly recognized that the cumulative effect of a trial court's errors, even if they are harmless when considered singly, may amount to a violation of due process requiring reversal of a conviction. See, e.g., Taylor v. Kentucky, 436 U.S. 478, 487 n. 15, 98 S.Ct. 1930, 56 L.Ed.2d 468 (1978) (finding that "the cumulative effect of the potentially damaging circumstances of this case violated the due process guarantee of fundamental fairness in the absence of an instruction as to the presumption of innocence"); Chambers v. Mississippi, 410 U.S. 284, 302-03, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973) (concluding "that the exclusion of... critical evidence, coupled with the State's refusal to permit Chambers to cross-examine [a witness], denied him a trial in accord with traditional and fundamental standards of due process. ... [U]nder the facts and circumstances of this case the rulings of the trial court deprived Chambers of a fair trial."). The "cumulative unfairness" doctrine is also firmly embedded in this Circuit's precedents. See, e.g., United States v. Guglielmini, 384 F.2d 602, 607 (2d Cir.1967) (holding that, even though not "any one of the errors committed during the trial would have required reversal of the convictions," "the total effect of the errors we have found was to cast such a serious doubt on the fairness of the trial that the convictions must be reversed."); see also United States v. Yousef, 327 F.3d 56, 172 (2d Cir.2003) (per curiam); United States v. Rahman, 189 F.3d 88, 145 (2d Cir.1999) (per curiam); Salameh, 152 F.3d at 157-58; United States v. Fields, 466 F.2d 119, 121 (2d Cir.1972).
We believe that, in the aggregate, the district court's errors deprived the defendants of a fair trial.[32] The district court's cumulated errors in admitting Al-Anssi's notes and the testimony of Gideon Black and Yahya Goba "cast such a serious doubt on the fairness of the trial" as to warrant reversal of the defendants' convictions. That doubt is especially grave when we also take into account the district court's erroneous admission of the mujahidin form, the wedding video, and the Croatian last will and testament, as well as its questionable handling of the derivative entrapment issue.

III. CONCLUSION
For the foregoing reasons, we VACATE the judgments of conviction and REMAND *179 to the district court for further proceedings consistent with this opinion before a different district court judge.[33]
NOTES
[1]  Many different spellings of the Arabic names, words, and phrases that arise in this case appear in the parties' briefs and appendices, the trial transcript, and other sources. For the sake of simplicity, we use only one spelling for each foreign name or word and do not indicate alterations in quotations.
[2]  At trial, the government did not contest the proposition that the bakery and school were charitable endeavors, although Al-Anssi testified that their establishment was politically motivated.
[3]  Al-Anssi testified that Al-Moayad "told me he is the chief of Al-Aqsa organization but from here I understand that is a terrorist organization." However, Al-Anssi was unable during his testimony to explain why he believed Al-Aqsa was affiliated with terrorist activity, and could not identify any statement by Al-Moayad that led him to that conclusion. As shown below, other evidence put forth at trial suggested that Al-Aqsa was a charitable organization that aids needy Palestinians.
[4]  At trial, Al-Moayad and Zayed did not challenge the government's assertion that the word "jihad" refers to a "holy war," but attempted to establish that it could also mean "personal or inner struggle."
[5]  Bin Laden originally founded Al-Qaeda in 1988 to support and train the Sunni Islamic extremist resistance against the Soviet Union in Afghanistan. See, e.g., Office of the Coordinator for Counterterrorism, U.S. Dep't of State, Country Reports on Terrorism2007, Terrorist Organizations (Apr. 30, 2008), available at http://www.state.gov/s/ct/rls/crt/2007/103714.htm. In the late 1980s, the United States supported the Islamic resistance fighters in this campaign by supplying them with weapons. See, e.g., Marvin G. Weinbaum, "Afghanistan," in Encyclopedia Brittanica, available at http://www.britannica.com/eb /print?articleId=106010 & fullArticle=true & tocId=21412. Therefore, the question of when Al-Moayad provided financial support to Al-Qaedain the late 1980s, when the United States was also supporting Bin Laden, or in recent years, when Al-Qaeda has engaged in attacks against United States interests was a crucial issue at trial.
[6]  For example, the following exchange was recorded:

Al-Moayad: No, wait, wait. First thing is the charitable bakery.
[Al-Anssi]: What does it stand for?
Al-Moayad: [Unintelligible] leave it as charitable bakery [unintelligible]. It doesn't stand for anything because....
[Al-Anssi]: Yeah.
Zayed: The bakery and the school are real entities.
[Al-Anssi]: Yeah. Fine.
[7]  When Al-Anssi told the defendants that Saeed had offered five percent for their charities, Zayed immediately said "[n]o," and Al-Moayad added, "[t]hat percentage is too small. Make it so the total is at least 30 or 35." They gradually negotiated to the ten percent figure, which both informants repeatedly emphasized was the most Saeed could give.
[8]  18 U.S.C. § 2339B(a)(1) provides:

Whoever knowingly provides material support or resources to a foreign terrorist organization, or attempts or conspires to do so, shall be fined under this title or imprisoned not more than 15 years, or both, and, if the death of any person results, shall be imprisoned for any term of years or for life. To violate this paragraph, a person must have knowledge that the organization is a designated terrorist organization (as defined in subsection (g)(6)), that the organization has engaged or engages in terrorist activity (as defined in section 212(a)(3)(B) of the Immigration and Nationality Act), or that the organization has engaged or engages in terrorism (as defined in section 140(d)(2) of the Foreign Relations Authorization Act, Fiscal Years 1988 and 1989).
At trial, neither defendant disputed that during the periods described in the indictment, the United States Department of State had designated Hamas and Al-Qaeda as foreign terrorist organizations (FTOs). See, e.g., Office of Counterterrorism, U.S. Dep't of State, Foreign Terrorist Organizations List 2003 (Jan. 30, 2003), available at http://www. state.gov/s/ct/rls/fs/2003/17065.htm.
[9]  In Crawford, the Supreme Court held that out-of-court testimonial statements by witnesses are barred unless the witness is unavailable and the defendant has had a prior opportunity for cross-examination. Crawford, 541 U.S. at 68, 124 S.Ct. 1354.
[10]  Zayed's counsel moved for a mistrial immediately following 10 the government's emotionally charged opening statement, referring to the fact that the government attorney, "with her voice cracking, pointed to the witness stand and said that a victim of a terrorist attack in Tel Aviv was going to testify. It was a highly emotional moment. It has nothing whatsoever to do with this case. There is no suggestion at all that the defendant in any waythe defendants had anything to do with that terrorist attack." The court denied the motion and instructed the jury that "whatever the lawyers say, whatever the prosecutor says is not evidence in this case."
[11]  To demonstrate that the defendants were guilty of violating 18 U.S.C. § 2339B(a)(1), the government had to show either that the defendants knew that Hamas and Al-Qaeda were designated foreign terrorist organizations, or that the defendants knew that those groups engaged in terrorist acts. Neither Al-Moayad nor Zayed asserted at trial that they lacked the requisite knowledge of Hamas's and Al-Qaeda's terrorist activities.
[12]  As discussed further below, there was some question about whether Zayed was induced by Al-Anssi or by Al-Moayad. See infra Part I.E.1.
[13]  Government expert Matthew Levitt described Al-Zindani at trial as "a Specially Designated Terrorist" who "is believed by the United States and others to be involved in procuring weapons under activities for terrorist organizations." Other evidence at trial, specifically Zayed's post-arrest statement, suggested that Al-Moayad was merely acquainted with Al-Zindani, as Al-Zindani was also a well-known scholar.
[14]  At trial, the government's expert Matthew Levitt described Ayman Al-Zawahiri as Bin Laden's "deputy." Al-Zawahiri was indicted for his alleged role in the 1998 bombings of the U.S. embassies in Tanzania and Kenya, and appears on the FBI's list of "Most Wanted Terrorists." Federal Bureau of Investigation, Most Wanted Terrorists, available at http://www.fbi.gov/wanted/terrorists/ teralzawahiri.htm.
[15]  See, e.g., United States v. Pilarinos, 864 F.2d 253, 256 (2d Cir.1988) (internal citations and quotation marks omitted):

A defendant is entitled to a derivative entrapment defense ... when the government's inducement was directly communicated to the person seeking [the] entrapment charge by an unwitting middleman.... Nevertheless, where a government agent induces a middleman to commit a crime, and the middleman, responding to the pressure upon him, takes it upon himself to induce another person to participate in the crime, the latter person is not entitled to a derivative entrapment charge.
[16]  The defendants also contend that the district court committed certain in errors during jury selection under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986). Because the judgments of conviction must be vacated, we need not reach this argument. We also note briefly that we find no merit in Al-Moayad's claim that his Confrontation Clause rights were violated by admission of an incriminating portion of Zayed's post-arrest statement. Even if the court erred in admitting Murphy's testimony about Zayed's statement, the error was harmless. After counsel for Al-Moayad voiced his Crawford objection, Zayed's counsel elicited testimony from Murphy that "there was no contradiction" in what Zayed said he knew, while still in Yemen, about the reason for the trip to Germany. Zayed's counsel highlighted this corrective testimony in his closing argument. We are confident that this clarification remedied any incriminating effect that Murphy's testimony might have had as to Al-Moayad.
[17]  The district court stated:

With respect to the Hamas issue in the Frankfurt videos, the defendants and the informants spoke about a Hamas suicide attack, this occurred in Palestine. Testimony about this event is very probative and I weighed this against the prejudicial effect and I conclude that it did not substantially outweigh the probative value and I'm going to allow that in with the proviso that I will not have the witness testify and, I don't know where I heard this from, that he had friends in his arms and he was bleeding profusely and he was bleeding to death ... and who what he observed and what he heard.
[18]  Black's highly emotionally charged account of the bombing was also not "legally and morally relevant to the conduct constituting the offenses" with which the defendants were charged. United States v. Velazquez, 246 F.3d 204, 211 (2d Cir.2001) (opining that autopsy photos could be admitted over a Rule 403 objection because they "established that cruel and unusual punishment had occurred" and "helped to resolve a disputed point at the trial.").
[19]  Judge Wesley notes that Old Chief states that "the prosecution may fairly seek to place its evidence before the jurors, as much to tell a story of guiltiness as to support an inference of guilt, to convince the jurors that a guilty verdict would be morally reasonable as much as to point to the discrete elements of a defendant's legal fault." 519 U.S. at 188, 117 S.Ct. 644. Hence, the prosecution may admit evidence not just to fill gaps in the specific narrative of how the defendant committed the crime, but also to illustrate the greater context in which the defendant committed the crime.

Judge Wesley believes that the Black testimony and accompanying video clip of the bus bombing may have served to illustrate how the defendants' activities, including the seemingly benign mass wedding and charity fund-raising, were linked to terror and bloodshed caused by a multi-national terrorist organization. However, the Black testimony remains inadmissible for two reasons. First, the inadmissibility of the wedding video severs the connection between defendants and the bus bombing and consequently renders Black's testimony irrelevant. Second, the Black testimony would be inadmissible to show the link between defendants' fund-raising for Hamas and Al Qaeda and these organizations' respective acts of terrorism because (1) with respect to Al Qaeda, there is no evidence that the bus bombing was committed by Al Qaeda; and (2) with respect to Hamas, the bus bombing was committed prior to defendants' fund-raising.
Judge Wesley further notes that this conclusion should not preclude future admissibility of evidence to demonstrate the larger consequences of a defendant's actions in spite of offers by the defendant to stipulate as to those consequences. Cf. United States v. Salameh, 152 F.3d 88, 122 (2d Cir.1998) (admitting photographs and testimony regarding the death and injury caused by the World Trade Center bombing as probative of the nature and location of the explosion where defendants were willing to stipulate that the bombing caused death and injury).
[20]  The government stated explicitly at trial that Black's testimony was relevant to the predisposition of both defendants, and Goba's testimony related to the mujahidin form, which was relevant to Al-Moayad's predisposition.
[21]  At trial, the government did not clearly distinguish between Al-Moayad and Zayed in terms of the evidence that would demonstrate their predispositions. For example, the government simultaneously addressed the predispositions of both defendants during its rebuttal summation. This approach makes sense given that Zayed was implicated in this case primarily due to his role as Al-Moayad's assistant. Therefore, Al-Moayad's arguments regarding predisposition evidence apply to Zayed as well.
[22]  Even if the improper admission of Black's and Goba's testimony does not in itself require reversal of the conspiracy and attempt convictions, this error, in combination with others, cast sufficient doubt on the fairness of the trial as to warrant new proceedings. See infra Section II.E.
[23]  There is no real dispute that the district court admitted Al-Anssi's notes as substantive evidence. The government concedes as much in its brief on appeal. It is also clear from the government's arguments at trial that it relied on the notes not simply for rehabilitation and corroboration, but also for their substance.

For example, the government stated during its rebuttal summation, with regard to Al-Anssi, "what he said about  what he said about the defendant Al-Moayad , unfortunately, I can't find it. But it's in 3500 MA-1 [the notes]. ... But what he said about the defendant Al-Moayad was  November 2001 he wrote it down and gave it to the FBI  Mohammed Al-Moayad, a VIP person, and he is the right hand to Al-Zindani." Of Al-Anssi's trips to Yemen, counsel for the government said, "Agent Murphy sent him to Yemen the first time. He took notes. They are in evidence of what he learned on that trip. 3500 MA-2 [the notes]." In response to the question of whether Zayed was present during the meetings between Al-Moayad and Al-Anssi, the government asserted, "[w]ell, in case you're concerned that my colleague was lying to you, please look at 3500 MA-5, Al-Anssi's notes three months before Frankfurt in which he says about that meeting, he told me the following, his assistant Mohammed Zayed was with us. It's in evidence. ... What he writes in those notes is all corroborated in the Frankfurt tapes." With regard to Al-Moayad's alleged support of Hamas, the government noted, "[Al-Anssi] took notes in Yemen describing that the defendant Moayad said these receipts were Hamas and had given money to Hamas."
[24]  We also believe that the notes would have been inadmissible even for the limited purpose of rehabilitating Al-Anssi's credibility. In United States v. Pierre, 781 F.2d 329 (2d Cir.1986), we stated that "the issue ought to be whether the particular consistent statement sought to be used has some rebutting force beyond the mere fact that the witness has repeated on a prior occasion a statement consistent with his trial testimony." Id. at 331. In that case, we stated that the use of a prior consistent statement would be appropriate where a witness has been impeached with a prior inconsistent statement, and the consistent statement either "tends to cast doubt on whether the prior inconsistent statement was made or on whether the impeaching statement is really inconsistent with the trial testimony," or "when the consistent statement will amplify or clarify the allegedly inconsistent statement." Id. at 333. Subsequent cases applying Pierre have generally involved the introduction of a prior consistent statement after a witness's impeachment by prior inconsistent statement. See, e.g., United States v. Khan, 821 F.2d 90, 94 (2d Cir.1987) (allowing use of a prior consistent statement when "[d]efense counsel specifically attacked [a witness's] credibility on cross-examination and clearly implied that his failure to mention Khan at various times was inconsistent with his testimony on direct examination."); United States v. Brennan, 798 F.2d 581, 588 (2d Cir.1986) (acknowledging that Pierre does not apply where there has only been a generalized attack on a witness's credibility, but concluding that the prior consistent statement was admissible because "Brennan attempted to impeach [a witness] with allegedly inconsistent statements made before the grand jury.").

None of the circumstances that we described in Pierre were present here. The defendants did not impeach Al-Anssi with prior inconsistent statements, nor did the notes have "some rebutting force beyond the mere fact that [Al-Anssi] ha[d] repeated on a prior occasion a statement consistent with his trial testimony." We do not have to finally resolve whether the notes were properly admitted for the limited purpose of rehabilitation, however, because it is undisputed that the notes were admitted without limitation as substantive evidence.
[25]  In arguing that the notes could be admitted without limitation in order to rebut a false impression, the government repeatedly quotes United States v. Gambino, 59 F.3d 353 (2d Cir.1995), in which a panel of this Court opined that "[o]therwise inadmissible testimony may be received on re-direct in order to rebut a false impression created by an opposing party during cross-examination." Id. at 368. That case cites Wiley, but  somewhat confusingly  also relies on United States v. Rosa, 11 F.3d 315 (2d Cir.1993). Rosa involves the superficially similar but separate doctrine of "curative admissibility," under which a trial court has discretion "to permit a party to introduce otherwise inadmissible evidence [for its substance] on an issue (a) when the opposing party has introduced inadmissible evidence on the same issue, and (b) when it is needed to rebut a false impression that may have resulted from the opposing party's evidence." Id. at 335; see also Elfgeeh, 515 F.3d at 128. In this case, no party argues that the defendants elicited inadmissible evidence during their examinations of Al-Anssi, thereby triggering the doctrine of curative admissibility and opening the door for the government to introduce otherwise inadmissible hearsay for its substance on cross-examination.
[26]  The government also put forth no evidence at trial contradicting Al-Moayad's statements during his post-arrest interview that his relationship with Bin Laden was long over, that he had since spoken out publicly against Bin Laden, and that Bin Laden had actually called for his death. See supra Part I.A.3.
[27]  It should be noted that although the defendants admitted ties to individuals who were leaders in Hamas, such as Siyam and Khaled Meshal, neither defendant was shown to be a Hamas figure or even a "member" of Hamas.
[28]  Judge Wesley believes the wedding video could have been admissible as a co-conspirator statement had the trial judge been able to make findings of fact regarding the extent of Al Moayad's advance knowledge of the content of Siyam's speech, or had the government argued that the conspiracy consisted of informing the wedding guests of the bombing. He believes that while the facts that Al Moayad organized the wedding and Siyam spoke at the wedding do not necessarily lead to the conclusion that Al Moayad knew the contents of Siyam's speech, these facts do, nonetheless, make it more likely that Al Moayad would have known the contents of the speech. Judge Wesley believes these facts constitute sufficient independent corroborating evidence that Al Moayad was in a conspiracy with Siyam to inform the wedding guests of the bombing. He believes that, while the wedding speech could have been admissible under 801(d)(2)(E), there was not a sufficient basis in the record and the arguments made by the government for the admission of the speech.
[29]  Throughout the trial, the government referred repeatedly to Siyam's speech and to the defendants' laughter when the informants brought up the speech during the Frankfurt meetings. Further, the jury viewed the tape and read the transcript of that meeting among the defendants and the informants.
[30]  The government also asserts that the documents would be admissible for their truth as co-conspirator statements, but because it concedes that this argument was not raised below, we decline to address it here.
[31]  It may be helpful at this point to observe that with regard to most of the evidentiary rulings we have reviewed herein, we have not held that the evidence would have been inadmissible under any circumstances. Rather, we have criticized the particular way in which the evidence was handled during this trial. For example, we found improper the admission of Al-Anssi's notes, the mujahidin form, the wedding video, and the Croatian will without limitation. The problems surrounding the Goba testimony were magnified by the fact that Goba testified far beyond the government's proffer.
[32]  Our identification of numerous errors by the district court distinguishes this case from Yousef, where we concluded that "[t]he District Court committed no trial errors" with respect to the defendant making the due process claim. Yousef, 327 F.3d at 172. Similarly, in Rahman, we found that "most of the `errors' [Rahman] cites in support of his cumulative-unfairness claim were not errors at all." Rahman, 189 F.3d at 145.
[33]  Because the defendants' convictions must be vacated, we do not address the issue of the substantive reasonableness of their sentences.
