concurring in the judgment.
I concur in the majority’s decision to affirm the district court’s judgments on all issues in this appeal. But because I found the questions concerning the sufficiency of the evidence and the exclusion of two defense witnesses particularly difficult under the circumstances of this case, I write separately to lay out my analysis of those issues.
I. SUFFICIENCY OF THE EVIDENCE
Amawi, Mazloum, and El-Hindi each disputes the sufficiency of the evidence supporting some or all of the convictions in this case. The superseding indictment, which was filed on February 2, 2007, charged the defendants as follows.
The first two of the counts in the superseding indictment involve conspiracies and applied to all three defendants. Specifically, Count 1 charged Amawi, Mazloum, and El-Hindi with willfully conspiring and agreeing “to kill or maim persons in locations outside of the United States, [including] U.S. armed forces personnel serving in Iraq,” in violation of 18 U.S.C. § 956(a)(1). R. 186 (Superseding Indictment ¶ 8). Count 2 charged the three with conspiring and agreeing in violation of 18 U.S.C. § 2339A “to provide material sup*491port and resources, knowing and intending they were to be used in preparation for and in carrying out a violation of Title 18, United States Code, Section 2332 (killing of U.S. nationals).” Id. ¶¶ 46, 58. The superseding indictment also charged Amawi and El-Hindi with two counts each of knowingly distributing to Griffin “information pertaining to, in whole or in part, the manufacture or use of an explosive or destructive device” with the intent that Griffin use those materials to train others “to commit and further a Federal crime of violence,” in violation of 18 U.S.C. § 842(p)(2)(A). Id. ¶¶ 60, 62, 64, 66. All three defendants contest the sufficiency of the evidence with respect to both conspiracy counts, and Amawi challenges his conviction on the two distribution charges.1
A. Conspiracy Charges
As to the conspiracy charges, the defendants maintain that the government failed to prove any actual agreement to commit the predicate offenses relating to killing or maiming U.S. nationals abroad. See Amawi Br. at 24 (“The evidence showed Amawi, at most, had a general interest in training in the tactics of self-defense, security, and combat, but did not have any plan or agreement -with others to put that training to use in any particular venue or at any particular time.”); El-Hindi Br. at 13 (“Not only was there no violent act in this case. There was not a plan for an attack. There was no bomb possessed by anyone, no gun acquired by any defendant, no explosive material, no map, no potential targets.”); Mazloum Br. at 13 (“It is not required that the Government prove that the conspirators agreed on specific details of a plan, only that they agreed to its essential nature. However, if there is no meeting of the minds, there is no conspiracy.” (citation omitted)). According to the defendants, there was no unified criminal objective, and thus, there also was no conspiracy.
“In reviewing the sufficiency of the evidence, the relevant inquiry is whether, after reviewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Sliwo, 620 F.3d 630, 633 (6th Cir.2010) (internal quotation marks omitted). We review the evidence de novo to determine whether, when taken in the light most favorable to the government, there is “substantial and competent evidence upon the record as a whole” to support each essential element of the offense. United States v. Barnett, 398 F.3d 516, 521-22 (6th Cir.2005) (internal quotation marks omitted). In doing so, however, “we may not reweigh the evidence, reevaluate the credibility of witnesses, or substitute our judgment for that of the jury.” United States v. Warman, 578 F.3d 320, 332 (6th Cir.2009) (quoting United States v. Martinez, 430 F.3d 317, 330 (6th Cir.2005)), cert. denied, — U.S. —, 130 S.Ct. 1103, 175 L.Ed.2d 918 (2010).
“[T]he essence of the crime of conspiracy is agreement,” and the government therefore “must show that each alleged member agreed to participate in what he knew to be a collective venture directed toward a common goal.” United States v. Warner, 690 F.2d 545, 549 (6th Cir.1982) (internal quotation marks omitted).2 *492Moreover, “[a] conspirator must intend to further an endeavor which, if completed, would satisfy all of the elements of a substantive criminal offense, but it suffices that he adopt the goal of furthering or facilitating the criminal endeavor.” Salinas v. United States, 522 U.S. 52, 65, 118 S.Ct. 469, 139 L.Ed.2d 352 (1997). Thus, “[a] conspiracy requires: ‘(1) An object to be accomplished. (2) A plan or scheme embodying means to accomplish that object. (3) An agreement or understanding between two or more of the defendants whereby they become definitely committed to cooperate for the accomplishment of the object by the means embodied in the agreement, or by any effectual means.’ ” United States v. Gibbs, 182 F.3d 408, 420 (6th Cir.) (quoting United States v. Bostic, 480 F.2d 965, 968 (6th Cir.1973)), cert. denied, 528 U.S. 1051, 120 S.Ct. 592, 145 L.Ed.2d 492 (1999).
In establishing the existence of a conspiratorial agreement, the government is not required to show that each conspirator knew every detail of the conspiracy. It does, however, have to “show that a particular defendant knew the object of the conspiracy and voluntarily associated himself with it to further its objectives.” United States v. Crossley, 224 F.3d 847, 856 (6th Cir.2000) (internal quotation marks omitted). “Although only slight evidence” is required to link a defendant to a conspiracy, “mere association with conspirators is not enough”; instead “[t]he evidence must at. least be sufficient that a reasonable juror could infer knowledge of and acquiescence in the agreement.” Gibbs, 182 F.3d at 422 (internal quotation marks omitted). Even so, an agreement need not be explicit to establish a common criminal objective; “tacit or material understanding among the parties is sufficient.” United States v. Walls, 293 F.3d 959, 967 (6th Cir.), cert. denied, 537 U.S. 1022, 123 S.Ct. 543, 154 L.Ed.2d 431 (2002). Thus, “[a] conspiracy may be inferred from circumstantial evidence which may reasonably be interpreted as participation in a common plan.” Id.
1. The Alleged Agreement
For both conspiracy charges, the government focuses on a single meeting among the defendants as the onset of their illicit agreement. The three defendants were together only once, at a meeting on February 16, 2005. There, the FBI informant, Darren Griffin, generally led the discussion concerning the alleged training program and the defendants’ respective plans for implementing the training abroad. Griffin’s proposals Were explicit; for example, he proposed training methods akin to those used by Osama bin Laden and the “brothers” in Hamas or Hezbollah, *493but “with a twist of what the U.S. does with their tactics.” The defendants — and particularly Amawi and Mazloum — responded positively to these descriptions. When Griffin stated that the training group needed “committed brothers,” for example, Mazloum responded that his brother “definitely” would join them. Both Mazloum and Amawi repeatedly requested training on particular topics, such as sniper use, explosives, and bomb making. El-Hindi similarly expressed interest in sniper training, noting that it was “the most important” because the U.S. Army is “petrified of snipers.” In response to Griffin’s proposals to do tactical training using paintball and eventually to teach demolitions, Mazloum responded, “We have to move on man ... time is gold.”
The men also discussed possible objectives for the training operation. Griffin explained that the tactics he would teach would differ slightly depending on where each of them wanted to go. He stated, “I know [Amawi] wants to go to Iraq, you know so, I’ll prepare him for that. And, you know, brother [El-Hindi], maybe you want to go to [Palestine], so there’ll be some different tactics and techniques in there.” Amawi then volunteered that most important to him was the ability to teach others, and Griffin responded that he considered the three of them his “lieutenants,” and that they would each eventually start their own “cells.” Amawi also stated that his “main targets” were presidents and leaders in the Arabic world. Mazloum indicated that he was thinking of going to Iraq or the al-Sham countries. A short time later, however, Mazloum asserted his interest in joining the Lebanese army, in part because he would receive helpful training through a six-month stint.
The February 16 meeting also included some discussion of funding. When asked whether he had looked into obtaining grants, El-Hindi responded that “there’s a lot of them.” Mazloum wondered what the grants were for and Griffin indicated that “it’s for support here and support, you know our brothers overseas too.” Mazloum then offered to give Griffin money to find the right supplies. Mazloum also asked whether it was possible to get money into Iraq. In Arabic, Amawi, El-Hindi, and Mazloum then debated whether fighters in Iraq needed money, and Mazloum stated “[t]hey need weapons but money brings weapons ... [w]e are here, how can we provide them with weapons?” El-Hindi suggested that the fighters needed manpower instead.3
Toward the end of the meeting, Griffin tried to solidify plans for all four to meet again for handgun training, though the effort proved unsuccessful. El-Hindi, however, reaffirmed his interest in training and suggested that he might be able to recruit some “brothers” in Michigan who already had a military background from serving in Qatar. Throughout the meeting, the four discussed the need to involve only those who could be trusted. After Griffin explained the need to be extremely “security conscious,” Mazloum asked Griffin what they should tell anyone who asked what they were doing with Griffin, and Griffin responded that they should use his security company as a cover.
The discussion continued after Griffin, Amawi, and Mazloum departed El-Hindi’s home. Mazloum at one point asked *494whether it was possible to access the Americans by dressing like them. Mazloum also suggested that they could forewarn the mujahideen of their arrival to avoid being mistaken for an enemy. Amawi expressed hesitancy about making too many connections in order to avoid implicating others if he were caught. On the question of reaching Iraq, Mazloum suggested that he had “many ways” to get there and that he could buy and sell parts using his legitimate business, and Amawi said that he could reach the area because he was a travel agent. Both Amawi and Mazloum, however, agreed that they needed to train first.
2. Count 1: Conspiracy in Violation of 18 U.S.C. § 956(a)(1)
In order to prove that Amawi, Mazloum, and El-Hindi conspired to kill or maim persons outside of the United States in violation of 18 U.S.C. § 956, the government had to demonstrate that the defendants agreed “to commit acts constituting murder, kidnapping, and maiming.” United States v. Hassoun, 476 F.3d 1181, 1187 (11th Cir.2007). The government also had to establish that each defendant (1) “willfully joined the agreement with the intent to further its purpose”; (2) that after the conspiracy was initiated, at least one of the defendants committed “at least one overt act in furtherance of the object of the conspiracy; and” (3) that “at least one of the conspirators was within the jurisdiction of the United States when the agreement was made.” United States v. Wharton, 320 F.3d 526, 538 (5th Cir.), cert. denied, 539 U.S. 916, 123 S.Ct. 2288, 156 L.Ed.2d 132 (2003).4
There is no doubt that the record is replete with reprehensible comments by the defendants and with instances in which the defendants watched and commented favorably on deplorable materials that relish the killing or maiming of many individuals and groups, including U.S. troops. Each defendant was also quite clear in a number of instances that one of the goals in receiving training was to enable him to go abroad and join the fight against the U.S. military. In furtherance of this objective, El-Hindi additionally took steps to obtain grant funding to cover some of the training costs, and Mazloum and Amawi actively began engaging in firearms training with Griffin.
Other evidence in the record, however, supports the view that the defendants also had other reasons for seeking out training. Most prominent of these was the need for self-protection, which was mentioned repeatedly. On one occasion, for example, Mazloum stated that “all we are doing is training I mean ... [i]f we are ever back in the home country one day, and something happens then maybe, but over here there is nothing. We are not this kind of people.” A few seconds later, Amawi responded, “[sjomeone comes to your house, why not know how to deal with them. You know? You do this for yourself first.” In a separate encounter, Amawi expressed a similar concern that people in Jordan “don’t know how to use a gun” and would therefore be unable to defend their country and their families if necessary.
*495Despite varying evidence concerning the nature of the training objective, the jury specifically determined that the object of the defendants’ conspiracy was twofold: to murder and to maim persons in another country. This is true notwithstanding the fact that the defendants did not agree on a particular target, though such specificity with respect to time, place, or victim generally is not required to support a conspiracy conviction. See, e.g., Williamson v. United States, 207 U.S. 425, 449, 28 S.Ct. 168, 52 L.Ed. 278 (1908) (“It was not essential to the commission of the crime that in the minds of the conspirators the precise persons to be suborned, or the time and place of such suborning, should have been agreed upon, ... as the criminality of the conspiracy charged consisted in the unlawful agreement to compass a criminal purpose.... ”); see also Robert M. Chesney, Beyond Conspiracy? Anticipatory Prosecution and the Challenge of Unaffiliated Terrorism, 80 S. Cal. L.Rev. 425, 451 (2007).
Notwithstanding concern regarding the degree of attenuation between the defendants and their alleged goals as well as the breadth of their purported criminal objective, I believe that a reasonable juror could have found the evidence sufficient to support the existence of a conspiratorial agreement. The Eleventh Circuit’s recent decision in United States v. Jayyousi, 657 F.3d 1085, 1105 (11th Cir.2011), cert. denied, — U.S. —, 133 S.Ct. 29, — L.Ed.2d—, 2012 WL 1079567 (2012), is somewhat illustrative. There, the defendants had formed a support cell that was connected to multiple strands of the global terrorism movement. The government also established that the defendants were engaged in coordinated efforts both to recruit members for the global movement and to send money and equipment overseas to various groups. Id. at 1104. In finding the evidence sufficient to support an illicit agreement, the court found it to be enough that the conspirators had a shared “intent to support jihad violence overseas to establish Islamic states.” Id. at 1105.
Although this case shares some characteristics with Jayyousi, the evidence here is not nearly as substantial. For example, the agreement at the February 16 meeting did not go much beyond the need to obtain tactical training, which is not in itself an unlawful act. Apart from sharing a common ideology and seeking training from Griffin, there was no specific common plan with respect to the larger goal of murdering or maiming persons abroad. Unlike Jayyousi, there was also little evidence to suggest that the defendants were engaged in coordinated efforts to support one another in furthering their objective of committing violent jihad abroad. See id. at 1105. The defendants in Jayyousi, moreover, had actual connections with groups in the jihad movement, whereas here, the defendants had no such ties. Thus, to some extent the defendants appear merely to have had similar individual objectives, which they sought to achieve through commonly available means.
Nevertheless, given the broad scope of prohibited conduct under § 956, I cannot conclude that no reasonable juror could have found the defendants guilty of the charged offense. Although the agreement did not extend to specific targets or locations, each defendant individually expressed an intent to pursue the objective of killing or maiming abroad at an indeterminate time in the future, and all agreed to obtain training from Griffin at least in part for the purpose of attaining that ultimate goal. Evidence also supports that the defendants each took steps directed at following through with the training objective. El-Hindi, for example, sought to obtain grant funding to support the training oper*496ations, and Mazloum and Amawi began their “training” by accompanying Griffin to a firing range where they could learn to use firearms. Moreover, both at the February 16 meeting and on multiple occasions before and after, each defendant also specified an interest in other particular types of training, often while watching and commenting on websites and videos, and identified why those skills — which included training in the use of explosives, sniper rifles, and IEDs — would be useful once overseas.
Furthermore, although the evidence supporting the defendants’ cooperation with one another to attain their objective was less than in Jayyousi, it was not nonexistent. At the February 16 meeting and on other occasions, the defendants discussed the size of their group and the need to find other “trusted brothers” in order to practice larger-scale tactical strategies. The record also shows that each defendant in fact sought to recruit other “trusted brothers” to join the jihad training. Amawi, for example, recruited Mazloum, who recruited his brother, Bilal, and ElHindi had multiple conversations with Griffin about training two of El-Hindi’s relatives, Khaleel and Zubair Ahmed, who had already traveled abroad in an attempt to perform jihad. El-Hindi also suggested at one point the possibility of recruiting a few “brothers” he knew from Michigan. Additionally, although the February 16 meeting was the only instance in which all three defendants were together, at least two of the three defendants met together with Griffin on a number of other occasions both before and after that date.
Taken together, these facts establish that the defendants agreed to engage in training that had the purpose of allowing the defendants to join the fight against individuals in Iraq and elsewhere, thereby engaging in acts constituting murder or maiming of U.S. personnel. Under basic principles of conspiracy law, it matters not that the defendants were far from achieving that ultimate objective. See Iannelli v. United States, 420 U.S. 770, 779, 95 S.Ct. 1284, 43 L.Ed.2d 616 (1975) (“The basic rationale of the law of conspiracy is that a conspiracy may be an evil in itself, independently of any other evil it seeks to accomplish.” (internal quotation marks omitted)). Even if, as the defendants maintain, Griffin proactively led the most pertinent discussions about the activities of the proposed training group, the defendants voluntarily associated themselves with those proposals with full knowledge of their intended objective. See Crossley, 224 F.3d at 856. Under our precedents, no more is required. Accordingly, I agree with the majority that the defendants’ convictions under § 956 must be affirmed.
3. Count 2: Conspiracy in Violation of 18 U.S.C. § 2339A
Title 18 U.S.C. § 2339A makes it a punishable offense to “provide[ ] material support or resources or conceal[ ] or disguise[] the nature, location, source, or ownership of material support or resources, knowing or intending that they are to be used in preparation for, or in carrying out, a violation of’ one of a number of enumerated sections, including 18 U.S.C. § 2332, which is the object offense identified in the superseding indictment. R. 186 (Superseding Indictment ¶ 46, at 10).5 The statute also makes it a crime to attempt or to conspire to take any of the stated actions. 18 U.S.C. § 2339A(a).
*497Section 2339A broadly defines “material support or resources” to include tangible items, such as money or weapons, intangible items, such as training or advice, and human personnel, which encompasses both the recruitment of others and a defendant’s own partnership with those seeking to carry out the substantive offense.6 The statute is, however, subject to a specific-intent requirement. The evidence therefore must also establish that the defendants provided or conspired to provide the support or resources as defined in § 2339A(b)(l) “with the knowledge or intent that such resources be used to commit specific violent crimes.” United States v. Stewart, 590 F.3d 93, 113 (2d Cir.2009); see also Chesney, supra at 485-86. But even so limited, § 2339A covers a broad range of both individual and conspiratorial conduct.
A recent case involving § 2339A is United States v. Khan, 461 F.3d 477 (4th Cir.2006), which, not unlike this case, involved a group that engaged in intensive simulated combat exercises using paintball guns, as well as firearms training and marksmanship. Id. at 483. The group was comprised of members of an Islamic center, some of whom discussed a desire to go to Pakistan to train with a militant group known as LET and ultimately to go to Afghanistan to fight with the Taliban against the United States. Id. at 484. Others sought to join the fight against India in Kashmir. Id. In addition, a handful of these members — including some of the defendants — actually traveled to LET camps in Pakistan and participated in training in that location. Id. at 485. One of these defendants challenged a conspiracy conviction under 18 U.S.C. § 2339A, contending that there was insufficient evidence that he intended that equipment provided to an LET contact would be used in furtherance of a conspiracy to kill or injure persons in a foreign country. Id. at 488. But because that defendant was engaged directly with LET and because he knew that LET’s goals included the destruction of India, the United States, and Israel, the Fourth Circuit upheld the conviction. Id. The court reached a similar result with respect to a different defendant who trained others in military techniques with the knowledge that those individuals planned to use the techniques upon joining a violent organization abroad, concluding that this too was sufficient to support § 2339A conviction. Id. at 490; see also United States v. Mustafa, 406 Fed.Appx. 526 (2d Cir.2011) (unpublished opinion) (providing specific training on methods for *498conducting violent jihad sufficient to support conviction under § 2339A).
As with Count 1, the parties’ arguments concerning Count 2 generally focus on the absence of an agreement among the defendants as to the nature of the conspiracy. Regarding Count 2, the superseding indictment charges that the defendants conspired to provide “money, training, explosives, communications equipment, computers or personnel, including the defendants, themselves.” R. 186 (Superseding Indictment ¶ 48). As overt acts, the superseding indictment identifies the debate on February 16, 2005, among all three defendants concerning whether the Iraqi insurgency most needed money, weapons, or manpower, but focuses much more on Amawi’s individual efforts to obtain astrolite for the Syrian individual and on Amawi’s alleged attempt, along with Griffin, to provide laptops to members of the mujahideen while in Jordan.
Given the breadth of the statutory language under § 2339A, the evidence provides sufficient support for the convictions on Count 2. The reason for this is twofold. First, as discussed above, it is clear that the defendants agreed on the need to obtain training, and each did so at least in part based on a stated intent to join an insurgency abroad. The recorded conversations between the various defendants further indicate that they had full knowledge of the fact that, once abroad, either they themselves or others in the training group would be the material support — i.e., as personnel — to the mujahideen or others who they knew were preparing for or carrying out murder, attempted murder, or the causing of serious bodily injury to a U.S. national. Under the statute, it does not matter whether the individual defendants intended to carry out such acts themselves. See Jayyousi, 657 F.3d at 1105-06 (noting that the government did not have to prove the defendants’ individual involvement in the object conspiracy, and instead needed to show only that the defendants knew they were supporting mujahideen who were engaged in such acts); see also 18 U.S.C. § 2339A(a); 18 U.S.C. § 2332.7 Furthermore, as discussed above, each of the defendants sought on at least one instance to bring “trusted recruits” into the training group.
Second, the record also provides some support for the government’s theory that the defendants additionally sought to send money or supplies to support the insurgency, though the February 16 meeting did not establish a specific plan to go about providing those resources. Mazloum, for example, asked whether it was possible to funnel money to Iraq and offered to provide Griffin with money if Griffin could obtain appropriate supplies to send over. Amawi, whose actions comprise most of the overt acts cited in the superseding indictment, sought to obtain astrolite and created a plan with Griffin that was purportedly intended to deliver laptops to the mujahideen. Thus, a reasonable juror could conclude that the February 16 meeting established an agreement to provide resources that were needed to help the insurgency, including money, supplies, and trained personnel.
The government’s heavy reliance on Amawi’s actions to support this conspiracy count is troubling. Although Amawi was clearly attempting to obtain supplies for *499the Syrian individual, El-Hindi and Mazloum appear to have been completely uninvolved in these activities. Nevertheless, it is well established that each coconspirator need not be involved in every aspect of a conspiracy, so long as each “is a party to the general conspiratorial agreement.” Gibbs, 182 F.3d at 421 (internal quotation marks omitted). Furthermore, once the agreement is in place, the coconspirators are liable for the acts of their coconspirators when such acts are in furtherance of the overall objective. Salinas, 522 U.S. at 63-64, 118 S.Ct. 469 (citing Pinkerton v. United States, 328 U.S. 640, 646, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946)). Thus, as long as the evidence is sufficient to support a conspiracy in violation of § 2339A, Amawi’s actions are admissible as part of the overall conspiracy.
As with the § 956 count, the evidence supporting the conspiracy under § 2339A is scattershot and disconcertingly attenuated from a realizable objective. Nevertheless, because I do not believe that the evidence was so sparse as to meet the demanding standard for overturning a jury verdict, the defendants’ convictions on Count 2 must also be affirmed.
B. Distribution of Materials Regarding Explosives
The final sufficiency challenge relates to Amawi’s convictions on two counts of violating 18 U.S.C. § 842(p)(2)(A), which makes it unlawful
to teach or demonstrate the making or use of an explosive, a destructive device, or a weapon of mass destruction, or to distribute by any means information pertaining to, in whole or in part, the manufacture or use of an explosive, destructive device, or weapon of mass destruction, with the intent that the teaching, demonstration, or information be used for, or in furtherance of, an activity that constitutes a Federal crime of violence.
The superseding indictment identifies the predicate crime-of-violence offenses8 for both counts as 18 U.S.C. § 2332(a), which criminalizes the killing of a U.S. national, and 18 U.S.C. § 1114, which criminalizes the killing of any U.S. officer or employee, including members of the armed forces. Both counts involved only the distribution-of-information portion of the statute and did not allege that Amawi had violated 18 U.S.C. § 842(p)(2)(A) by “teaching] or demonstrating] the making or use of an explosive.”
1. Count 3: The Bomb-Vest Video
With respect to Count 3, the superseding indictment alleged that Amawi “accessed a secure mujahideen web site and opened, viewed, and discussed with [Griffin] certain instructional materials and videos, including a video entitled ‘Martyrdom Operation Vest Preparation,’ which depicted the step-by-step construction and use of a suicide bomb vest.” R. 186 (Superseding Indictment ¶ 60, at 13). The indictment further asserted that Amawi “displayed and translated [the video for Griffin], with the intent that [Griffin] use said instruc*500tional materials for training individuals in the construction and use of such bomb vests to commit and further a Federal crime of violence.” Id. The facts supporting the charge are as follows.
On January 10, 2005, Amawi and Griffin together watched a number of videos, including the bomb-vest video. At trial, Griffin indicated that they were viewing the videos with the purpose of compiling training materials. As they viewed the bomb-vest video, Amawi translated parts of it, and, during other points, Griffin added explanation about using those types of explosives. Griffin also requested a copy of the bomb-vest video, and asked that Amawi put together CDs with training materials to facilitate tactics and bomb-making instruction. Griffin made this request on multiple occasions, and Amawi continually agreed to provide a copy of the video. Nevertheless, the CDs that Amawi provided never contained a usable copy of the file.9 This was despite Griffin’s observation that, given Amawi’s technical knowledge, transferring the video to Griffin would not have been difficult for Amawi.
According to the government, even absent a successful transfer, the above facts establish that Amawi intended to distribute the information to Griffin so that Griffin could either make a bomb himself or teach others to do so. Amawi, on the other hand, argues that he did not distribute anything and that the failure to transfer is significant evidence that he also lacked the requisite intent, particularly given Amawi’s demonstrated acumen in technology. The government responds by pointing out that translation alone is enough to constitute distribution and that Amawi expressly stated a purpose of compiling training materials. The government also asserts that the repeated attempts to transfer the materials, though unsuccessful, nonetheless demonstrate intent.
The first question to be addressed is whether Amawi’s actions in sharing and translating the video suffice to establish distribution. Title 18 U.S.C. § 841 (n) states that “distribute,” for purposes of the chapter that includes 18 U.S.C. § 842, “means sell, issue, give, transfer, or otherwise dispose of.” Title 18 U.S.C. § 842(p)(2)(A), however, broadly prohibits the distribution- “by any means” of “information pertaining to, in whole or in part, the manufacture or use of an explosive.” Thus, by its plain language, however, the phrase “by any means” in the applicable subsection facially supports the government’s assertion that the statutory definition of distribution includes merely sharing and translating the information at issue, despite the arguably narrower language in § 841(n).10
*501Although Amawi presents a colorable argument showing lack of intent, it is not enough, in order to overturn a jury verdict, simply to offer an alternative explanation of the evidence. Barnett, 398 F.3d at 522 (“Circumstantial evidence alone is sufficient to sustain a conviction and such evidence need not remove every reasonable hypothesis except that of guilt.” (internal quotation marks omitted)). The question instead is whether “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Sliwo, 620 F.3d at 633 (internal quotation marks omitted). Here, Amawi was well aware that Griffin sought to compile training materials, and Amawi agreed to help Griffin do so. Although the issue is close, a reasonable juror could conclude that this endeavor was intended to facilitate the killing or injuring of U.S. nationals abroad.
2. Count 4: The Arabic Explosives Manual
Count 4 of Amawi’s indictment arose from Amawi’s distribution to Griffin of a CD that contained a six-page Arabic document that described the process for manufacturing an explosive device. Amawi asserts that there is no evidence that he intended for Griffin to use the document for any violent purpose. In particular, Amawi maintains that, in light of the large amount of superfluous information on the CDs, including personal information and a number of videos that would have been of no value to any training operation, a single document relating to explosives cannot evidence an intent to carry out violent acts using the document’s instructions. In response, the government argues that the purpose of all the materials was to create a training library and that the jury easily could have concluded that Amawi intended eventually to translate the material to permit Griffin to use it for training purposes.
Because this material was actually distributed to Griffin on a disk, the first element of Count 4 is easily met. Thus, the question again comes down to intent. On that point, the district court concluded that because Amawi sought to be trained on “jihadist tactics, ... [t]he jury could reasonably conclude beyond a reasonable doubt that Amawi, himself fluent in Arabic, gave the explosives manual to Griffin in anticipation' that Griffin would use the manual during his training of Amawi and the other defendants,” and that the manual “had been given to Griffin to enable him to make its information available to Amawi and others, and thereby facilitate their actions against Americans in Iraq.” R. 948 (Dist. Ct. Order at 7).
Based on the record, the question of intent is a close one. Amawi transferred various materials to Griffin knowing that Griffin’s stated purpose was to use those materials to train others to commit violent jihad against U.S. forces overseas. On the other hand, the other materials that were on the same disk included a random assortment of videos and music, many of which contain no content that could be used to facilitate training. Moreover, the government does not appear to have produced evidence that Amawi necessarily even knew that the manual was on the transferred disk. Nevertheless, given that Amawi and Griffin had multiple discussions concerning gathering materials to provide training to the mujahideen or those seeking to join them, Amawi’s subsequent distribution of CDs containing materials relevant to that cause is enough for a rational fact finder to infer his intent to use the materials for that purpose.
*502II. THE DISTRICT COURT’S EXCLUSION OF DEFENSE WITNESSES ALTERMAN AND ASLAN
In addition to challenging the sufficiency of the evidence supporting their convictions, the defendants also alleged a number of evidentiary errors relating to the admission or exclusion of certain witnesses. Although I believe that the majority is correct in affirming the district court’s decision to admit part of Evan Kohlmann’s testimony, I find troubling the district court’s corresponding refusal to permit at least some of the proposed testimony by defense witnesses Jon Alterman and Reza Aslan. Nevertheless, because I do not believe that any resulting error was reversible, I join the majority in affirming the district court’s judgment.
The defendants contend that the proffered testimony from Alterman and Aslan would have provided the jury with the knowledge necessary to “consider innocent explanations for Appellants’ behavior and statements.’’ Mazloum Br. at 28. Much of this came in the way of background. Alterman, who was the Director and Senior Fellow for the Center for Strategic and International Studies, proposed to testify about typical Middle Eastern views of the United States, as well as the proliferation of religious and political materials in the early 2000s. Specifically, he sought to elucidate the mainstream, non-radical use of certain Arabic terms, such as ahki and Inshallah. Alterman also would have informed jurors that, although mainstream opinion in Jordan considered the U.S. actions in Iraq to be acts of terrorism, very little material support for the insurgency actually came out of Jordan. Finally, Alterman would have covered certain media developments, including the rise in internet use in the Middle East and the spread of internet videos as a source for those seeking to know more about the developments in Iraq than what was covered in American news media.
Aslan, a religious scholar, fellow at the University of Southern California’s Center on Public Diplomacy, and CBS news analyst, also sought to provide what, to a large extent, could be classified as background information, though his testimony would have related to the Islamic faith, the meaning of the term “jihad,” and the rise of jihad as a global social movement. In addition, Aslan would have presented the “Social Movement Theory,” which “holds that 99.9% of those purporting to imitate a radical stance are really ‘free riders’ ... who talk[ ] the talk, but never walk[ ] the walk.” Mazloum Br. at 36-37; see also R. 920-8 (Aslan Proffer at 5-6).
In excluding the two witnesses’ testimony, the district court concluded that much of it was “ancillary to the issues in the case” and therefore likely to confuse the jury. R. 754 (Dist. Ct. Op. at 9); see also id. at 7. Although the district court recognized that some of the proposed testimony was of limited probative value in establishing the defendants’ states of mind, it found that the tenuous nexus between the defendants and the more generalized observations about Middle Eastern beliefs and attitudes rendered speculative any insights that could be derived. See, e.g., id. at 9 (concluding that whether the overwhelming majority of Jordanians who viewed such material failed to act was irrelevant because it “says nothing about whether Amawi himself would have gone, or wanted to go, as the government alleges, to Iraq”). Instead, the district court emphasized the need to focus on what the “defendants did and wanted to do, rather than what others, with whom the defendants had no affiliation, have done, continue to do and want to do.” Id. at 4.
Federal Rule of Evidence 702 broadly permits testimony by qualified expert wit*503nesses if such “scientific, technical, or other specialized knowledge will help the trier of fact to understand the evidence or to determine a fact in issue.” Fed.R.Evid. 702(a). But because we review a district court’s exclusion of evidence only for abuse of discretion, we will reverse its decision “only if we are firmly convinced of .a mistake that affects substantial rights and amounts to more than harmless error.” United States v. Baldwin, 418 F.3d 575, 579 (6th Cir.2005) (internal quotation marks omitted); see also Pressman v. Franklin Nat’l Bank, 384 F.3d 182, 187 (6th Cir.2004). In other words, the defendants must show that the proffered but excluded testimony was “likely to have had [a] substantial effect on [the] conviction,” which in turn requires us to “consider the relation of the wrongfully admitted (or excluded) evidence to the critical question for the jury, the importance of the evidence, and the closeness of the case.” United States v. White, 492 F.3d 380, 404 (6th Cir.2007).
Contrary to the apparent majority position, I believe that Aslan and Alternan sought in part to address issues that are unfamiliar to the average juror and offered evidence that would have provided alternative explanations for the conduct about which Kohlmann testified. This information was relevant and should have been permitted.
Admittedly, much of the proposed evidence was overly broad and may not have been particularly helpful to the jury. For example, the meaning of words like ahki and Inshallah — which Alterman proposed to elucidate — is readily apparent from listening to the recordings that were already entered into evidence. Similarly, although the term “jihad” may have engendered some confusion that Aslan’s testimony could have cleared up, the parties had already stipulated to the meaning of the term, thereby providing the jury with appropriate guidance concerning the broader definition of the word, which is not limited to violent Islamic warfare. Other evidence, such as broad-based descriptions of the geographic and geo-political conditions and cultural attitudes in the Middle East, was also of limited relevance to the question of the defendants’ intent in this case. The district court thus did not abuse its discretion in determining that the rather generic testimony proffered on these subjects either would not have been helpful to the jury or would have risked confusing the issues. Cf. United States v. Verduzco, 373 F.3d 1022, 1034 (9th Cir.2004) (holding that the district court did not err in excluding expert testimony that purported to establish the defendant’s mental state “solely by the application of generic cultural and ethnic stereotypes and data”).
The district court’s decision to exclude other portions of Aslan and Alterman’s proposed testimony is more problematic given the unique circumstances of this case. Most troubling is the exclusion of testimony from both witnesses that would have explained the pervasive nature of the videos and websites admitted into evidence and the fact that such materials are commonly viewed by non-extremists in the Middle East. Such facts would likely be unknown to many Midwestern jurors, but they are relevant to those jurors’ conclusions regarding the appropriate inference to be drawn from the defendants’ frequent viewing of such materials. This is especially so in light of Kohlmann’s testimony, which the government offered as evidence of the defendants’ intent to support and engage in terrorist activities based in part on the high level of dedication required to monitor and maintain access to these sites. See Gov’t Br. at 61 (stating that Kohlmann’s testimony showed the “extraordinary lengths” to which Amawi and El-Hindi went to ac*504cess certain websites and indicating that, “[particularly when considered in conjunction with [the defendants’] comments as they watched the videos, it demonstrated [the defendants’] intent to support the objectives and activities of such organizations”).11 And, as the majority concedes, Kohlmann’s testimony concerning these efforts was “quite probative to show, [the defendants’] intent as part of the conspiracy.” Majority Op. at 479-80.
It is true, as the majority points out, that none of the charges directly related to global terrorism, and, to the extent that the defense witnesses sought to enlighten the jury on wide-ranging principles of Islamic or fundamentalist theology or the state of the global jihadist movement, their testimony was not relevant to the factual issues in this case. Cf United States v. Rahman, 189 F.3d 88, 134-35 (2d Cir.1999) (concluding that generalized testimony about Islam and Islamic law was properly excluded as irrelevant to the question whether the defendant conspired to levy war or commit crimes of violence against the United States). But even though such charges were absent, Kohlmann’s testimony concerning the defendants’ access to Al Qaeda-sponsored websites and their dedication to collecting materials that depict deliberate acts of violence against a variety of targets nevertheless raised the specter of global terrorism, and the defendants were entitled to challenge the inference of nefarious intent that may have resulted from Kohlmann’s descriptions of the efforts required to obtain such materials. To some extent, both Aslan and Alterman could have presented that alternate perspective, thereby undermining the government’s suggestion that watching and commenting on the videos and websites necessarily evinced the defendants’ intent to engage in similar activities. Furthermore, I do not agree that such evidence, if properly limited, would have risked confusing the jury to such an extent as to outweigh substantially its probative value. Accordingly, I believe that the district court erred insofar as it excluded defense testimony that could have shed light on the defendants’ intent as evidenced by their monitoring and viewing of the websites and videos about which Kohlmann testified.
The question then becomes whether the exclusion of this evidence substantially prejudiced the defense. In the defendants’ favor on this point is the closeness of the case, particularly given the government’s heavy reliance on the defendants’ repeated viewings of these materials in order to establish their intent to undertake similar action at some point in the future. It is also true, however, that the relatively small portion of the proffered testimony that would have shed light on the issue of intent — e.g., the proposed testimony concerning the number of viewers of these materials in the Middle East as compared to the actual number of individuals who take action on them — does not relate directly to whether the defendants themselves sought to kill or maim U.S. citizens abroad. Nor is it likely that the proposed experts’ broad cultural generalizations *505could have outweighed the highly inflammatory nature of the defendants’ statements while viewing various materials. Furthermore, the district court also appropriately recognized that some of the proposed testimony risked not only opening the door to more of Kohlmann’s testimony but also incorporating broader issues concerning global terrorism that were not relevant to the issues presented in this trial. Given these legitimate concerns and the relatively limited probative value of the testimony that the defendants sought to have admitted, I cannot conclude that the district court’s ultimate balancing of interests with respect to the admissibility of Alterman and Aslan’s testimony resulted in reversible error.
. Although El-Hindi’s statement of issues challenges the sufficiency of the evidence supporting his two convictions under 18 U.S.C. § 842(p)(2)(A), El-Hindi's brief thereafter fails to mention the issue again or present any arguments against the convictions. Thus, his failure to present any substantive challenge waives the issue on appeal.
. Although the statutory requirements for engaging in a particular type of conspiracy may *492vary — for instance, 18 U.S.C. § 371 requires proof of an overt act and 21 .U.S.C. § 846 does not, see United States v. Shabani, 513 U.S. 10, 14, 115 S.Ct. 382, 130 L.Ed.2d 225 (1994) — in cases where the statute is otherwise silent on the requirements for a conspiratorial agreement, courts’ descriptions of what suffices as proof of that element are generally consistént across various conspiracy statutes. Cf. Robert M. Chesney, Beyond Conspiracy? Anticipatory Prosecution and the Challenge of Unaffiliated Teirorism, 80 S. Cal. L.Rev. 425, 451 (2007) (applying general principles of conspiracy to determine the scope of liability under various terrorism-related statutes 'and noting that "[m]ost conspiracy statutes — including the general federal conspiracy provision, § 371 — are silent regarding the issue of agreement specificity, leaving the issue to be worked out in the case law”). Because there is no case law that directly addresses the requirements for a conspiratorial agreement under either § 956 or § 2339A and because both statutes are silent on the issue, this analysis will apply the general common-law principles that are applied in cases involving other conspiracy statutes in order to evaluate whether the evidence supports an agreement here.
. Although El-Hindi was less vocal about his desire to train at the February 16 meeting, his statements on other occasions suggest that he was in agreement with the goal of receiving training in order to join the fight abroad. For instance, El-Hindi affirmatively expressed interest in participating in a plan to train that involved "stuff that is going to take us away from our kids.”
. In full, 18 U.S.C. § 956(a)(1) provides
Whoever, within the jurisdiction of the United States, conspires with one or more other persons, regardless of where such other person or persons are located, to commit at any place outside the United States an act that would constitute the offense of murder, kidnapping, or maiming if committed in the special maritime and territorial jurisdiction of the United States shall, if any of the conspirators commits an act within the jurisdiction of the United States to effect any object of the conspiracy, be punished as provided in subsection (a)(2).
. 18 U.S.C. § 2332 establishes criminal penalties for attempting or conspiring to kill or killing a U.S. national abroad and for engaging in physical violence against such individuals with intent to cause serious bodily injury.
. Specifically, the statute defines " ‘material support or resources’ ” as
any property, tangible or intangible, or service, including currency or monetary instruments or financial securities, financial sex-vices, lodging, training, expert advice or assistance, safehouses, false documentation or identification, communications equipment, facilities, weapons, lethal substances, explosives, personnel (1 or more individuals who may be or include oneself), and transportation, except medicine or religious materials.
Id. § 2339A(b)(l). Notably, the term “personnel” has been read fairly generously. As one court observed, "[g]iven the ordinary meaning of the word ‘personnel,’ and its context within the statute, the statute prohibits the provision of persons who will be used in preparing for, or carrying out, the crimes listed in § 2339A — that is, persons who are jointly involved in participating in those crimes.” United States v. Sattar, 314 F.Supp.2d 279, 298 (S.D.N.Y.2004), aff'd sub nom. United States v. Stewart, 590 F.3d 93 (2d Cir.2009). Thus, for example, transmitting a fatwa from an incarcerated well-known terrorist leader, which the defendants knew would lead directly to the termination of a cease-fire, in effect constituted a "call to arms” that supported the defendants' convictions for providing material support in the form of personnel. Stewart, 590 F.3d at 114— 16.
. Notably, none of the defendants appears to have raised any challenge to the sufficiency of the evidence with respect to their intent to support the underlying object conspiracy or any type of vagueness challenge to the attenuated nature of their charges under § 2339A. Instead, they focus only on the absence of any conspiratorial agreement. Because these other arguments have not been raised, I express no opinion about them here.
. The "crime of violence” language in this statute engages the standard crime-of-violence language employed under 18 U.S.C. § 16. See Leocal v. Ashcroft, 543 U.S. 1, 7 n. 4, 125 S.Ct. 377, 160 L.Ed.2d 271 (2004) ("[A] number of statutes criminalize conduct that has as an element the commission of a crime of violence under § 16. See, e.g., 18 U.S.C. § 842(p) (prohibiting the distribution of information relating to explosives, destructive devices, and weapons of mass destruction in relation to a crime of violence).”); see also United States v. Hull, 456 F.3d 133, 138 (3d Cir.2006), cert. denied, 550 U.S. 970, 127 S.Ct. 2877, 167 L.Ed.2d 1155 (2007). The subsection is relatively new, and courts across the country therefore have had few opportunities to address it. See Hull, 456 F.3d at 138.
. Griffin did not actually obtain a usable copy of the bomb-vest video until El-Hindi provided website information that enabled Griffin to download it himself. *501bombs or teach others how to do so.” R. 948 (Disl. Ct. Order at 5-6).
. The district court reached a similar conclusion in its order denying Amawi's motion to dismiss the charges under Count 3. Specifically, the district court concluded that
[gliving of information “by any means” about making an explosive can occur as effectively from having someone watch a video as by having him read a manual or reciting for him the steps orally. The statute contains no requirement that the person receiving the information also get an elecIronic or paper copy. What matters is giving the proscribed information to someone else. That’s what the indictment charges the defendant did.
R. 655 (Dist. Ct. Order at 6). In a subsequent order denying Amawi’s motion for a judgment of acquittal, the district court similarly concluded (1) that “[sjhowing the video sufficed to establish distribution”; and (2) that "[t]he jury could reasonably conclude beyond a reasonable doubt that Amawi showed the video to Griffin intending that Griffin, the former Special Forces soldier, would use the information from the video either to make similar
. As a general matter, Kohlmann's testimony was limited to providing additional context regarding items already in evidence, including how the websites operated, when certain information was available, and how and why the web addresses for obtaining certain videos changed over time. The district court sought to cabin any prejudicial effect from Kohlmann's testimony by issuing a cautionary instruction reminding jurors that, in spite of Kohlmann's references to Al-Qaeda and other terrorist groups running the websites from which the defendants obtained their information, no evidence actually linked any defendant to those organizations or supported an inference that the defendants had been in communication with anyone associated with such groups.