WILLIAM PRYOR, Circuit Judge:

This appeal requires us to decide three issues arising from Mark Alexander's conviction for conspiring to sell cutting machines to companies in Iran, in violation of the International Emergency Economic Powers Act, 50 U.S.C. § 1705, associated regulations, 31 C.F.R. §§ 560.203-.204, and the federal conspiracy statute, 18 U.S.C. § 371: (1) whether the district court abused its discretion when it refused to permit a deposition of one of Alexander's codefendants, a fugitive residing in Iran; (2) whether the district court abused its discretion when it denied Alexander's motion for a mistrial after a juror stated that her car had been impeded temporarily by unknown persons in the parking lot adjacent to the courthouse; and (3) whether the district court erred when it addressed the jury on legal issues that arose during the trial. No reversible error occurred. We affirm.

I. BACKGROUND

We divide the background in two parts. First, we explain the facts that led to Alexander's indictment. Second, we explain the relevant proceedings at trial.

A. Facts of Alexander's Conspiracy

Alexander was the chief executive officer and part-owner of Hydrajet Technology, LLC, a company based in Dalton, Georgia, that manufactures waterjet cutting systems. Alexander was also the chief executive officer, manager, and part-owner of Hydrajet Mena, a company located in Dubai, United Arab Emirates. Hydrajet Mena sold machines made by Hydrajet Technology to customers in the Middle East and provided technical support to those customers.

In 2006, Alexander received a request for prices of cutting machines from Ali Shojale, the managing director of Parand Machine Company, located in Iran. Alexander directed his employees to quote a "reasonable" price, "at least" for the "first system" they sent to Iran, to help build a strong "base," and Alexander advised his employees that Shojale was an Iranian dealer. Shojale then communicated with a representative of Hydrajet Mena about a potential sale for several months. At a meeting in Dubai, Alexander also negotiated the price for the machines with Karim Babakhani, an Iranian businessman. Babakhani was associated with Parand and with the Negin Sanat Sadr Company in Iran. At Alexander's instruction, employees of Hydrajet Mena wrote "Kareem Country" on documents with information about sales to Iran because the United States "was not selling any machines to Iran."

In 2007, Hydrajet Technology shipped two waterjet cutting machines to Hydrajet Mena in Dubai, where the machines then were shipped to Parand and the Negin Sanat Sadr Company, both in Tehran. Alexander also sold a pump system to Babakhani, who then corresponded with an employee of Hydrajet Mena to schedule installation of the machines. Alexander informed two employees of Hydrajet Mena that they would travel to Iran to install the machines and provide training for the users of the machines.

In 2008, Nabil Mansour, a silent partner in Hydrajet Technology, informed a special agent of the Office of Export Enforcement that Alexander had exported machines to Iran without a license. Special agents then executed a warrant to search Alexander's home and the business offices of Hydrajet Technology, where they made copies of hard drives that contained invoices and emails about the sales. The day after the searches, Alexander volunteered to meet with special agents from the Office. At the meeting, Alexander admitted that he knew about the sales and had "the final say" in the price of the machines, but he told the special agents that he had been "pressured" into making the sale by one of his employees. In 2011, a special agent arrested Alexander when he entered the United States at the Atlanta airport. A federal grand jury later indicted Alexander on one count of conspiracy to export products to Iran without a license, in violation of the International Emergency Economic Powers Act, 50 U.S.C. § 1705, associated regulations, 31 C.F.R. §§ 560.203-.204, and the federal conspiracy statute, 18 U.S.C. § 371.

B. Proceedings in District Court

Before trial, Alexander moved to conduct six depositions outside of the United States, Fed.R.Crim.P. 15(c)(3), including a deposition of Babakhani, who was named as a codefendant in the indictment. Alexander alleged that Babakhani would not come to the United States to testify, but if deposed would testify that he met Alexander on only one occasion; that his dealings regarding the purchase of the machines were done through a manager of the Dubai office, Parvez Ahmad; and that the shipment was stopped at one point because, according to Ahmad, Alexander did not want to sell to Iran. The district court granted Alexander's motion to depose five other witnesses, including Ahmad, but not the motion to depose Babakhani. The district court ruled that Babakhani's proposed testimony was immaterial or cumulative and that there were countervailing factors that weighed against granting his deposition.

During the trial, a juror informed the district court that she had been treated rudely in the parking lot. The district judge, outside of the presence of the jury, explained the situation to the parties as follows:

Alexander moved for a mistrial, but asserted that no one knew who the people in the parking lot were or whether the incident was related to Alexander. The district court denied Alexander's motion in chambers.

The district court then addressed the jury and explained that there had been an incident in the parking lot where "rude people" stood behind a juror's vehicle and would not move as the juror attempted to back out. The district court stated that this conduct would not be tolerated. The district court also explained that the jury should not hold the incident against either party, as no one knew who the people in the parking lot were. The district court instituted security measures intended to make the jury feel secure. The district court then made clear that this incident should not affect their view of the defendant:

The district court asked the jury whether they could remain impartial:

None of the jurors responded.

Twice during the trial, the district court addressed the jury about relevant legal issues. The first address followed an exchange in which Alexander cross-examined a witness from the Office of Foreign Asset Controls. After counsel for Alexander asked the witness what conduct would violate a federal regulation, the witness testified that the regulation prohibits people from "entering into a contract in order to bring about" an export to Iran. Counsel then asked the witness a leading question about the legality of negotiations in the absence of a contract: "There's nothing illegal about having negotiations as long as... there's not ultimately a contract; am I correct?" The witness responded: "Yes." The district court then informed the jury that a negotiation to violate the law would constitute an illegal conspiracy:

The district court then explained the correct definition of a conspiracy. The second address came after Alexander had elicited testimony from multiple witnesses about a "feud" he had with his business partners. The district court explained to the jury that "all this testimony we're hearing about, this feud between some of these people, is admissible for only one purpose[:] ... to what extent it goes to... credibility."

The jury convicted Alexander on the sole count of the indictment. The district court sentenced Alexander to a term of imprisonment of 18 months, followed by a period of supervised release of three years.

II. STANDARDS OF REVIEW

We review for abuse of discretion a decision about the taking of depositions for a criminal trial. United States v. Drogoul, 1 F.3d 1546, 1552 (11th Cir.1993). We review for abuse of discretion the denial of a motion for a mistrial based on allegations of extraneous influence on the jury. United States v. Khanani, 502 F.3d 1281, 1291 (11th Cir.2007). And we review for abuse of discretion the conduct of a district judge during trial. United States v. Williams, 526 F.3d 1312, 1320 (11th Cir.2008).

III. DISCUSSION

We divide our discussion in three parts. First, we explain that the district court did not abuse its discretion when it refused to permit a deposition of Babakhani. Second, we explain that the district court did not abuse its discretion when it denied Alexander's motion for a mistrial. Third, we explain that the district court did not abuse its discretion when it explained to the jury the legal standard for conspiracy and the limitations on the use of certain testimony during the trial.

A. The District Court Did Not Abuse Its Discretion When It Refused to Permit a Foreign Deposition of Babakhani.

Alexander argues that the district court abused its discretion when it denied his request to depose Babakhani in Iran. A district court may permit a deposition for a criminal trial in "exceptional circumstances," Drogoul, 1 F.3d at 1551 (quoting Fed.R.Crim.P. 15(a)(1)), based on considerations of unavailability, materiality, and countervailing factors, id. at 1552. The parties agree that Babakhani was unavailable, but dispute whether the district court abused its discretion when it ruled that the remaining considerations weighed against granting a deposition. Our review establishes that no error occurred.

Much of Babakhani's proposed testimony was immaterial or cumulative. He would have testified that he conducted his dealings with Hydrajet Mena through Parvez Ahmad, that he only met with Alexander on one occasion, and that Ahmad told Babakhani that Alexander stopped the shipment once because he "did not want to do business with Iran." But evidence that Babakhani dealt primarily with Ahmad is not exculpatory because the government need not prove "direct contact with each of the other alleged co-conspirators." United States v. McNair, 605 F.3d 1152, 1196 (11th Cir.2010) (internal quotation marks and citation omitted). Testimony that Babakhani and Alexander met briefly also would not have rebutted the proof that Alexander made arrangements and agreed to sell machines to Iranian interests, as evidenced by sales documents and his admissions to federal agents. And other witnesses could have presented testimony identical or similar to Babakhani's testimony. Ahmad could have testified about his dealings with Babakhani, and Alexander could have testified about why he stopped the shipment to Babakhani. Cf. United States v. Cuthel, 903 F.2d 1381, 1384 (11th Cir.1990) (concluding that, where defendants could have testified to exculpatory information, district court did not err when it refused to grant immunity to another witness who could testify to the same information).

Several countervailing factors weighed against granting a deposition too. Ahmad's statement to Babakhani that Alexander did not "want to do business with Iran" would have been inadmissible hearsay. Fed.R.Evid. 802. The statement was not made "in furtherance of the conspiracy," Fed.R.Evid. 801(d)(2), and Alexander has identified no exception to the prohibition on hearsay that would make the statement admissible. "The court need not ... engage in an act of futility by authorizing depositions that clearly will be inadmissible at trial." Drogoul, 1 F.3d at 1555. The district court also expressed concern about Babakhani's right against self-incrimination. Babakhani was a codefendant who did not have legal counsel, and the district court could not "grant immunity to a defense witness merely because that witness possesses ... exculpatory information." Cuthel, 903 F.2d at 1384 (internal quotation marks and citation omitted). And the district court found that it would be unjust to allow Babakhani, a "fugitive from justice," to testify for Alexander. See, e.g., United States v. Hernandez-Escarsega, 886 F.2d 1560, 1569 (9th Cir.1989) (recognizing that it can be "unjust" to allow a fugitive to participate via deposition). The district court did not abuse its discretion when it weighed the relevant factors and denied Alexander's motion to depose Babakhani.

B. The District Court Did Not Abuse Its Discretion When It Denied Alexander's Motion for a Mistrial and Declined to Inquire Further Into the Incident in the Parking Lot.

Alexander argues that the district court violated his right to a fair trial when it declined to investigate the juror's incident in the parking lot and denied Alexander's motion for a mistrial, but we disagree. Alexander failed to make a "colorable showing" that anyone communicated with the juror about a matter pending before the jury. The district court provided an adequate response to the incident.

To establish a violation of his right to a fair trial, Alexander initially "ha[d] the burden of making a colorable showing that [jury] exposure ha[d], in fact, occurred." United States v. Siegelman, 640 F.3d 1159, 1182 (11th Cir.2011). A "presumption of prejudice" arises when a defendant establishes "that an extraneous contact with or by a member of the jury took place, and that the contact was about the matter pending before the jury." Boyd v. Allen, 592 F.3d 1274, 1305 (11th Cir.2010) (internal quotation marks and citation omitted). "In a criminal case, any private communication, contact, or tampering directly or indirectly, with a juror during a trial about the matter pending before the jury is ... deemed presumptively prejudicial," Remmer v. United States, 347 U.S. 227, 229, 74 S.Ct. 450, 451, 98 L.Ed. 654 (1954), but, in the absence of a "colorable showing," we "presume" that the jury remains "impartial," Siegelman, 640 F.3d at 1182.

Alexander failed to satisfy this burden. The district court told counsel for the parties that the juror informed the rest of the jury that "supporters of the defendant" momentarily blocked her car, but Alexander's counsel apparently convinced the district court that no one knew who the people were or what their connection to the trial, if any, might be. Alexander concedes that it is not clear whether the people behind the car meant to intimidate the juror and that "it may have been a complete misunderstanding." In this circumstance, Alexander has not established that the incident had anything to do with a "matter pending before the jury." Remmer, 347 U.S. at 229, 74 S.Ct. at 451. There was no allegation that anyone communicated with the juror in any way. And the district court later informed the jury that there was no certainty who the people were or whether they were associated with the defendant or with the government. Because Alexander did not make a "colorable showing" that the incident involved a "matter pending before the jury," the district court did not abuse its discretion when it denied Alexander's motion for a mistrial.

Alexander argues that the district court was obliged to investigate the incident, but we disagree. To be sure, where "a colorable showing of extrinsic influence is made, a trial court ... must make sufficient inquiries or conduct a hearing to determine whether the influence was prejudicial." United States v. Barshov, 733 F.2d 842, 851 (11th Cir.1984) (citation omitted). But "there is no per se rule requiring an inquiry in every instance. The duty to investigate arises only when the party alleging misconduct makes an adequate showing of extrinsic influence to overcome the presumption of jury impartiality." Id. (citations omitted). Where allegations are "speculative or unsubstantiated," the "burden to investigate" does not arise. See United States v. Caldwell, 776 F.2d 989, 998 (11th Cir.1985). "In other words, there must be something more than mere speculation." Barshov, 733 F.2d at 851. And Alexander concedes that "[v]ery little was known about the incident" and that most discussion of the details was "speculative."

Our decision in Barshov is instructive. 733 F.2d 842. In Barshov, we affirmed a decision not to conduct an inquiry about speculation that a juror's son had spoken with jurors about the case:

Id. at 851. The district court did not abuse its discretion because "nothing in the affidavits attached to the [d]efendants' motion ... indicate[d] the improper conveyance of information to the jury." Id. at 852. (internal quotation marks omitted). We explained, "Although the pattern of behavior attributed to the juror[`s] ... son may be characterized as unusual and peculiar, that in itself does not suffice to mandate further inquiry. In the absence of a colorable showing that the conduct complained of impugned in any way the integrity of the trial process," the district court need not interrupt the trial to conduct further inquiry. Id. Because the defendants could only "speculat[e]" about what the son might have said to a juror, the district court did not abuse its discretion. Id. at 851.

In contrast with this appeal, our precedents and those of the Supreme Court make clear that communications between a litigant or witness and the jury create a colorable showing of prejudice that requires judicial inquiry. For example, in United States v. Betner, our predecessor court reversed a denial of a mistrial where the district court had failed to conduct an inquiry after jurors had been seen talking with staff of the United States Attorney. 489 F.2d 116 (5th Cir.1974). We explained that "[t]he district court's investigation went no further than to ascertain that the case on trial was not mentioned" and that this investigation was "insufficient." Id. at 118. We relied on the decision of the Supreme Court in Turner v. Louisiana that a defendant's right to a fair trial was violated when two key witnesses against him were deputy sheriffs charged with sequestering the jury. 379 U.S. 466, 474, 85 S.Ct. 546, 550, 13 L.Ed.2d 424 (1965). The Supreme Court explained that "it would be blinking reality not to recognize the extreme prejudice inherent in this continual association throughout the trial between the jurors and these two key witnesses for the prosecution." Id. at 473, 85 S.Ct. at 550. In Betner, we were troubled by the defendant's "contention ... that the fraternizing by the U.S. Attorney's office with the jury created, intentionally or unintentionally, a relationship or common ground" and a "spirit of friendship and cooperation between the office of the U.S. Attorney and the jurors." Betner, 489 F.2d at 118. And in Richardson v. United States, our predecessor court reversed a denial of a motion for a new trial because the district court conducted no inquiry after the main witness against the defendant allegedly "engaged in a private conversation with one of the jurors." 360 F.2d 366, 369 (5th Cir.1966). But, unlike in Betner, Turner, and Richardson, this appeal involves no presumptively prejudicial communication between a litigant or witness and the jury.

Nor does this appeal involve evidence of an extraneous influence about the case before the jury. For example, in United States v. Brantley, we remanded for the district court to conduct an inquiry after the defendant presented evidence that a juror knew the defendant's sister and had told the jury that the defendant had "been in this kind of trouble before." 733 F.2d 1429, 1439 (11th Cir.1984) (internal quotation marks omitted). We ruled that the district court "must conduct a full investigation" to determine whether the jurors discussed evidence outside the record. Id. (internal quotation marks and emphasis omitted). And in United States v. Forrest, our predecessor court ruled that a "party claiming that an improperly influenced jury returned a verdict against him must be given an opportunity to prove that claim," where a juror had admitted that an outside party had attempted to affect her vote. 620 F.2d 446, 457 (5th Cir.1980).

We cannot fault the district court for declining to speculate that a juror's brief encounter in a parking lot with unknown persons had anything to do with the trial, especially when Alexander's counsel argued that it might not and when the jurors later affirmed that they could remain impartial. Since Barshov, we have made clear that a defendant must first make a "colorable showing" of extraneous influence. See, e.g., United States v. Whatley, 719 F.3d 1206, 1219 (11th Cir.2013); McNair v. Campbell, 416 F.3d 1291, 1307 (11th Cir.2005); United States v. De La Vega, 913 F.2d 861, 870 (11th Cir.1990); Cuthel, 903 F.2d at 1382-83; United States v. Ayarza-Garcia, 819 F.2d 1043, 1051 (11th Cir.1987). Alexander failed to make that showing. In the light of its instructions to the jury, its imposition of security measures, and its repeated questions to the jury about their ability to remain impartial, the district court did not abuse its discretion when it denied Alexander's motion for a mistrial.

C. The District Court Did Not Abuse Its Discretion When It Addressed the Jury About Issues That Arose During Trial.

Alexander argues that the district court erred on two occasions when it addressed the jury, but we disagree. First, the district court did not err when it explained to the jury the legal standard for conspiracy. To be sure, a district court should "make commentary only with great care." United States v. Jenkins, 901 F.2d 1075, 1083 (11th Cir.1990) (citation omitted). But the district court did not comment on the evidence; the district court instead clarified the law. A witness had spoken about the underlying substantive offense, and Alexander was charged with conspiracy. The district court was entitled to explain that issue to the jury. Second, the district court did not err when it explained the limited purpose of admitting testimony about a "feud" between Alexander and his business partners. The district court explained to the jury that "all this testimony we're hearing about, this feud between some of these people, is admissible for only one purpose[:] ... what extent it goes to the credibility ... of witnesses." A district court must "see that there is no misunderstanding of a witness's testimony." Kyle v. United States, 402 F.2d 443, 444 (5th Cir.1968). And a district court can "curtail pursuit of irrelevant matters." United States v. Butera, 677 F.2d 1376, 1382 (11th Cir.1982). The explanation by the district court was again limited to legal instruction and had no capacity to mislead the jury or bias them against Alexander.

IV. CONCLUSION

We AFFIRM Alexander's conviction.

JORDAN, Circuit Judge, concurring.

I agree that, under the abuse of discretion standard, the district court did not commit reversible error in its handling of the reported incident in the parking lot. See United States v. Duperval, 777 F.3d 1324, 1338 (11th Cir.2015) (Jordan, J., concurring). But my rationale differs somewhat from that of the majority, and as to this issue, I concur only in the judgment.

In my mind, there was no abuse of discretion because the defense jumped the gun and sought an immediate mistrial without first requesting that the district court interview the juror in question. See generally United States v. Herring, 568 F.2d 1099, 1104-05 (5th Cir.1978). Nevertheless, from my perspective, questioning the juror would have been a wise thing to do.

To recap, after the lunch recess on the first day of trial, the district court told the parties in chambers that one of the jurors had reported — apparently to someone on the court's staff — that "several of the supporters of the defendant in this case were standing behind [that] juror's car and would not move and let her get out. Ultimately they did move and she got out. I understand she was upset about it and all the other jurors now know about it." Trial Tr. [D.E. 201] at 68. From what we can tell, the district court never spoke to the juror in question, and learned of the incident only because the juror told someone on the court's staff, who then relayed the information to the court.

The majority says that there was no showing that anyone communicated with the juror "about a matter pending before the jury," and that is true. But that is too narrow a perspective. The incident, as reported, suggested that at least one of the jurors felt (rightly or wrongly) that she had been the target of an attempt by the defendant or his supporters to intimidate her, and was understandably upset as a result. And given what the district court was told, it appears that all of the other jurors had since learned of the incident. Because a threat against a juror is an improper outside influence, see United States v. Jones, 132 F.3d 232, 245 (5th Cir.1998), regardless of whether the threat is communicated verbally or through conduct, interviewing the juror who reported the incident would have been a good way for the district court to assess the potential harm and calibrate the appropriate judicial response.

There was no interview, so a number of critical questions remained unanswered. Was the incident accurately reported to the district court, or did the account get lost in translation on the way from the jury room to chambers? Why did the juror believe that her car had been blocked by "supporters of the defendant," as opposed to anyone else? Did the juror exchange any words with those who blocked her car? Exactly what did the juror tell the other members of the jury about the incident? Did the members of the jury discuss the incident amongst themselves? If so, did any of the jurors form any opinions about the defendant or the case against him? Had it known the answers to these questions, the district court would have been in a better position to determine the appropriate response.