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PRYOR, Circuit Judge: Five agents of the Cuban Directorate of Intelligence who were members of La Red Avispa (in English, “The Wasp Network”) challenge their convictions and sentences for their espionage against the military of the United States and Cuban exiles in southern Florida. A special mission of the Cuban network, Operación Escorpión, led to the murder of four men when Cuban military jets shot down two private aircraft over international waters in 1996. Each Cuban agent was convicted of espionage charges, and one agent was convicted of conspiracy to murder, following a trial in Miami that lasted more than six months. Our Court, en banc, affirmed the denial of the Cuban agents’ motions for a change of venue and a new trial and remanded this appeal to this panel for consideration of the remaining issues. United States v. Campa, 459 F.3d 1121, 1154-55 (11th Cir.2006) (en banc). The Cuban agents raise a host of issues on appeal. The Cuban agents challenge rulings about the suppression of evidence from searches conducted under the Foreign Intelligence Surveillance Act, sovereign immunity, discovery of information under the Classified Information Procedures Act, the exercise of peremptory challenges, alleged prosecutorial and witness misconduct, jury instructions, the sufficiency of the evidence in support of their convictions, and several sentencing issues. We conclude that the arguments about the suppression of evidence, sovereign immunity, discovery, jury selection, and the trial are meritless, and sufficient evidence supports each conviction. We also affirm the sentences of two defendants, but we remand in part for resentencing of the other three defendants. I. BACKGROUND Before we address the merits of this appeal, we review four matters. First, we review the relevant facts in the trial record. Second, we review the procedural history in the district court. Third, although we have previously described the details of the trial, Campa, 459 F.3d at 1126-42, we describe the details that are relevant to the issues that are now before this panel. Finally, we review the convictions and sentences of each Cuban agent. A. Facts The primary intelligence agency of Cuba, the Directorate of Intelligence, maintained an organization for espionage in South Florida known as La Red Avispa. Gerardo Hernandez, Ruben Campa (also known as Fernando Gozales-Llort), and Luis Medina III (also known as Ramon Labañino-Salazar) were intelligence officers in the Wasp Network. They supervised network agents, including Rene Gonzalez and Antonio Guerrero. Among other things, the Wasp Network reported information to Cuba about the operation of military facilities, political and law enforcement activities, and activities of organizations based in the United States who support a change in the regime of Cuba. One organization that the Wasp Network targeted is known as “Brothers to the Rescue,” which is a Miami-based organization that flew small aircraft over the Florida straits in efforts to rescue rafters fleeing Cuba. Gonzalez and an unarrested codefendant, Juan Pablo Roque, successfully infiltrated the Brothers organization. In January 1996, aircraft of Brothers twice dropped leaflets over Havana. Some of these leaflets contained excerpts from the Universal Declaration of Human Rights of the United Nations. Because the Cuban government believed that, during some flights, pilots of Brothers intentionally violated Cuban airspace, the Cuban government launched a special mission codenamed “Operation Scorpion” “in order to perfect the confrontation of’ the “[counterrevolutionary] actions of [Brothers].” Cuban intelligence officers transmitted encrypted radio messages that directed Hernandez to instruct Gonzalez and Roque to determine the flight plans of Brothers. Hernandez was instructed to inform Cuban intelligence officials when Gonzalez and Roque would be flying in aircraft of Brothers. Gonzalez and Roque were not to fly from February 24 through 27, and they were instructed to use code phrases during radio communication with Cuban air traffic control if they could not avoid flying on those dates. On February 24, 1996, three aircraft of Brothers flew toward Cuba, but two did not return. While the planes were flying away from Cuba in international airspace, Cuban military jets shot down two of the aircraft and killed two pilots, Mario de la Peña and Carlos Costa, and two passengers, Armando Alejandre and Pablo Morales. A third plane, flown by Jose Basulto, the founder and leader of Brothers, escaped. In addition to his infiltration of Brothers, Gonzalez performed several other functions for the Cuban government under Hernandez’s supervision. Gonzalez acted as a fraudulent informant to the Federal Bureau of Investigation. He monitored the activities of other Cuban-American organizations in Florida, and he sought for his wife, who was also an agent of the Cuban Directorate of Intelligence, the assistance of a Member of Congress to enter the United States. Medina and Campa also engaged in other activities. Medina and Campa constructed false identities, which they corroborated with numerous fraudulent identification documents such as United States passports. Medina and Campa supervised attempts by other agents to penetrate the Miami facility of Southern Command, which plans and oversees operations of all military forces of the United States in Cuba, Latin America, and the Caribbean. Under the supervision of Medina, Cam-pa, and Hernandez, Guerrero obtained employment as a laborer at the Key West Naval Air Station. Guerrero sent his supervisors frequent and detailed reports about the movement of aircraft and military personnel, and comprehensive descriptions of the layout of the facility and its structures. Guerrero reported on the renovations of buildings that were to be used for top-secret activities, and he was urged to determine the purpose for which new top-secret facilities would be used. B. Procedural History Much of the evidence that the government introduced at trial was obtained through searches that were conducted under the Foreign Intelligence Surveillance Act, 50 U.S.C. §§ 1801-1845 (2000), and approved by the court created by that Act. Campa moved to suppress this evidence and argued that the government had failed to adhere to the requirements of the Act. After the Attorney General filed an affidavit that stated that an adversary hearing on the motion to suppress would harm national security, the district court reviewed the motion and affidavit in camera. See 50 U.S.C. § 1806(f). The district court denied the motion to suppress. Before trial, the government requested and received an ex parte hearing under section four of the Classified Information Procedures Act, which allows the district court to permit the government to provide substitutes in place of classified information that would otherwise be discoverable. 18 U.S.C. app. 3 § 4. The district court denied defense counsel’s request to participate in this hearing. After the trial ended, the defendants argued that the district court did not have the authority to hold the hearing and moved to have the records of the hearing unsealed. The district court denied this motion. Before trial, the defendants requested a change of venue. The district court denied this request. Before, during, and after the trial, the defendants challenged the fairness of the proceedings and sought new trials. They argued that, because of the pervasiveness of anti-Castro sentiment in the area, it was impossible for the defendants to receive a fair trial in Miami-Dade County. The defendants argued that the fairness of the trial was further undermined by prosecutorial misconduct that occurred during the trial and by statements made by Jose Basulto, a defense witness, which we describe below. During the jury selection process, the government used nine of its eleven peremptory challenges. The defendants objected to seven of these challenges and argued that the government excluded the jurors because they were black. The district court asked the government to provide a race-neutral reason for each challenged strike, and the court found that the reasons proffered by the government were race neutral. The jury that was seated included three black jurors and one black alternate juror. After the government closed its case, Hernandez moved to dismiss the murder conspiracy count. He argued that the Foreign Sovereign Immunities Act, 28 U.S.C. §§ 1330, 1602-1611, deprived the court of jurisdiction. The district court disagreed and denied the motion. C. Trial and Closing Arguments The defendants were charged in a 26-count indictment. They were convicted after a jury trial that lasted more than six months. We described the details of the indictment and the trial in our en banc opinion. Campa, 459 F.3d at 1127-42. During the course of the trial, attorneys for the government and witnesses made several statements that the defendants allege were improper. In response to our request at oral argument, defense counsel filed a chart that listed each instance of alleged misconduct, whether an objection was raised, and the response by the court. The chart includes several allegations that were not raised in the initial briefs of the defendants, but any issues arising out of these allegations were abandoned. See United States v. Levy, 416 F.3d 1273, 1275 (11th Cir.2005) (“[Pjarties cannot properly raise new issues at supplemental briefing. ...” (quoting United States v. Nealy, 232 F.3d 825, 830 (11th Cir.2000))). Because we address the allegations of misconduct that the defendants raised in their initial briefs, we describe those facts that give rise to these allegations. The government on several occasions asked questions of witnesses and otherwise referred to the presence of military facilities in Fayetteville, North Carolina, where Campa once lived. The district court instructed the government to avoid this line of questioning because the government had presented no evidence that connected Campa to those facilities. After counsel for the government persisted with this line of comments and questions and defense counsel objected, the court instructed the jury that the suggestion “that Mr. Cam-pa’s presence in North Carolina was related to a military installation” was “improper” and “to completely disregard” it. The government again connected Campa with military bases in Fayetteville in its closing argument, but the district court sustained Campa’s objection to the remarks by the government. We described in our en banc opinion as follows an instance of misconduct by a witness, Jose Basulto: During the defendants’ case, Hernandez called as a hostile witness Jose Ba-sulto, founder of Brothers to the Rescue and the pilot of the only plane that escaped the February 24, 1996, shoot-down. After a series of questions about Basulto’s travel outside of the United States, in which Hernandez’s counsel suggested that Basulto had attempted to smuggle weapons into Cuba, Basulto retorted, “Are you doing the work of the intelligence government of Cuba[?]” ... The court struck Basulto’s remark, admonished him, and instructed the jury to disregard the comment, noting that the remark was “inappropriate and unfounded” and that Hernandez’s counsel was properly providing a “vigorous defense for his client.” Campa, 459 F.3d at 1138 (footnotes omitted) (alteration in original). During closing arguments, the government uttered several statements that the defendants now challenge. In reference to the shootdown, the government said, “What kind of justification is that to shoot people out, or in [defense attorney] Mr. McKenna’s word, the final solution, I heard that word before in the history of mankind.” In his closing argument, Mr. McKenna had stated that “finally, somebody in a command bunker was given authority to exercise the final option and the final option was exercised,” but there was no reference to the “final solution” in Mr. McKenna’s closing argument. The government said that the Cuban Directorate of Intelligence sponsored “book bombs,” “threats,” and “sabotage,” and that they used the identities of “dead babies” to construct false identification documents. The government argued, “My God, these guys are spies” “bent on the destruction of the United States of America” and said that Campa was sent “to destroy the United States.” The government also said that the date of the shootdown, “February 24, 1996[,] like December 7, 1941[,] is a day that will live in the hearts and minds of these families, these four families forever destroyed.” The defendants did not object to any of these statements in closing arguments. After defense counsel mentioned in closing argument that counsel was appointed and said that “[w]e are working and serving the [C]onstitution of the United States,” the government said that the defendants “forced us to prove their guilt beyond a reasonable doubt” and that the defendants who were “bent on destroying the United States” received “able counsel who argued every point and cross-examined our witnesses,” “paid for by the American taxpayer.” The defendants objected to these arguments. Campa also objected to the statement that the court “takes into account all other factors that may be relevant for what would be the appropriate sentence,” which the government made in closing argument after Cam-pa’s attorney said that Campa is “looking at ten years in prison.” The district court sustained all these objections. D. Convictions and Sentences After the trial, Hernandez was convicted of 13 counts: one count of conspiracy to gather and transmit national-defense information, 18 U.S.C. § 794(c); eight counts of acting as an agent of a foreign government without notifying the Attorney General, 18 U.S.C. § 951, and one count of conspiracy to do so, 18 U.S.C. § 371; two counts of fraud and misuse of documents, 18 U.S.C. § 1546(a); one count of possession with intent to use five or more fraudulent identification documents, 18 U.S.C. § 1028(a)(3); and one count of conspiracy to murder, 18 U.S.C. § 1117. Hernandez was sentenced to concurrent terms of life imprisonment on the counts of conspiracy to murder and conspiracy to gather and transmit national-defense information. On the other counts, Hernandez was sentenced to shorter terms of imprisonment, which run concurrently with one another and with his life sentences. Campa was convicted of five counts: two counts of acting as an agent of a foreign government without notifying the Attorney General, 18 U.S.C. § 951, and one count of conspiracy to do so, 18 U.S.C. § 371; one count of fraud and misuse of documents, 18 U.S.C. § 1546(a); and one count of possession with intent to use five or more fraudulent identification documents, 18 U.S.C. § 1028(a)(3). He was sentenced to a total of 228 months of imprisonment. Medina was convicted of ten counts: four counts of acting as an agent of a foreign government without notifying the Attorney General, 18 U.S.C. § 951, and one count of conspiracy to do so, 18 U.S.C. § 371; one count of conspiracy to gather and transmit national-defense information, 18 U.S.C. § 794(c); two counts of fraud and misuse of documents, 18 U.S.C. § 1546(a); one count of making a false statement in a passport application, 18 U.S.C. § 1542; and one count of possession with intent to use five or more fraudulent identification documents, 18 U.S.C. § 1028(a)(3). Medina was sentenced to life imprisonment on the conspiracy charge. On the other charges he was sentenced to shorter terms of imprisonment that run concurrently with his life sentence. Rene Gonzalez was convicted of two counts: one count of acting as an agent of a foreign government without notifying the Attorney General, 18 U.S.C. § 951, and one count of conspiracy to do so, 18 U.S.C. § 371. He was sentenced to five years of imprisonment on the conspiracy count and a consecutive term of ten years of imprisonment on the substantive count. Antonio Guerrero was convicted of three counts: one count of acting as an agent of a foreign government without notifying the Attorney General, 18 U.S.C. § 951, and one count of conspiracy to do so, 18 U.S.C. § 371; and one count of conspiracy to gather and transmit national-defense information, 18 U.S.C. § 794(c). Guerrero was sentenced to life imprisonment for conspiracy to gather and transmit national-defense information, 18 U.S.C. § 794(c). For each of the other counts, Guerrero was sentenced to shorter terms of imprisonment, which run concurrently with Guerrero’s life sentence. II. STANDARDS OF REVIEW The multiple issues in this appeal are governed by several standards of review. We review the denial of a motion to suppress evidence obtained under the Foreign Intelligence Surveillance Act de novo, see United States v. Squillacote, 221 F.3d 542, 554 (4th Cir.2000), but our scope of review is no greater than that of the court that approved the searches and surveillance, United States v. Badia, 827 F.2d 1458, 1463 (11th Cir.1987). We review de novo the interpretation of the Classified Information Procedures Act, see United States v. Gilbert, 130 F.3d 1458, 1461 (11th Cir.1997), but we review discovery rulings for abuse of discretion, see United States v. Quinn, 123 F.3d 1415, 1425 (11th Cir.1997). We review the denial of a motion for a mistrial based on improper testimony for abuse of discretion. United States v. Mendez, 117 F.3d 480, 484 (11th Cir.1997). Allegations of prosecutorial misconduct present mixed questions of law and fact that we review de novo. United States v. Noriega, 117 F.3d 1206, 1218 (11th Cir.1997). We review jury selection under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), de novo, but we review underlying factual findings for clear error. United States v. Allen-Brown, 243 F.3d 1293, 1296-97 (11th Cir.2001). We review a determination whether participation by a foreign state in litigation is so extensive as to waive a defense of sovereign immunity for abuse of discretion. Canadian Overseas Ores Ltd. v. Compania de Acero del Pacifico S.A., 727 F.2d 274, 278 (2d Cir.1984); Restatement (Third) of Foreign Relations Law § 456 reporters’ note 4 (1987). We review jury instructions de novo to determine whether they misstate the law or mislead the jury to the prejudice of the party who objects to them. United States v. Grigsby, 111 F.3d 806, 814 (11th Cir.1997). If the instructions accurately reflect the law, the district court enjoys “wide discretion as to the style and wording employed in its instruction[s].” Bogle v. McClure, 332 F.3d 1347, 1356 (11th Cir.2003). We review the sufficiency of the evidence de novo and view the evidence in the light most favorable to the government with all reasonable inferences and credibility choices made in favor of the government to determine whether a reasonable jury could convict. United States v. Khanani, 502 F.3d 1281, 1293 (11th Cir.2007); United States v. Keller, 916 F.2d 628, 632 (11th Cir.1990). We review the application of the Sentencing Guidelines de novo, but we review the factual determinations of the district court for clear error. United States v. Bradford, 277 F.3d 1311, 1316 (11th Cir.2002). III. DISCUSSION The defendants present several arguments about the procedural rulings made by the district court and the jury instructions, and each defendant challenges the sufficiency of the evidence in support of his convictions and his sentence. We first discuss the five procedural issues: (1) whether the district court erred when it denied the defendants’ motion to suppress under the Foreign Intelligence Surveillance Act; (2) whether the district court erred about the discovery of classified information; (3) whether the district court was required to grant a new trial or declare a mistrial based on alleged prosecu-torial and witness misconduct; (4) whether the government exercised its peremptory challenges to prospective jurors on the basis of race; and (5) whether the Foreign Sovereign Immunities Act deprived the court of jurisdiction of the charges against Hernandez. We then turn to the three issues about the jury instructions: (1) whether the district court instructed the jury erroneously about the offense of acting as a foreign agent without notifying the Attorney General; (2) whether the district court erred when it declined to instruct the jury on the defense of necessity; and (3) whether the district court instructed the jury erroneously about Hernandez’s murder-conspiracy charge. We then address the sufficiency of the evidence in support of each defendant’s conviction. Finally, we address whether the district court correctly sentenced each defendant. A. The District Court Did Not Err When It Denied the Defendants’ Motion to Suppress. Hernandez, Medina, Campa, and Guerrero argue that the district court erred by denying their motion to suppress evidence obtained from searches and surveillance conducted under the Foreign Intelligence Surveillance Act. 50 U.S.C. §§ 1801-1845 (2000). Although the defendants concede that they do not know why the searches and surveillance were approved by officials in the executive branch and the FISA Court, whether the district court determined that the searches and surveillance were for proper purposes, or whether the minimization procedures of the Act were met, the defendants argue that the searches did not comply with the Act. Because only Campa challenged this evidence in the district court, we review the arguments of his codefendants for plain error. See United States v. Gray, 626 F.2d 494, 501 (5th Cir.1980). In 2001, after the searches were approved, Congress amended the Act and relaxed some of its standards, but we assume that the more stringent standards imposed by the earlier version of the Act governed the applications in this appeal. See United States v. Hammoud, 381 F.3d 316, 333 n. 6 (en banc) (4th Cir.2004), vacated and remanded, 543 U.S. 1097, 125 S.Ct. 1051, 160 L.Ed.2d 997, opinion reinstated in part, 405 F.3d 1034 (4th Cir.2005). No plain or other error occurred. The district court must grant a motion to suppress the fruits of a search or surveillance if it determines that the search or surveillance “was not lawfully authorized or conducted.” 50 U.S.C. §§ 1806(g), 1825(h) (2000). An application for a search or surveillance under the Act must contain certifications by a designated official of the executive branch, such as the Director of the Federal Bureau of Investigation, that the information sought is foreign-intelligence information, 50 U.S.C. §§ 1804(a)(7)(A), 1823(a)(7)(A); the purpose of the searches and surveillance is “to obtain foreign intelligence information,” 50 U.S.C. §§ 1804(a)(7)(B), 1823(a)(7)(B); and the information sought cannot “reasonably be obtained by normal investigative techniques,” 50 U.S.C. §§ 1804(a)(7)(C), 1823(a)(7)(C). The certification also must designate the “type of foreign intelligence information being sought,” 50 U.S.C. §§ 1804(a)(7)(D), 1823(a)(7)(D); and include a statement that describes the basis for the certifications that the information sought is the type designated and that the information could not reasonably be obtained by normal investigative techniques, 50 U.S.C. §§ 1804(a)(7)(E), 1823(a)(7)(E). When, as here, the applications contain the required certifications, they are subject “only to minimal scrutiny by the courts.” Badia, 827 F.2d at 1463; United States v. Duggan, 743 F.2d 59, 77 (2d Cir.1984). The reviewing court has no greater authority to review the certifications of the executive branch than the FISA court has. Badia, 827 F.2d at 1463. We have explained that, in the absence of a prima facie showing of a fraudulent statement by the certifying officer, procedural regularity is the only determination to be made if a non-United States person is the target. Id. (quoting H.R.Rep. No. 95-1283, pt. 1, at 92-93 (1978)). The defendants have not identified a fraudulent statement, but at least one of the targets of the searches and surveillance, Guerrero, is a “United States person” because he is a citizen, 50 U.S.C. § 1801®. Because a United States person was a target, we must determine whether at least some of the certifications in the application are clearly erroneous. When we make this determination, we review the statement contained in the application of the basis for the certifications and any other information furnished in connection with the application. 50 U.S.C. § 1824(a)(5). Our independent review of all the applications satisfies us that the certifications were not clearly erroneous, so we need not decide whether the other defendants are United States persons or whether the clearly erroneous standard of review applies to them. The defendants argue that the searches were conducted for purposes not allowed under the Act, but we disagree. A designated executive official certified that the purpose of each search and surveillance was “to obtain foreign intelligence information,” 50 U.S.C. §§ 1804(a)(7)(B), 1823(a)(7)(B). We have reviewed the information contained in the applications and conclude that each certification is not clearly erroneous. The defendants next argue that, with respect to surveillance, the government “may have” violated the procedures that FISA requires to minimize the “acquisition and retention, and prohibit the dissemination, of nonpublicly available information concerning unconsenting United States persons.” See 50 U.S.C. §§ 1801(h), 1804(a)(5), 1823(a)(5). The defendants base this argument on a factual finding by another court in an unrelated case, which in turn was based on concessions made by the government that it had erred in several applications and had violated its own rules about information sharing. See In re All Matters Submitted to Foreign Intelligence Surveillance Court, 218 F.Supp.2d 611, 620-21 (FISA Ct.), rev’d on other grounds, In re Sealed Case, 310 F.3d 717 (FISA Ct. Rev.2002). These findings tell us nothing about the searches or surveillance at issue in this appeal, and they do “not establish that the government failed to appropriately minimize surveillance.” Hammoud, 381 F.3d at 334. Finally, Campa argues that the evidence against him must be suppressed because the government did not know of his existence or identity when it submitted applications under the Act. This argument fails. The applications named other defendants as targets, and, as the Court of Appeals for the Second Circuit has explained, when “the proper preconditions are established with respect to a particular target, there is no requirement in FISA that all those likely to be overheard engaging in foreign intelligence conversations be named.” Duggan, 743 F.2d at 79. B. The District Court Did Not Err In Its Rulings About the Discovery of Classified Information. Hernandez, Medina, Campa, and Guerrero challenge the manner in which the district court managed the discovery of classified information by the defense. They present three arguments: (1) the district court should not have held an ex parte hearing under section four of the Classified Information Procedures Act, 18 U.S.C. app. § 4; (2) the court should have unsealed the records of that hearing after the trial; and (3) the government used the Act to violate its discovery obligations under Federal Rule of Criminal Procedure 16. These arguments fail. We address each argument in turn. The district court did not err when it held an ex parte hearing under section four of the Act. Although it does not expressly provide for a hearing, section four “contemplates an application of the general law of discovery in criminal cases to the classified information area,” United States v. Yunis, 867 F.2d 617, 621 (D.C.Cir.1989). The broad authority of the district court to regulate discovery includes the power to hold hearings. See, e.g., Fed.R.Crim.P. 16(d); 2 Charles Alan Wright, Federal Practice and Procedure § 258 (3d ed.2000). Nothing in section four circumscribes this power. As the Ninth Circuit has explained, “a hearing is appropriate if the court has questions about the confidential nature of the information or its relevancy.” United States v. Klimavicius-Viloria, 144 F.3d 1249, 1261 (9th Cir.1998). The district court did not abuse its discretion when it held a hearing. The district court also did not err by holding the hearing ex parte. Section four, which concerns only “[discovery of classified information by defendants,” 18 U.S.C. app. 3 § 4, expressly calls for an “ex parte showing.” “[W]hile these statutes specify written submissions, they do not rule out hearings in which government counsel participate.” Klimavicius-Viloria, 144 F.3d at 1261. When the discovery obligations of the government would otherwise require it to disclose documents that contain classified information, section four allows the district court to permit the government either to redact the classified information or to substitute a summary or a statement of factual admissions in place of the classified documents. 18 U.S.C. app. 3 § 4. If the government provides adequate redacted documents or substitutions and obtains the permission of the district court, section four gives the government the right to keep defense counsel from seeing the original documents. The right that section four confers on the government would be illusory if defense counsel were allowed to participate in section four proceedings because defense counsel would be able to see the information that the government asks the district court to keep from defense counsel’s view. See United States v. Mejia, 448 F.3d 436, 457-58 (D.C.Cir.2006); H.R.Rep. No. 96-831, pt. 1, at 27 n.22 (1980) (“[S]ince the government is seeking to withhold classified information from the defendant, an adversary hearing with defense knowledge would defeat the very purpose of the discovery rules.”). The defendants argue that the ex parte hearing prejudiced them and violated their due-process rights, but we disagree. Ordinarily, the government alone determines whether material in its possession must be turned over to a defendant. When the defendant requests exculpatory material under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), for example, “the government decides which information must be disclosed.” United States v. Jordan, 316 F.3d 1215, 1252 n. 81 (11th Cir.2003) (citing Pennsylvania v. Ritchie, 480 U.S. 39, 59, 107 S.Ct. 989, 1002, 94 L.Ed.2d 40 (1987)). “Unless the defense counsel becomes aware that other exculpatory evidence was withheld and brings it to the court’s attention, the prosecutor’s decision on disclosure is final.” Id. (quoting Ritchie, 480 U.S. at 59, 107 S.Ct. at 1002) (internal quotation marks omitted). In contrast with this ordinary rule of unre-viewability, neither the decision of the prosecutor nor the decision of the district court, under section four, is final. Any information that the government withholds under section four must be replaced with redacted documents or substitutes. A defendant can examine these redacted documents and substitutes and, if he believes that they are inadequate, move for an order compelling discovery. Fed R.Crim. P. 16(d). The defendants do not argue that this remedy was either inadequate or unavailable to them. We conclude that the district court did not abuse its discretion by holding an ex parte hearing. The defendants next argue that the district court erred when it declined to unseal the records of its ex parte hearing after the trial, but again we disagree. Section four requires the statement of the government to be “sealed and preserved in the records of the court to be made available to the appellate court in the event of an appeal.” 18 U.S.C. app. 3 § 4. The statute has no provision for the unsealing of this statement or other sealed records. The right of the government to keep some classified information from defense counsel would be ineffective if, after the trial, the government had to expose the very information that a court ruled the government had a right to keep secret before the trial. The district court did not err when it declined to unseal the records. Finally, the defendants argue that the government used the Act to violate its discovery obligations under Federal Rule of Criminal Procedure 16 by withholding classified documents and tangible items that were seized from the defendants. This argument also fails. The defendants’ bare assertion that they did not receive unspecified information does not establish a discovery violation. See Jordan, 316 F.3d at 1250. The defendants are entitled to discovery of these items upon a motion under Federal Rule of Criminal Procedure 16(a)(1)(E), see id., and if the government has not provided adequate substitutes under section four of the Act. The defendants do not argue either that they filed a motion under Rule 16(a)(1)(E) or that the government failed to provide adequate substitutes under section four, and they do not identify any error in a discovery ruling by the district court. If the government was required to disclose more about the information seized from the defendants, then the defendants who earlier possessed that information should have been able to explain to the district court why the disclosure was inadequate. Without more, we cannot say that the government violated its discovery obligations. C. The District Court Did Not Err When It Declined to Order a New Trial or a Mistrial. Hernandez, Medina, Campa, and Guerrero challenge statements made by a witness and by the government during the trial and statements of the government during closing arguments. The defendants argue that the statements improperly appealed to “the fears and passions of the jury” and require a new trial. We disagree. The parties dispute whether we resolved this issue in our en banc decision, when we affirmed the denial of the defendants’ motions for new trials under Federal Rule of Criminal Procedure 33. Campa, 459 F.3d at 1153. In its order denying the motions, the district court addressed two separate arguments: (1) that the venue was prejudicial; and (2) that the government engaged in prejudicial misconduct. The district court addressed the statements of the government during trial and closing argument that connected Campa with military bases in North Carolina and other closing arguments by the government that the defendants contend were improper. The district court found no prejudicial misconduct, and we affirmed. The decision of the en banc Court resolved these issues of prosecutorial misconduct. We explained that “the prosecution’s closing arguments did not prejudice the defendants because the court granted the defendants’ objections and specifically instructed the jury to disregard the improper statements. These alleged incidents of government misconduct ‘were so minor that they could not possibly have affected the outcome of the trial.’ ” Id. (quoting United States v. Alvarez, 755 F.2d 880, 859 (11th Cir.1985)). Because our en banc Court expressly decided this issue, we will not reconsider it. See Hester v. Int’l Union of Operating Eng’rs, 941 F.2d 1574, 1581 n. 9 (11th Cir.1991). Our en banc decision also resolved any issue of witness misconduct by Jose Basul-to. The misconduct of a witness does not require the district court to “vitiate the trial” in the absence of prejudice, Spach v. Monarch Ins. Co. of Ohio, 309 F.2d 949, 953 (5th Cir.1962); see also 66 C.J.S. New Trial § 29, at 113 (1998) (“[Vlolunteered statements by a witness, where prejudicial, may under the circumstances warrant a new trial.” (emphasis added)), and no prejudice occurred here. We explained in our en banc decision, “Basulto’s comment that Hernandez’s counsel was a spy for Cuba did not prejudice the defendants because it was merely a single remark during a seven-month trial by the defense’s own witness, which the court struck and instructed the jxxry to disregard.” Campa, 459 F.3d at 1153. Hernandez argues that the closing argument by the government prejudicially misstated its bxxrden of proof for the count of murder conspiracy. Contrary to the argument of the government, we did not address this prosecutorial-misconduct argument in our en banc decision. Id. at 1126 n. 1. We address it now and conclude that it fails. During closing argument, the government said that an element of the murder-conspiracy charge “requires the proof of the crime occurring in international airspace” and that the government “has proven that the shootdown occurred in international air space.” The government also said, “[T]he United States must prove there was a conspiracy to kill[,] and we have proven the conspiracy to kill.” Hernandez objected to each of these statements, and the district court sustained each objection but declined to grant Hernandez’s motions for judgment of acquittal and a new trial. The district court did not err. We subject allegations of prosecu-torial misconduct to a “two-part test.” United States v. Obregon, 893 F.2d 1307, 1310 (11th Cir.1990). We “assess (1) whether the challenged comments were improper and (2) if so, whether they preju-dicially affected the substantial rights of the defendant.” United States v. Castro, 89 F.3d 1443, 1450 (11th Cir.1996) (citing Obregon, 893 F.2d at 1310). The statements by the government were neither improper nor prejudicial. The jury instructions required proof of one of the overt acts included in the indictment, and one of the overt acts alleged was the killing of individuals in the special maritime and territorial jurisdiction of the United States. The statements by the government were accurate and did not misstate the burden borne by the government. D. The Government Did Not Engage in Racial Discrimination in Its Exercise of Peremptory Challenges. The defendants argue that the government violated the Constitution by engaging in a “systematic pattern of striking black jurors.” We disagree. The district court did not err when it found that the peremptory strikes by the government were not discriminatory. “Although a prosecutor ordinarily is entitled to exercise permitted peremptory challenges ‘for any reason at all, as long as that reason is related to his view concerning the outcome’ of the case to be tried, [the Constitution] forbids the prosecutor to challenge potential jurors solely on account of their race.... ” Batson, 476 U.S. at 89, 106 S.Ct. at 1719 (quoting United States v. Robinson, 421 F.Supp. 467, 473 (D.Conn.1976)). The procedure for evaluating an objection to a peremptory challenge involves three steps: “(1) the objector must make a prima facie showing that the peremptory challenge is exercised on the basis of race; (2) the burden then shifts to the challenger to articulate a race-neutral explanation for striking the jurors in question; and (3) the trial court must determine whether the objector has carried its burden of proving purposeful discrimination.” Allen-Brown, 243 F.3d at 1297. In response to the defendants’ challenges, the district court required the government to give race-neutral explanations for its peremptory challenges. We understand the district court to have ruled implicitly that the defendants had made a prima facie showing of racial discrimination because “a district court cannot ignore the prima facie showing requirement.” Id. at 1297. The government stated the reasons for each challenged strike, and the district court found that the proffered reasons were race neutral. We may affirm the decision of the district court on any ground that finds support in the record, United States v. Simmons, 368 F.3d 1335, 1342 (11th Cir.2004), and we conclude that the defendants did not establish a prima facie case of discrimination. Our well-established precedent, United States v. Dennis, 804 F.2d 1208 (11th Cir.1986), controls this issue. In Dennis, the government exercised some of its peremptory challenges to remove black venire members; it did not use all of its peremptory challenges; and the jury that was seated included two black persons. Id. at 1209, 1211. We concluded, as a matter of law, that there had been no Batson violation: It is thus obvious that the government did not attempt to exclude all blacks, or as many blacks as it could, from the jury. Moreover, the unchallenged presence of two blacks on the jury undercuts any inference of impermissible discrimination that might be argued to arise from the fact that the prosecutor used three of the four peremptory challenges he exercised to strike blacks from the panel of potential jurors or alternates. Id. at 1211. As occurred in Dennis, the government did not attempt to exclude as many black persons as it could from the jury. The government chose not to use two of its peremptory challenges at all, and the jury included three black jurors and an alternate black juror. No Batson violation occurred. E. The District Court Did Not Err in Its Instruction of the Jury. The defendants argue that the district court erred in three of its jury instructions: (1) the instruction about acting as a foreign agent without notifying the Attorney General; (2) the instruction about the offense of conspiracy to murder; and (3) the instruction about the defense of necessity. Each argument fails. We address each argument in turn. 1. Acting as a Foreign Agent Without Notifying the Attorney General Hernandez, Medina, Campa, Gonzalez, and Guerrero argue that the district court erroneously instructed the jury about the elements of the offense of acting as a foreign agent without notifying the Attorney General. 18 U.S.C. § 951. The defendants argue that the statute requires the government to prove that the defendants knew that they were required to register with the Attorney General and that the district court erred when it declined to instruct the jury on this requirement. We disagree. The language of the statute is silent about mens rea: Whoever, other than a diplomatic or consular officer or attaché, acts in the United States as an agent of a foreign government without prior notification to the Attorney General if required in subsection (b), shall be fined under this title or imprisoned not more than ten years, or both. 18 U.S.C. § 951(a). The accompanying regulations, promulgated under subsection (b), explain who is required to notify the Attorney General and describe the procedures for notification. See 28 C.F.R. §§ 73.1-.6. These regulations are also silent about mens rea. The silence of the statute is dis-positive: “Where no specific intent element is apparent on the face of the statute, the crime is one of general intent.” United States v. Ettinger, 344 F.3d 1149, 1158 (11th Cir.2003). “[A] defendant need not intend to violate the law to commit a general intent crime, but he must actually intend to do the act that the law proscribes.” United States v. Phillips, 19 F.3d 1565, 1576-77 (11th Cir.1994). We join the Seventh Circuit and hold that section 951 does not require proof that the defendant knew of the requirement to register. See United States v. Dumeisi, 424 F.3d 566, 581 (7th Cir.2005) (“Knowledge of the requirement to register is not an element of § 951.”). The defendants cite several decisions in support of their argument that the government must prove a heightened mens rea under section 951. These decisions are inapposite because they interpret statutory language that expressly requires a heightened mens rea. See United States v. Adames, 878 F.2d 1374, 1377 (11th Cir.1989) (“willfully”); United States v. Frade, 709 F.2d 1387, 1391-92 (11th Cir.1983) (“willfully”); United States v. Hernandez, 662 F.2d 289, 291-92 (5th Cir. Oct.1981) (“willfully”); United States v. Warren, 612 F.2d 887, 890 (5th Cir.1980) (“knowingly” and “willfully”). This language is absent from section 951. The defendants’ argument that general principles of criminal law and the doctrine of constitutional doubt require a mens rea of specific intent for section 951(a) also fails. The government was required to prove a mens rea of general intent. The district court instructed the jury that the defendants must have acted “knowingly,” and that they must have known “that [they] had not provided prior notification to the Attorney General,” to be found guilty under section 951. The defendants’ request for an instruction that requires the government to prove that the defendants knew that they were required to register is not an argument for a mens rea requirement but an argument for a heightened mens rea requirement. A heightened requirement has no basis in the statutory language and would be contrary to the ordinary rule, “deeply rooted in the American legal system,” Cheek v. United States, 498 U.S. 192, 199, 111 S.Ct. 604, 609, 112 L.Ed.2d 617 (1991), that ignorance of the law is no defense to a criminal prosecution. The district court did not err when it declined to require proof of more than general intent. See United States v. Knight, 490 F.3d 1268, 1271 (11th Cir.2007) (a general intent requirement is “sufficient to separate proper conduct from improper actions”). 2. Conspiracy to Murder Hernandez argues that the jury instructions allowed the jury to convict him on a finding of fewer elements than required for the charge of conspiracy to murder, but we disagree. The district court gave the instruction that the defense requested during the charge conference. “It is well established in this Circuit that to invite error is to preclude review of that error on appeal.” United States v. Silvestri, 409 F.3d 1311, 1337 (11th Cir.2005). Hernandez attempts to evade the invited error doctrine by arguing that other instructions that were given about International Civil Aviation Organization guidelines and arguments that the government made in closing argument somehow lowered the government’s burden. This argument fails. Nothing that Hernandez identifies in other instructions or in closing argument suggests that the government bore a burden lower than the burden stated in the murder-conspiracy instruction that the defendants requested. 3. Necessity Guerrero argues that the district court erred when it declined to instruct the jury on the defense of necessity. We disagree. Guerrero did not establish that he was entitled to that instruction. Guerrero argues that his illegal actions and those of his codefendants were necessary as “a last-resort means of impeding continuing actions and threats— by virulently anti-Castro Cuban-exile groups in south Florida — that had terrorized Cuba.” We have explained that a defendant has the burden of establishing his entitlement to an instruction on his theory of defense “separate and apart from instructions given on the elements of the charged offense.” United States v. Ruiz, 59 F.3d 1151, 1154 (11th Cir.1995). This burden is low. “[A] defendant is entitled to have the court instruct the jury on his theory of the case, ‘as long as it has some basis in the evidence and has legal support.’ ” United States v. Presley, 487 F.3d 1346, 1350 (11th Cir.2007) (quoting United States v. Nolan, 223 F.3d 1311, 1314 (11th Cir.2000) (per curiam)). Guerrero has identified no basis in the evidence for a necessity instruction. A defense of necessity requires some evidence that the threat of harm that makes the criminal activity necessary was “unlawful ... present, imminent, and impending,” and that “there was a direct causal relationship between the criminal action and the avoidance of the threatened harm.” United States v. Deleveaux, 205 F.3d 1292, 1297 (11th Cir.2000). Even if we accept Guerrero’s interpretation of the facts on appeal, he has not established that the Cuban exile groups posed any imminent threat, nor has he established any causal relation between the conduct that gave rise to his convictions — espionage against the military of the United States — and the avoidance of any harmful activities of Cuban exile groups. F. Hernandez Waived Any Defense Under the Foreign Sovereign Immunities Act. Hernandez argues that the court did not have jurisdiction over the criminal action against him because he is entitled to sovereign immunity under the Foreign Sovereign Immunities Act, 28 U.S.C. §§ 1330, 1602-1611. The Supreme Court has stated that the Act governs “claims of immunity in every civil action” against foreign states. Verlinden B.V. v. Cent. Bank of Nig., 461 U.S. 480, 488, 103 S.Ct. 1962, 1968, 76 L.Ed.2d 81 (1983). We have stated in dicta that the Act does not address “foreign sovereign immunity in the criminal context,” United States v. Noriega, 117 F.3d 1206, 1212 (11th Cir.1997), but some of our sister circuits disagree about whether the Act affects the jurisdiction of federal courts in criminal actions. Compare Keller v. Cent. Bank of Nig., 277 F.3d 811, 820 (6th Cir.2002) (“[T]he FSIA grants immunity to foreign sovereigns from criminal prosecution, absent an international agreement stating otherwise.”), with Southway v. Cent. Bank of Nig., 198 F.3d 1210, 1214 (10th Cir.1999) (“If Congress intended defendants ... to be immune from criminal indictment under the FSIA, Congress should amend the FSIA to expressly so state.”). We need not address the availability of sovereign immunity as a defense, under the Act, to the criminal jurisdiction of federal courts if we conclude that Hernandez waived any sovereign immunity. A foreign state (or its agent or instrumentality) may waive its sovereign “immunity either explicitly or by implication.” 28 U.S.C. § 1605(a)(1). “[A]n appearance ... in an action, without challenge to the jurisdiction of the court, is a waiver of immunity from jurisdiction to adjudicate that action.” Restatement (Third) of Foreign Relations Law § 456(2)(c) & cmt. b (1987). This principle applies whether the party asserts immunity from criminal or civil jurisdiction. Id. § 421(3) & cmt. b. Hernandez waived any defense of sovereign immunity. Hernandez first appeared before the district court on September 14, 1998, but first raised the defense of sovereign immunity more than two years later at the close of the evidence presented by the government. During this interim, Hernandez appeared before the court on numerous occasions, filed several motions, which included motions to dismiss on other grounds, responded to motions by the government, agreed to a trial date, and appeared at trial. Hernandez’s long and active participation in the action waived any defense of sovereign immunity. See id. § 456 reporters’ note 4. We recognize that district courts ordinarily “have discretion ... to determine when the participation of a party in ... litigation is so extensive as to constitute a waiver,” id.; Canadian Overseas Ores Ltd. v. Compania de Acero del Pacifico S.A., 727 F.2d 274, 278 (2d Cir.1984), but Hernandez’s participation was so extensive by the time he first raised the defense that we conclude as a matter of law that he waived any defense, see Richardson v. Fajardo Sugar Co., 241 U.S. 44, 46-47, 36 S.Ct. 476, 477, 60 L.Ed. 879 (1916) (holding that a defendant who appeared, filed answers to an original and several amended complaints, set a trial date, and first raised the defense of sovereign immunity eight months after the action began waived the defense). We do not decide whether the defense would have been available to Hernandez if it had been timely raised. See id. G. Sufficient Evidence Supports the Convictions of Each Defendant. Gonzalez, Campa, Hernandez, Medina, and Guerrero each argue that the evidence at trial was insufficient to support their respective convictions. We disagree. We address the arguments of each defendant in turn. 1. Sufficient Evidence Supports Gonzalez’s Convictions. Gonzalez argues that the evidence introduced at trial was insufficient to convict him of acting as an agent of a foreign government without notifying the Attorney General, 18 U.S.C. § 951, and conspiracy to violate section 951 and to defraud the United States, 18 U.S.C. § 371. We disagree. Sufficient evidence supports each conviction. Gonzalez concedes that evidence presented at trial established that he and his codefendants acted as “emissaries of the Government of Cuba,” but he argues that the evidence is insufficient to establish that he violated section 951(a) and that he conspired to do so because the evidence implies that Gonzalez “was never instructed as to the reporting requirements.” Gonzalez’s argument is based on a misunderstanding of the law. As we have previously explained, section 951 establishes a general intent crime, so the government was required to prove the intent only to do the acts that the law proscribes. Phillips, 19 F.3d at 1576. The government was not required to prove that Gonzalez knew of the registration requirement, so Gonzalez’s argument fails. Gonzalez’s argument that the evidence introduced at trial was insufficient to prove three of the overt acts alleged in the indictment also fails. To sustain a conviction for conspiracy, “the Government must prove the existence of an agreement to achieve an unlawful objective, the defendant’s knowing and voluntary participation in the conspiracy, and the commission of an overt act in furtherance of it.” United States v. Suba, 132 F.3d 662, 672 (11th Cir.1998). The government does not need to prove that the defendants accomplished the purpose of the conspiracy. “The overt act requirement in the conspiracy statute can be satisfied much more easily. Indeed, the act can be innocent in nature, provided it furthers the purpose of the conspiracy.” Iannelli v. United States, 420 U.S. 770, 786 n. 17, 95 S.Ct. 1284, 1293 n. 17, 43 L.Ed.2d 616 (1975). “While it is error to submit to the jury an overt act as to which there is a total lack of proof, questions of whether or not a proven overt act is in furtherance of the conspiracy are ordinarily for the jury to decide.” United States v. Fontenot, 483 F.2d 315, 322 (5th Cir.1973) (citations omitted). The government presented sufficient evidence to establish that the overt acts that Gonzalez challenges furthered the conspiracy. We address each challenged act in turn. The twelfth overt act alleged in the indictment charges that Gonzalez provided Hernandez with a report about a letter that Gonzalez solicited from a “United States Congressional Representative” seeking the admission of Gonzalez’s wife into the United States. Gonzalez argues that the evidence introduced in support of this overt act does not prove that Gonzalez’s efforts were “tantamount to the interference with any governmental function.” Gonzalez’s argument misunderstands the law. The purpose of the conspiracy, as alleged in the indictment, included “sowing disinformation ... in dealings with United States private and public institutions.” The report that Gonzalez sent to Hernandez described his efforts to secure his wife’s entry into the United States and explained that Gonzalez’s efforts were “designed more to give an appearance, rather than to seek action to have my family leave.” A reasonable jury could have found that this report furthered the conspiracy by keeping other members of the conspiracy informed about Gonzalez’s efforts. Whether this report actually interfered with any governmental function is irrelevant. The fifteenth overt act alleged in the indictment, which Gonzalez also challenges, charges that Gonzalez “met with the FBI in the guise of a cooperating individual.” Gonzalez concedes that evidence established that he met with the FBI, and the government introduced communications from Cuba that directed Gonzalez to meet with FBI agents and specifically instructed him how to act during the meetings. The government also introduced reports from Gonzalez to Hernandez that described Gonzalez’s meetings with the FBI and opined that Gonzalez’s performance was convincing. A reasonable jury could have found based on this evidence that the overt act furthered the conspiracy. Gonzalez’s challenge to the twentieth overt act alleged in the indictment, which charges that Gonzalez reported to Hernán-dez that “Gonzalez had been flying close to Homestead Air Base with the aim of observing any strange movement,” also fails. The government introduced a report in which Gonzalez wrote to Hernandez, “As you told me to do, I have been flying in the vicinity of Homestead Air Base in order to be able to observe any strange movement,” and described Gonzalez’s observations of aircraft, their movement, and their positioning. The report supports the finding that this overt act furthered the conspiracy. 2. Sufficient Evidence Supports Campa’s Convictions. Campa presents two arguments that the evidence introduced at trial was insufficient to convict him, but both fail. Campa first adopts the arguments of Gonzalez with respect to his convictions for acting as an agent of a foreign government without notifying the Attorney General and conspiracy to do so. For the reasons we have previously explained, these arguments fail. Campa next argues that the government failed to offer sufficient evidence to support his remaining convictions for fraud and misuse of documents, 18 U.S.C. § 1546(a), and possession with intent to use five or more fraudulent identification documents, 18 U.S.C. § 1028(a)(3). These convictions are based on an allegation that Campa possessed a fraudulent passport. Campa argues that there is insufficient evidence that he possessed this passport, but we disagree. Two counts of the indictment charged that Campa knowingly possessed a passport that bore Campa’s likeness along with the name of someone else. We have explained that “[t]he government need not prove actual possession in order to establish knowing possession; it need only show constructive possession through direct or circumstantial evidence. Constructive possession exists when the defendant exercises ownership, dominion, or control over the item or has the power and intent to exercise dominion or control.” United States v. Greer, 440 F.3d 1267, 1271 (11th Cir.2006) (citation omitted). The government introduced into evidence a document that appears to be a standard United States passport. The document bears Campa’s photograph and the name and signature of “Osvaldo Rei-na.” A government expert testified that the document was a counterfeit passport. An agent of the Federal Bureau of Investigation, who was present when the counterfeit passport was seized, testified that the counterfeit passport was found along with a social security card, a Florida driver’s license, business cards for an agent of a Spanish book publishing company, and a membership card for a Florida club, all bearing the name of Reina. Some of these other documents also bear Campa’s photograph. These items were found hidden inside a concealment device in a notebook that was found in a dresser in Hernandez’s apartment. The government also introduced into evidence an encrypted report found in Cam-pa’s residence of “work directives,” which contains descriptions of primary, “intermediate,” and “reserve” legends. The primary legend is in the name of Ruben Campa and contains biographical data associated with that name. The reserve legend is in the name of Osvaldo Reina and includes the biographical data that appears on the counterfeit passport. The government also introduced an “escape plan,” found at Campa’s residence, which instructs Campa to “change identity, assuming the one in your reserve documentation” in the event of a situation that “might demand an emergency exit from the country.” From this evidence a reasonable jury could have found that Campa had the power and intent to exercise dominion or control over the counterfeit passport. Campa’s argument that “the government proceeded simply on the legally unsustainable theory of possession due to past temporary stay in another’s premises” fails. Although mere presence in an area where an item is found is insufficient to support a conviction based on possession