
608 F.3d 818 (2010)
UNITED STATES of America, Appellee
v.
Jose Antonio CELIS, also known as Calvo, Appellant.
Nos. 07-3075, 07-3076, 07-3078.
United States Court of Appeals, District of Columbia Circuit.
Argued November 13, 2009.
Decided June 18, 2010.
*825 Carmen D. Hernandez, appointed by the court, argued the cause and filed the briefs for appellant Anayibe R. Valderama.
Elita C. Amato, appointed by the court, argued the cause and filed the briefs for appellant Jose A. Celis.
Manuel J. Retureta, appointed by the court, argued the cause and filed the briefs for appellant Juan D. Giraldo.
Mary E. Mogavero, Trial Attorney, U.S. Department of Justice, argued the cause for appellee. With her on the brief were Lanny Breuer, Assistant Attorney General, Teresa A. Wallbaum, Appellate Counsel, and Tritia Yuen, Trial Attorney. Roy W. McLeese III, Assistant U.S. Attorney, entered an appearance.
Before: ROGERS and GRIFFITH, Circuit Judges, and SILBERMAN, Senior Circuit Judge.
Opinion for the Court filed PER CURIAM.
PER CURIAM.
Appellants Jose Antonio Celis, Juan Diego Giraldo, and Anayibe Rojas Valderama were convicted by a jury of conspiring to import cocaine and to manufacture and distribute cocaine for import into the United States, in violation of 21 U.S.C. §§ 952, 959, 960, and 963. The events underlying these convictions occurred principally in Colombia, South America. Because appellants' actions were tied to a terrorizing drug trafficking organization in Colombia, the district court issued a protective order to ensure the safety of certain government witnesses. Appellants contend that the protective order and other rulings by the district court require reversal of their convictions.[1] Specifically, appellants contend *826 that the protective order allowing government witnesses to testify under pseudonyms violated their confrontation and effective counsel rights under the Sixth Amendment. They further contend that their ability to prepare for cross-examination was impeded by the government's belated production of discovery materials it was obligated to disclose. Additionally appellants contend they were denied a fair trial because the district court rejected their objections to discovery violations by the government, denied requests for a continuance, and failed to require translation of discovery materials from Spanish into English and from English into Spanish. Finally, they contend the district court erred by denying a motion for severance, admitting audio recordings and statements in a video recording, finding no prejudicial variance between the indictment and evidence presented at trial, ruling there was sufficient evidence to support the verdict, and denying a motion for a new trial.
We hold that in issuing and managing the protective order the district court accommodated the government's law enforcement interests in a manner that did not impermissibly intrude upon appellants' Sixth Amendment rights and did not result in prejudice that would require reversal of their convictions. We further hold that appellants' procedural and evidentiary challenges are unpersuasive. Accordingly, we affirm the judgments of conviction.

I.
The Fuerzas Armadas Revolucionaras de Colombia ("FARC") is the most significant drug trafficking organization in Colombia. An area in Colombia known as the Caguan region is a major source of the FARC's cocaine production. The 14th Front, a division of the FARC, controls the region, forcing local peasants to sell their coca crop exclusively to the organization.
At the time of the events in this case, the 14th Front was commanded by Fabian Ramirez. Under orders from Ramirez, Anayibe Rojas Valderama served as the leader and chief financial officer for the 14th Front's drug trafficking operations in the Caguan region. In her position, Valderama was responsible for ensuring that peasants in the Caguan region sold cocaine base only to the FARC. She made frequent trips throughout the region to exchange pesos for cocaine base. After the cocaine base was acquired, Valderama arranged for it to be delivered to different processing facilities where it was converted into cocaine powder. She often traveled to these laboratories to observe operations. Once the cocaine was in powder form, buyers would fly in to small airstrips near the laboratories to take possession of the cocaine with Valderama overseeing the exchange.
In 2001 Jose Antonio Celis, a drug trafficker who had done business with the FARC ten years prior, sought to make contact with the FARC with hopes of another partnership. Celis contacted Rocio Alvarez, an associate of Valderama's who would later become a DEA cooperating informant, and told her that he wished to obtain cocaine from the FARC. Celis informed Alvarez that he still had drug contacts throughout the world. He proposed a scheme in which he would ship FARC cocaine via boat to Panama and then on to the United States in containers. Celis asked Alvarez to deliver his proposal to her FARC contacts.
*827 Alvarez contacted Juan Diego Giraldo, a drug trafficker with ties to Fabian Ramirez, and communicated the Celis proposal to him. Giraldo then arranged a meeting between Alvarez and Fabian Ramirez, at which Alvarez gave Ramirez a letter outlining Celis's plan. Giraldo later contacted Alvarez and asked her to tell Celis that he should travel to San Vicente del Caguan to meet with Ramirez. While the parties did not reach an agreement at this initial meeting, Giraldo arranged a second meeting six or seven months later in which an agreement was reached. Under the agreement, Celis would transport 1,400 kilograms of cocaine to the United States. The cocaine was to come from the Caguan region where Valderama led the FARC's drug operation. Mr. Celis would not purchase the entire load; other investors included Fabian Ramirez and Valderama.
The plan proved only partially successful. Celis did receive cocaine from the FARC and sold some of it in Miami, Florida. But a portion of the shipment was lost in Panama where, as Celis later recounted to Alvarez, there were "some problems" and "even deaths." Apparently some of the drugs were seized by law enforcement. When Celis did not promptly repay the FARC investors due to the loss, Valderama complained to Alvarez that if he did not pay his debts, he would be killed. After hearing this news, Alvarez arranged a meeting with Giraldo and Celis. At the meeting Celis gave Giraldo newspaper accounts from Panama showing that drugs had been seized by the law and asked Giraldo to show the articles to Ramirez and Valderama. Celis later told Alvarez that he was trying to pay Ramirez and Valderama back through new shipments of drugs to the United States.
Later in mid-2003, Celis invited Rodrigo Jardinero (a/k/a "Lechuga"), a Colombian drug trafficker with whom Celis had a longstanding business relationship, to a meeting in Panama. Among others, Valderama, Celis, and Giraldo were present at this meeting. Valderama led the discussion and told Celis that "he owed us a lot of money." Though Jardinero was initially reluctant to work with Valderama, he agreed to assist in transporting some cocaine to Charleston, South Carolina and Miami in order to help Celis. Celis eventually sent Jardinero two different loads of cocaine; Jardinero sent 40 kilos on to Charleston, but they were not successfully received by his contacts there. Jardinero did successfully send 41 kilos to Miami.
Valderama also worked with traffickers other than Celis and Giraldo to sell FARC cocaine. A drug trafficker named Gordo Andres brokered a deal with Valderama in which she would provide FARC cocaine to a trafficker known as "El Burro," who would arrange for the cocaine to be sent to a laboratory near Venezuela and then on to the United States. Pursuant to that agreement, Andres and El Burro both made trips to meet Valderama in the Caguan region and purchased a total of 1,600 kilograms worth of cocaine. Valderama counted their money and authorized the release of the cocaine. Later, after El Burro and Andres had a falling out, El Burro turned to Alvarez to broker a deal for him to purchase additional cocaine from the FARC. Alvarez, with the assistance of Giraldo, put El Burro in contact with Valderama. This time El Burro sent a pilot to pick up 420 kilograms of cocaine from Valderama.
In addition to the schemes described above, the appellants in this case formed a number of other plans to traffic cocaine out of the Caguan region that never came to fruition. For example, Valderama and Ramirez hatched a plan in November of 2002 in which they would provide Gordo Andres with cocaine for him to sell to enemies of the FARC, only to later steal it *828 back so that Giraldo could ship it to the United States. Later, in May 2003, Giraldo and Celis asked Andres to invest in a plan to ship cocaine to the United States, but that deal fell through when Andres refused to participate. And while Andres initially agreed to assist Celis in another deal to purchase 3,000 kilograms of 14th Front cocaine to ship to a drug boss in Mexico, that deal also fell through when Andres went missing.
Valderama's role in distributing FARC cocaine ultimately came to an end on February 10, 2004, when Colombian army soldiers raided her farm and captured her. Various items were seized including six kilograms of cocaine, thirteen weapons, money, military uniforms, a satellite telephone, a video camera, and several documents one of which included a phone number and the handwritten name "Flaco," which was Giraldo's alias.
Valderama, Ramirez, Celis, and Giraldo were indicted for conspiracy to manufacture and distribute five kilograms or more of cocaine, knowing or intending that it be imported into the United States in violation of 21 U.S.C. §§ 952, 959, 960, and 963. The district court denied Giraldo's pre-trial motions for severance and Valderama, Giraldo, and Celis were tried together.[2] At trial, the government introduced testimony from an expert knowledgeable with the operations of the FARC and from a number of witnesses who were associates of the appellants. The government also introduced audio and video recordings capturing each of the appellants discussing drug trafficking.
The jury convicted all three appellants. Valderama and Giraldo were sentenced to 200 months' incarceration; Celis was sentenced to 175 months' incarceration. The appellants have appealed, each presenting grounds for reversal.

II.
Protective Order; Brady. Valderama and Giraldo contend the government's use of pseudonyms for its witnesses and limitations on disclosure of the witnesses' true identities prevented adequate investigation of the witnesses and violated appellants' confrontation rights under the Sixth Amendment.[3] Valderama also contends that her right to the effective assistance of counsel under the Sixth Amendment was violated. Further, Valderama challenges the timeliness of the government's disclosures of information and evidence pursuant to Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), maintaining that the delayed disclosures impeded counsel's ability to investigate and prejudiced counsel's ability to prepare for cross-examination of protected government witnesses.
Disclosure of government witness lists and of exculpatory or impeachment information and evidence implicates the due process considerations of the Fifth Amendment.[4]See United States v. Ruiz, 536 U.S. 622, 631-32, 122 S.Ct. 2450, 153 L.Ed.2d 586 (2002). Determining whether to require such disclosure involves considering "the nature of the private interest at *829 stake ... the value of the additional safeguard, and ... the adverse impact of the requirement upon the Government's interests." Id. at 631, 122 S.Ct. 2450. Because the timing of such disclosure may affect a defendant's ability to confront witnesses at trial, these disclosure requirements also implicate the confrontation considerations of the Sixth Amendment, as, for example, where the credibility of a key incognito prosecution witness is in issue. See, e.g., Smith v. Illinois, 390 U.S. 129, 131-32, 88 S.Ct. 748, 19 L.Ed.2d 956 (1968). These considerations can burden both the interests of the government in enforcing the law and the ability of a defendant to prepare a defense. Valderama's and Giraldo's Sixth Amendment challenge to the use of pseudonyms requires this court to determine whether the district court's restriction on defense access to the true identities of protected witnesses until six days before the witness testified at trial impermissibly impeded appellants' ability to cross-examine the protected witnesses in violation of the Sixth Amendment. We note that in support appellants cited at least one Fifth Amendment due process case that reflects some overlap between the concepts of Fifth Amendment due process and the right of confrontation under the Sixth Amendment. Thus, a related question this court must address is whether the government's manner of disclosure pursuant to Brady and Giglio as to the protected witnesses, by providing redacted materials and information to the defense on the first day of trial and unredacted materials several days before each witness testified, prejudiced appellants' ability to prepare for cross-examination.

A.
The district court issued the protective order under seal on the first day of jury selection, January 8, 2007. Two months earlier the government had filed under seal a motion in limine seeking a protective order barring the release of the true identities of witnesses from Colombia and allowing these witnesses to testify under pseudonyms. The motion set out in vivid detail the reasons underlying the request. The district court granted the motion for a protective order but not exactly as the government had requested. Instead of barring the defense from ever learning the true identifies of the protected witnesses, the district court issued a protective order including provisions under which the defense could obtain the true identities of these witnesses. Referencing concerns about witness safety, the protective order allowed the witnesses from Colombia to testify under pseudonyms but required the government to disclose the witnesses' true identities to defense counsel. The protective order also allowed each defense counsel to share the protected witnesses' true identifies with the represented defendant and one member of the defense team located in the United States. The true identities, however, could not be shared with anyone located in Colombia without the district court's prior permission.
At the motions hearing on January 8, 2007, the district court reviewed the flexibility of the protective order. For instance, Valderama's counsel expressed concern that the protected witnesses' identities could never be released to individuals located in Colombia. The district court responded by emphasizing that the identities could not be released only "without leave of court." The district court explained that defense counsel would not need to "file formal written motions" for permission to disclose protected witness identities in Colombia, but could "come up to the side-bar [in the courtroom] and talk about it, and we'll deal with them one at a time if we need to." Mot. Hr'g Tr. 23, Jan. 8, 2007. The government, in turn, proposed providing to defense counsel the true identity of each protected witness seven *830 days before the witness testified at trial. Although at this hearing Valderama's counsel instead sought the true identities of two witnesses immediately and Giraldo's counsel expressed concern that the trial schedule might not reflect the volume of new information the government had begun providing to the defense, appellants do not suggest that at this hearing they raised other objections to these time constraints.
The government began presenting its case in chief on January 10, 2007, with FARC expert Lieutenant Colonel Camilio Santiago of the Colombian military as its first witness, and the jury heard closing arguments on February 7, 2007. The government's witnesses included a number of Colombian witnesses who testified under pseudonyms.[5] One, "Juan Valdez," was scheduled to testify on January 30, 2007. On January 25, the district court granted Valderama's counsel permission to speak with a Colombian official in the United States and by telephone with a prosecutor in Colombia about "Valdez," and told Valderama's counsel "to get back" to the district court "if [defense counsel] needed more." Trial Tr. 1420-21, Jan. 29, 2007. On January 29, the district court granted permission for Valderama's counsel to investigate "Valdez" in the United States and in Colombia using his true identity. "Valdez" began testifying on January 31. On January 29, 2007, the district court also granted Valderama's counsel permission to investigate protected witness "Mauricio Moreno" in Colombia using his true identity; the district court postponed cross-examination of "Moreno" to "give [Valderama's counsel] all the time [she] want[s] to do the investigation." Trial Tr. 1263, Jan. 29, 2007.

B.
Valderama and Giraldo contend that the government's use of pseudonyms for its witnesses prevented proper investigation of the witnesses and thereby violated their confrontation rights under the Sixth Amendment. Valderama also contends her right to the effective assistance of counsel under the Sixth Amendment was violated.
Although the true identities of protected witnesses who testified under pseudonyms eventually were made known to the defense, the protective order's limitation on defense access to and ultimate use of information regarding these witnesses presents concerns similar to those where witnesses are prevented from disclosing information on cross-examination or when confidential informants do not testify in court. The Supreme Court has addressed such disclosure issues on a case-by-case basis. In Alford v. United States, 282 U.S. 687, 51 S.Ct. 218, 75 L.Ed. 624 (1931), and Smith v. Illinois, 390 U.S. 129, 88 S.Ct. 748, 19 L.Ed.2d 956, the Court held, much as Valderama and Giraldo contend, that the witnesses in those cases should have been required to disclose their addresses, and in Smith to disclose his true name, in order to give the defense "the opportunity to place the witness in his proper setting" and to test the witnesses' credibility at *831 trial. Smith, 390 U.S. at 132, 88 S.Ct. 748 (quoting Alford, 282 U.S. at 692, 51 S.Ct. 218); see also Smith at 133-34, 88 S.Ct. 748 (White, J., concurring). Similarly, in Roviaro v. United States, 353 U.S. 53, 77 S.Ct. 623, 1 L.Ed.2d 639 (1957), relied on by Valderama, the Supreme Court held as a matter of "the fundamental requirements of fairness" that the prosecution could not refuse to disclose the identity of an undercover informant who was "the sole participant, other than the accused, in the transaction charged," because the informant's identity was "relevant and helpful to the defense of an accused," id. at 60-61, 64, 77 S.Ct. 623. The Court cautioned, however, that "no fixed rule with respect to disclosure is justifiable." Id. at 62, 77 S.Ct. 623. Instead "[t]he problem is one that calls for balancing the public interest in protecting the flow of information against the individual's right to prepare his defense," and "[w]hether a proper balance renders nondisclosure erroneous must depend on the particular circumstances of each case, taking into consideration the crime charged, the possible defenses, the possible significance of the informer's testimony, and other relevant factors." Id.
The Supreme Court held, in addressing a Brady claim, that "[t]here is no general constitutional right to discovery in a criminal case," and "[i]t does not follow from the prohibition against concealing evidence favorable to the accused that the prosecution must reveal before trial the names of all witnesses who will testify unfavorably." Weatherford v. Bursey, 429 U.S. 545, 559, 97 S.Ct. 837, 51 L.Ed.2d 30 (1977). Prior to Weatherford, this court also had held in United States v. Bolden, 514 F.2d 1301, 1312 (D.C.Cir.1975), that under Brady the prosecution has no duty to disclose its witness list prior to trial in a noncapital case, citing the provision in 18 U.S.C. § 3432 that a person charged with a capital offense "shall ... be furnished with ... a list ... of the witnesses to be produced on the trial for proving the indictment," and noting the defeat in 1975 of a proposal to amend Federal Rule of Criminal Procedure 16[6] to require disclosure of witness lists.
This court held in United States v. White, 116 F.3d 903, 918 (D.C.Cir.1997), citing Weatherford and Criminal Rule 16, that "[t]he constitutional right to cross examine has never been held to encompass a right to pretrial disclosure of prosecution witnesses." See also United States v. Nevels, 490 F.3d 800, 803 (10th Cir.2007); United States v. Edwards, 47 F.3d 841, 843 (7th Cir.1995); United States v. Alessi, 638 F.2d 466, 481 (2d Cir.1980); 2 Charles Alan Wright & Peter J. Henning, Federal Practice & Procedure: Criminal § 258 (4th ed.2008); cf. United States v. Edmonson, 659 F.2d 549, 551 (5th Cir.1981). "[T]he right to confrontation is a trial right, designed to prevent improper restrictions on the types of questions that defense counsel may ask during cross-examination," Pennsylvania v. Ritchie, 480 U.S. 39, 52, 107 S.Ct. 989, 94 L.Ed.2d 40 (1987) (plurality opinion), and "does not create a right to pretrial discovery," United States v. Mejia, 448 F.3d 436, 458 (D.C.Cir.2006). See United States v. Wilson, 605 F.3d 985, 1003 (D.C.Cir.2010); United States v. Tarantino, 846 F.2d 1384, 1415-16 (D.C.Cir. 1988).
Further, in White the court held that precluding pretrial discovery of the prosecution's witness list does not automatically infringe a defendant's right to present a *832 defense, especially where "security concerns for the witnesses plainly militated against it." 116 F.3d at 918. The court reasoned that the district court's denial of a defendant's motion to discover the prosecution's witness list was within its discretion because the defendant had "offered no special reason in favor of disclosure" and because "potential witnesses had been threatened, assaulted, even murdered." Id. at 913, 918. Other circuits are in accord. See Clark v. Ricketts, 958 F.2d 851, 855 (9th Cir.1991); United States v. Watson, 599 F.2d 1149, 1157 (2d Cir.1979), amended on reh'g on other grounds, 690 F.2d 15 (2d Cir.1979), modified on reh'g on other grounds sub nom. United States v. Muse, 633 F.2d 1041, 1042 n. 1 (2d Cir. 1980); Caldwell v. Minnesota, 536 F.2d 272, 273-74 (8th Cir.1976); United States v. Alston, 460 F.2d 48, 51-52 (5th Cir. 1972); United States v. Palermo, 410 F.2d 468, 472 (7th Cir.1969). The Supreme Court observed, in rejecting the view that Fifth Amendment due process required the prosecution to disclose material impeachment evidence prior to entry of a plea, that the "careful tailoring that characterizes most legal Government witness disclosure requirements" helps prevent "disrupt[ing] ongoing investigations" and "expos[ing] prospective witnesses to serious harm." Ruiz, 536 U.S. at 631-32, 122 S.Ct. 2450. Indeed, concern about witness security contributed to the 1975 defeat of a proposed revision of Criminal Rule 16 that would have required pretrial disclosure of prosecution witnesses, because such disclosure was considered "not in the interest of the effective administration of criminal justice" due to "[d]iscouragement of witnesses and improper contacts directed at influencing their testimony." H.R.Rep. No. 94-414, at 12 (1975) (Conf.Rep.), reprinted in 1975 U.S.C.C.A.N. 713, 716.[7] Contrary to appellants' implicit assumptions, then, pretrial disclosure of the prosecution's case is not always without limitation.
On the record before the district court there can be little question that a protective order for certain Colombian government witnesses was appropriate in light of the government's submissions in its sealed in limine motion for a protective order. Valderama and Giraldo object that the protective order was unnecessary because the government never demonstrated that any of the appellants had personally threatened any government witness. However, the government's sealed motion recounted how the FARC, with which appellants were associated in varying degrees, had [REDACTED] issued bulletins threatening death to anyone who "betrayed... Valderama," and directly threatened to kill at least two cooperating witnesses; the in limine motion indicated the FARC had routinely used violence against its enemies. The appropriateness of using pseudonyms to protect witnesses does not depend on whether the threat to the witness comes directly from a defendant or from another source. Valderama's reference to Giles v. California, ___ U.S. ___, 128 S.Ct. 2678, 171 L.Ed.2d 488 (2008) is inapposite, because here the protected witnesses testified at trial while Giles addressed possible forfeiture of a defendant's Sixth Amendment right to confront a witness when the defendant wrongfully made the witness unavailable to testify. *833 See Giles, ___ U.S. at ___, 128 S.Ct. at 2678, 2687-88. In addition, Valderama's reliance on Roviaro, 353 U.S. 53, 77 S.Ct. 623, 1 L.Ed.2d 639, for the proposition that the government may not prosecute a case while protecting the identity of a witness is misplaced. Unlike here, where the government disclosed the true identities of protected witnesses to defense counsel and those witnesses testified at trial under pseudonyms, Roviaro involved a non-testifying confidential informant.
The protective order and its management by the district court reflect an appropriate balancing of interests in the relevant case-specific context in view of the factors described in Alford and Smith as well as Roviaro, 353 U.S. at 61-62, 77 S.Ct. 623. On the one hand, Valderama, Giraldo, and Celis were indicted for engaging in a drug conspiracy with ties to the FARC, and the government presented evidence that in Colombia the FARC had killed people suspected of helping to arrest Valderama [REDACTED] and had threatened to kill cooperating witnesses. On the other hand, there were special circumstances affecting the ability of appellants to prepare for cross-examination. The prosecution rested on witnesses and events located in a foreign country in which another language was spoken. Because the government planned to have some of the threatened government witnesses testify under pseudonyms about their own involvement with appellants and the FARC in drug trafficking, the defense would attempt to attack the credibility of these witnesses at trial. To enable such confrontation, the district court balanced the reality of potentially life-threatening dangers to the protected witnesses and their families, and the defense need to prepare to cross-examine the protected witnesses by allowing defense access to the true identities of the protected witnesses days before their testimony and, when shown to be necessary for those purposes, allowed investigation using these true identities in the United States and in Colombia. Upon defense requests, the district court permitted investigations using protected witnesses' true identities, albeit not pretrial as defense counsel would have preferred and not always for as long a period of time as defense counsel desired. For example, the district court granted the requests of Valderama's counsel to investigate two protected witnesses using their true identities.
On appeal appellants' objections to the use of pseudonyms reflect frustration and disagreement with the district court's refusal to grant additional time for investigation and review of disclosed materials rather than identifying instances of actual prejudice to their Sixth Amendment confrontation rights. To the extent more investigation was needed and discovery burdened defense counsel, determining whether to grant a continuance is a question that lies within the sound discretion of the district court. See infra Part III. Although defense counsels' frustrations with proceeding under a protective order calling for a "may I" procedure are understandable, the question the court is addressing here is limited to whether appellants' confrontation rights were violated, and appellants fail to demonstrate that the district court's protective order procedure allowing the use of pseudonyms did so.
Valderama's contention that the protective order so limited investigation of the protected witnesses that she was denied her Sixth Amendment right to the effective assistance of counsel is unpersuasive. There is a "strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance" under Strickland v. Washington, 466 U.S. 668, 689, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Valderama's counsel pursued vigorous cross-examination of the *834 protected witnesses and the one instance she cites for prejudice, regarding a belatedly noticed date in the header of a fax transmission regarding "Valdez," reveals upon examination no prejudice at all. See infra Part III. Valderama's reliance on United States v. DeCoster, 487 F.2d 1197, 1204 (D.C.Cir.1973), for the proposition that trial counsel is constitutionally ineffective if counsel does not investigate witnesses, fails to acknowledge that DeCoster predated Strickland and that the circumstances of the two cases are not comparable; DeCoster involved counsel's dereliction not, as here, limitations on investigation imposed by a court. Neither is Valderama's reference to Geders v. United States, 425 U.S. 80, 91, 96 S.Ct. 1330, 47 L.Ed.2d 592 (1976), persuasive; Geders involved a court's restriction on communications between a defendant and defense counsel rather than a restriction on international investigation of endangered witnesses. Even by analogy to Valderama's cases, the record shows the district court accommodated Valderama's requests for additional time to investigate "Valdez" and "Moreno." Although purporting to deny Valderama's request for a continuance on January 25, 2007 to investigate "Moreno," the district court postponed cross-examination of "Moreno" to allow such investigation and on January 29 permitted investigation in Colombia using the true identity of "Moreno." Again, although denying Valderama a continuance on January 29 to investigate "Valdez," the district court allowed Valderama's counsel to investigate "Valdez" in the United States and in Colombia using his true identity and adjourned the trial early the day before Valderama's February 1 cross-examination of "Valdez."
Doubtless out-of-the-country events and the protected status of witnesses allowed to testify under pseudonyms create inconveniences for the parties in a criminal case that a district court must accommodate. But in addressing the law enforcement interests of the government, the district court protected appellants' constitutional rights by affording a means for the defense to obtain time for investigations and for processing disclosed information. The protective order and the district court's management of it involved a delicate balancing of interests necessitated by extraordinary circumstances warranting special measures to protect key witnesses. On appeal, the burden was on appellants to show prejudice, which they have not done. "Under all the circumstances, given the seriousness of the threat and the extensiveness of the cross-examination," Watson, 599 F.2d at 1157; see infra Part III, we hold the district court did not impermissibly intrude upon appellants' Sixth Amendment rights.

C.
In Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), the Supreme Court held that "suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution." Id. at 87, 83 S.Ct. 1194. The Supreme Court recognized the obligation to disclose even in the absence of a defense request. United States v. Agurs, 427 U.S. 97, 107, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976). Further, in Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), the Supreme Court extended the prosecution's Brady obligation to include the disclosure of evidence affecting the credibility of a witness. Such information and evidence is "material" under Brady "if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Kyles v. Whitley, 514 U.S. 419, 433, 115 S.Ct. 1555, *835 131 L.Ed.2d 490 (1995) (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985) (opinion of Blackmun, J.)). The Supreme Court continues to reaffirm that prosecutors have an "affirmative duty to disclose evidence favorable to a defendant," Kyles, 514 U.S. at 432, 115 S.Ct. 1555, and that "the prudent prosecutor will resolve doubtful questions in favor of disclosure," Agurs, 427 U.S. at 108, 96 S.Ct. 2392; see Kyles, 514 U.S. at 439, 115 S.Ct. 1555.
The timing of the government's disclosures of Brady and Giglio evidence and information to the defense is important. In United States v. Pollack, 534 F.2d 964 (D.C.Cir.1976), this court instructed that "[d]isclosure by the government must be made at such a time as to allow the defense to use the favorable material effectively in the preparation and presentation of its case, even if satisfaction of this criterion requires pre-trial disclosure." Id. at 973. Similarly, in Bagley, 473 U.S. at 678, 105 S.Ct. 3375, the Supreme Court had observed that "[t]he constitutional error, if any, in this case was the Government's failure to assist the defense by disclosing information that might have been helpful in conducting the cross-examination." Cf. Leka v. Portuondo, 257 F.3d 89, 103 (2d Cir.2001). Where the prosecution tardily discloses material pursuant to Brady or Giglio, however, appellants "must establish that had the information or evidence been disclosed earlier, there is a probability sufficient to undermine our confidence in the actual outcome that the jury would have acquitted." Tarantino, 846 F.2d at 1417. The prosecution also must disclose under the Jencks Act, 18 U.S.C. § 3500, statements of a prosecution witness after the witness has testified on direct examination, see United States v. Oruche, 484 F.3d 590, 597 (D.C.Cir.2007); FED.R.CRIM.P. 26.2, in a manner allowing the defense "a reasonable opportunity to examine it and prepare for its use in the trial," United States v. Holmes, 722 F.2d 37, 40 (4th Cir.1983); cf. United States v. Stanfield, 360 F.3d 1346, 1357 (D.C.Cir. 2004).
The district court stated at the motions hearing on December 8, 2006, in response to defense requests for Brady, Giglio, and Jencks material, that "[t]he government says it's well aware of its obligations and is going to do what it needs to do, and if it hasn't already done it, I'm confident they will do it." Mot. Hr'g Tr. 8, Dec. 8, 2006. The record indicates, however, that witness security concerns influenced the government's decisions on disclosure. At the motions hearing on January 8, 2007, the government recommended "restrictive conditions for the disclosure of any information [it] turn[s] over to the defense because of the high security concerns for [its] witnesses." Mot. Hr'g Tr. 22, Jan. 8, 2007. The government also cautioned that the Jencks material "gives a lot of information that could lead to security concerns." Id. at 24. When defense counsel inquired, in light of the district court's protective order, when Giglio and Jencks material would be provided, the government stated it would turn over Giglio evidence to defense counsel at the start of trial but with the identities of the witnesses who would testify under pseudonyms redacted. The true identities of the protected witnesses would, the government proposed, be disclosed seven days before each witness testified. Jencks statements would be turned over at least two days before each witness testified. In responding to a defense request for the true identities of two particular protected witnesses, the government proposed disclosing the identities only after the jury was sworn, but the district court directed the disclosure occur before the jury was sworn.
As it turned out, the government sometimes made disclosures earlier or later *836 than it had proposed. On occasion the government did not receive material from Colombia until the trial had started, as, for example, with the written and video statements by protected witness "Moreno." Even so, the government disclosed Jencks material for "Moreno" on January 22, more than two days before he testified on January 25, and nine days before his cross-examination on January 31. On January 25, the government disclosed Jencks material for protected witness "Valdez" and other witnesses expected to testify the next week. However, the government did not disclose some Giglio evidence for "Valdez" until January 29 and he was scheduled to testify the following day, although he did not actually testify until January 31. In the district court Valderama challenged the government's disclosures as untimely, and this court's review of the materiality of potential violations of Brady and Giglio is de novo. See Oruche, 484 F.3d at 596; United States v. Cuffie, 80 F.3d 514, 517 (1996).
Valderama contends the disclosed Brady and Giglio materials were turned over too late for the defense to make effective use of them. Although counsel for the United States asserted during oral argument that the prosecution has no obligation to disclose impeachment evidence prior to the first day of trial, even if it has been redacted in accord with a protective order, counsel acknowledged that the critical point is that disclosure must occur in sufficient time for defense counsel to be able to make effective use of the disclosed evidence. Cf. Bagley, 473 U.S. at 678, 105 S.Ct. 3375; Pollack, 534 F.2d at 973.
One of Valderama's (and Giraldo's) objections is that so much information was being disclosed by the government that effective use was prejudiced once the redacted names were disclosed to the defense. The record indicates that the volume of material turned over by the government presented practical difficulties for the defense. At trial the government noted it had provided between six thousand and seven thousand pages of material to the defense during the months before trial, including five thousand wiretap calls, and had turned over eighteen "discovery packages" in the eighteen months before trial. The government did not provide redacted Giglio material until the first day of trial, and later provided the true identities that defense counsel could "then match to the Giglio." Mot. Hr'g Tr. 24, Jan. 8, 2007. Thus defense counsel needed to process this Giglio material in light of the pretrial discovery materials, as well as the Jencks material later disclosed by the government, during trial.
Counsel for Valderama suggested to the district court that the use of redactions should have allowed the government to disclose the redacted material earlier, and counsel for Valderama and Giraldo informed the district court that they were having difficulty during trial processing the disclosed material quickly enough for use. During trial, the district court observed that it was "the government's case to overtry," such as by "bring[ing] on evidence on too short notice as to which [defense counsel] make either now or later... some showing of prejudice." Trial Tr. 1421-22, Jan. 29, 2007. Under the circumstances, Valderama's objection that required disclosures under Brady and Giglio were not timely is not without some persuasive force. See Pollack, 534 F.2d at 973-74. But the question now is whether this untimeliness was "sufficient to undermine our confidence in the actual outcome" of the trial. Tarantino, 846 F.2d at 1417.
Valderama maintains that the government should have disclosed earlier both the statements of "Valdez" to Colombian authorities that did not implicate Valderama *837 in certain drug trafficking and a report and interviews related to "Valdez" that did not implicate Valderama in particular violent crimes. Perhaps so. However, Valderama's counsel's discussion of the report and interviews and her February 1 cross-examination of "Valdez" demonstrate that she was able to make effective use of the materials nonetheless. For example, Valderama's counsel told the district court that the report and interviews did not implicate Valderama in any murders, and Valderama's counsel cross-examined "Valdez" regarding inconsistencies raised by these materials about the length of time he was a member of the FARC and his work for Valderama. Valderama's reliance on Pollack, 534 F.2d at 973; United States v. Enright, 579 F.2d 980, 989 (6th Cir.1978); United States v. Beasley, 576 F.2d 626, 630 (5th Cir.1978); Leka, 257 F.3d at 103; and United States v. Cobb, 271 F.Supp. 159, 163 (S.D.N.Y.1967), are unhelpful to her. In Pollack and Enright, the courts held that the actual or probable Brady violations had not sufficiently disadvantaged the defendants to change the results of the trial; Beasley and Leka involved failed or suppressed rather than untimely disclosure; in Cobb the court discussed why timely disclosure is important.
Even assuming Valderama's counsel might have made more effective use of tardily disclosed information and evidence had the government timely fulfilled its disclosure obligations in all respects, the government's evidence against appellants was overwhelming. For example, not only were there video and wiretap recordings, there was extensive testimony by "Rocio Alvarez" and other government witnesses about Valderama's central role in managing and carrying out the conspiracy to manufacture and export cocaine from Colombia into the United States. Appellants therefore fail to show the untimely disclosures were "material." See Kyles, 514 U.S. at 433-34, 115 S.Ct. 1555.

III.
Valderama raises four objections relating to her ability to challenge the government's case at trial. First, Valderama contends that the trial court prevented her from cross-examining several of the government's witnesses in violation of her Sixth Amendment right to confrontation. Second, she argues that the district court abused its discretion by denying her motions for a continuance so that she could review materials turned over by the government pursuant to the Jencks Act. Third, she argues that she was denied the right to participate in her own defense because she did not receive written translations in Spanish of all documents turned over in discovery. Finally, she argues she was denied a fair trial because the government denied her access to government witnesses. We do not think any of the grounds relied upon merit reversal.

A.
Beginning with the Confrontation Clause argument, Valderama's primary contention is that the district court violated her rights by placing limits on her cross-examination of Juan Valdez. Valdez testified that, as part of his role as a security guard for the FARC, he accompanied Valderama on several trips throughout the Caguan region where Valderama delivered money and picked up large shipments of cocaine base.
During cross-examination, counsel for Valderama attempted to impeach Valdez with a statement he gave to Colombian authorities. Initially, however, Valdez denied that the signature on the statement was his. On appeal, Valderama claims the district court prevented her from impeaching Valdez by demonstrating that the signature was in fact his. Discussion at a side-bar conference indicated, however, that Valdez denied that it was his signature *838 because he was concerned about not disclosing his real name. In any event, the district judge instructed the jury that, despite Valdez's initial confusion, the signature and statement did belong to him. Given this instruction from the judge, the jury would not have received a "significantly different impression" of Valdez's credibility had Valderama's counsel been allowed to press Valdez about his initial denial and thus no confrontation clause violation can be shown. United States v. Davis, 127 F.3d 68, 70-71 (D.C.Cir.1997).
In addition to the signature issue, Valderama argues that the trial court violated her Sixth Amendment rights by prohibiting her from impeaching Valdez with the substance of the written statement. Specifically, Valderama argues that the trial court prevented her (a) from asking Valdez why the statement mentioned Valderama but did not refer to the frequent drug-running trips with her he testified to on direct examination and (b) from probing inconsistencies between his trial testimony and the written statement regarding his length of service in the 14th Front. But Valderama did have the opportunity to effectively question Valdez on both of these points. The trial court explicitly permitted Valderama's counsel to ask Valdez if the statement referred to his drug-running trips with Valderama. Counsel did so and Valdez conceded it did not. And while Valderama argues she was prevented from asking Valdez why he omitted such a significant fact in his statement, Valdez did provide an explanation, stating that the Colombian authorities to whom he gave the statement did not ask him about that subject.
As for the length of Valdez's service, in both cross-examination and re-cross Valderama's counsel pressed Valdez on the discrepancy between the written statement that said he had been with the 14th Front for five years and his trial testimony that he had spent approximately nine years with the group. Ultimately, Valdez responded that the five years listed in the written statement was incorrect. While the trial court did eventually limit defense counsel's questions on this issue, Valderama's counsel was able to effectively point out the discrepancy. That is all the Sixth Amendment requires. See Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985) ("[T]he Confrontation Clause guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish.").
Valderama raises one additional complaint with respect to her cross-examination of Valdez. She claims that the trial court prevented her from asking Valdez about a fax header on the written statement that indicated Valdez gave the statement in 2003. She asserts the date is material because the statement was purportedly given when Valdez turned himself in to Colombian authorities and thus contradicts Valdez's testimony that he remained with the FARC through 2005. Although the trial court did say that it would not allow questions regarding the date listed in the text of the statement because it believed it was the result of a typographical error, apparently neither the parties nor the court noticed the fax header at all. Indeed, even Valderama admits that the date on the fax header was "faint" and that even her counsel did not discover it until after trial. Appellant Valderama Br. 25. Because Valderama's counsel did not even notice the date in the fax header, much less attempt to use it to impeach Valdez at trial, we cannot say that the court somehow deprived Valderama of her right to confront Valdez on this issue.
Valderama also raises Confrontation Clause challenges concerning *839 her questioning of other witnesses, but these challenges also lack merit. For instance, she claims that the court did not allow her to cross-examine Mauricio Moreno with records showing a prior conviction, but the government and Valderama's counsel agreed at trial that the records in question were, at best, inconclusive as to whether they referred to Moreno. In addition, she claims that she was prevented from impeaching Moreno with video testimony he gave in a prior Colombian proceeding. It is simply not the case, however, that the court prevented Valderama from pursuing this line of questioning. Valderama acknowledges she did not pursue it because she did not have an English transcript of that prior testimony, yet her counsel received the video six days before cross-examination began and neither had a transcript produced nor asked the court to produce one. And while Valderama claims she was forced to cut short her cross-examination of Rocio Alvarez when her counsel learned that Alvarez was not the confidential source listed in a report produced by the DEA, we simply do not understand how this confusion on the part of her attorney could have violated Valderama's Confrontation Clause rights.[8]
Finally, Valderama claims her counsel could not effectively cross-examine Rodrigo Jardinero because the government misled her into believing that Jardinero had never met her client, leaving counsel unprepared when Jardinero testified that he discussed drug dealing with Valderama at a meeting in a Panama restaurant. We have no need to probe the government's motives nor whether Valderama's counsel was genuinely surprised at the testimony, for it is clear that counsel more than overcame any initial shockshe cross-examined Jardinero at length about the meeting at issue and his general credibility. This was undoubtedly effective cross-examination under the Sixth Amendment.

B.
Turning to Valderama's next argument, she asserts that her conviction should be overturned because the district court improperly denied several motions for continuances. Valderama sought continuances to review material produced by the government pursuant to the Jencks Act, 18 U.S.C. § 3500. We review the denial of a motion for a continuance to review Jencks material for an abuse of discretion. United States v. Stanfield, 360 F.3d 1346, 1358 (D.C.Cir.2004). In order to obtain reversal, an appellant must show that actual prejudice resulted from denial of the continuance. United States v. Kelley, 36 F.3d 1118, 1126 (D.C.Cir.1994). We find no grounds for reversal.
Valderama makes much of the district court's statement at the outset of trial that there would be "100 percent no continuances." This unflinching desire for expeditiousness, she contends, resulted in an abuse of discretion when the court refused to adjourn proceedings to allow appellants to review Jencks material and prepare for its use.[9] But while the district court did *840 wish to avoid continuances, it did in fact make adjustments in the trial schedule to give the appellants time to review Jencks material. For example, when the appellants sought a continuance to review Jencks statements by Mauricio Moreno, the district court denied the continuance motion but postponed Moreno's cross-examination and moved on to other witnesses, giving defense counsel six additional days to review the Jencks material for Moreno. We found no abuse of discretion in a case in which the district court gave defense counsel nine minutes to review "a very thick stack of papers," Stanfield, 360 F.3d at 1358, so we surely could not criticize the district court for providing six days.
We view similarly the district court's denial of a continuance to review Jencks material concerning Juan Valdez. The Jencks material concerning Valdez was provided on January 25, but counsel did not request a continuance until January 29, and cross-examination did not begin until February 1. Counsel thus had seven days to review the material before cross-examination.
To be sure, Valderama points out that, at least with respect to Valdez, she sought a continuance not only to review the Jencks material but also to use the material as a basis to perform an investigation of Valdez; she asserts she simply did not have enough time to conduct an adequate investigation into an individual who resides in a foreign country. Valderama did, however, have the opportunity to communicate with a Colombian law enforcement official and a Colombian prosecutor familiar with Valdez. And while she may have wished to conduct a fuller investigation, she does not identify any other people she would have interviewed with additional time, much less what information she believes she may have uncovered and how any such information could have affected the result at trial in any way. Moreover, as discussed supra, Valderama's counsel vigorously cross-examined Valdez using the statement he gave to Colombian authorities to challenge his credibility. As a result of all of this, Valderama cannot demonstrate actual prejudice and is thus not entitled to reversal.[10]

C.
Next, Valderama argues her conviction should be overturned because the court did not require that all discovery documents containing English be translated into Spanish. This was required, Valderama asserts, because she has a right to assist in preparing her own defense and her inability to comprehend English prevented her from doing so. It is simply not the case, however, that a language barrier completely prevented Valderama from assisting in her own defense. After all, she had the benefit of interpreters for all courtroom proceedings and her defense counsel was bilingual, and thus could have effectively discussed any relevant discovery materials with Valderama. In light of *841 these facts, Valderama's constitutional claim is actually quite audacious: she asks us to hold that the Constitution compels that in every case in which defendant is not fluent in English, all discovery documents must be translated, in written form, into the defendant's native tongue, even if defendant's counsel is bilingual.
There is simply no support for such a claim. In United States v. Mosquera, 816 F.Supp. 168, 175 (E.D.N.Y.1993), the strongest case for Valderama's position, a district court ordered the government to turn over a copy of the indictment translated into Spanish and additionally ordered that "[a]ll documents, except motion papers and original evidence" be translated, id. at 171.[11] In doing so, however, the court explained that the scope of translation in a given case is committed to the district court's discretion, id. at 174, and noted special factors that led it to require written translations in that case the case included eighteen defendants that did not understand English, each defendant was represented by separate counsel, and the defendants were unable to understand even the charges and evidence against them. Id. at 170, 176. Furthermore, a number of other courts have recognized that "Mosquera does not stand for the proposition that criminal defendants enjoy a constitutional right to written translations of [all] court documents." United States v. Gonzales, 339 F.3d 725, 729 (8th Cir.2003); see also Canizales-Satizabal v. United States, 1995 WL 759472 *1 n. 2 (7th Cir.1995) ("This court... has never held that a defendant has a constitutional right to have documents translated into his own language."); Sanders v. United States, 130 F.Supp.2d 447, 449 (S.D.N.Y.2001) ("The Constitution does not require that [information in court documents] be communicated in writing in a foreign language."). We agree. "A court may decide to provide written translations in difficult and complicated cases," Gonzales, 339 F.3d at 729 (emphasis supplied), but that decision, like the management of discovery in general, is committed to the district court's discretion. See Islamic Am. Relief Agency v. Gonzales, 477 F.3d 728, 737 (D.C.Cir.2007). And in this case, in which Valderama was assisted by bilingual counsel and where there is no reason to believe Valderama was unable to understand the charges and evidence against her, we find no abuse of discretion.

D.
Finally, we reject Valderama's claim that she is entitled to reversal because the government impeded her access to witnesses. At one point in the trial, Valderama's counsel claimed that she had requested to interview government witnesses before they testified but she had not received a response. Lawyers for the government responded by saying that the witnesses had responded, but they did not wish to be interviewed by the defense. Valderama raised no further objections. Without more, we have no basis to find that the government acted in bad faith to keep witnesses from talking with lawyers for the defense.

IV.
Appellants also raise challenges to the admission into evidence of certain recorded conversations. None is persuasive.

A.
Giraldo contends the district court erred by admitting wiretapped recordings *842 of his telephone conversations. He maintains the tapes were inadequately authenticated and that the government did not prove a proper chain of custody. We review the district court's rulings on these points for abuse of discretion. See United States v. Lawson, 494 F.3d 1046, 1052 (D.C.Cir.2007).
To authenticate audio recordings, the government must prove that, "as a matter of reasonable probability, possibilities of misidentification and adulteration have been eliminated." White, 116 F.3d at 920-21 (internal quotation marks omitted); see also FED.R.EVID. 901(a) ("The requirement of authentication ... is satisfied by evidence sufficient to support a finding that the matter in question is what its proponent claims."). At trial, the government introduced evidence that the equipment used to record Giraldo's phone calls was in proper working order and that only authorized personnel had access to the recordings. Four witnesses identified Giraldo and the other individuals recorded. Camila Vargas, one of the officials responsible for copying the tapes, stated that the duplication process resulted in an "exact" copy of the original recording. Trial Tr. at 217, Jan. 16, 2007. Giraldo argues this evidence was insufficient because neither Vargas nor Pablo Diaz, another official involved in duplicating the tapes, had listened to all of the tapes to ensure a perfect duplication. But that is not the standard for authentication. Despite the fact that no one listened to each tape from beginning to end, the district court heard evidence relating to the integrity of the duplication procedures and the quality of the machinery. Based upon this showing, we conclude that the court did not abuse its discretion by determining that the recordings were authentic "as a matter of reasonable probability." White, 116 F.3d at 920-21.
Giraldo also argues that the government failed to establish an adequate chain of custody because it provided no evidence of who transferred the original recordings from their maker, Alfonso Sanabria, to Vargas. But the government need not show the identity of each person who had custody of the tapes. See Robinson v. United States, 283 F.2d 508, 509 (D.C.Cir.1960). Instead, the government must only "demonstrate that, as a matter of reasonable probability, possibilities of misidentification and adulteration have been eliminated." United States v. Stewart, 104 F.3d 1377, 1383 (D.C.Cir.1997) (internal quotation marks omitted). The government easily met its burden. Sanabria testified regarding his office's protocols: "Each DVD receives a number, and then it is put in its package, in its case, and it's given to another division, another agency within that same work area. And they are in charge of keeping the chain of custody of the DVD, and they place it in the vault, which is in an area with restricted access." Trial Tr. at 175, Jan. 16, 2007. Sanabria and his staff followed these procedures. See id. at 166-70, 172-75, 192-94. On this evidence, the district court did not abuse its discretion by admitting these recordings.

B.
Celis contests the admission of a videotaped recording of a conversation between Alvarez, a cooperating witness, and Giraldo. The video contained numerous statements by Giraldo, which the government offered as direct evidence of the conspiracy. Over appellants' objections, the district court admitted the statements under Federal Rule of Evidence 801(d)(2)(E), which permits admission of statements made by coconspirators in furtherance of a conspiracy. Celis argues the statements were not meant to further the conspiracy and, in any event, the conspiracy *843 had ended by the time they were made. We review for clear error the court's determinations that a particular statement was made during and in furtherance of a conspiracy. See United States v. Edmond, 52 F.3d 1080, 1110 (D.C.Cir.1995). To find clear error, we must be "left with the definite and firm conviction that a mistake has been committed." Anderson v. Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985) (internal quotation marks omitted). Our clear error review requires that we defer to the district court's evaluation of the statements in light of the other evidence that has been presented. See Edmond, 52 F.3d at 1111 (declining to find clear error when the statements "plausibly may be interpreted" as advancing the conspiracy).
A statement is made "in furtherance of a conspiracy" when it
can reasonably be interpreted as encouraging a [coconspirator] or other person to advance the conspiracy, or as enhancing a [coconspirator] or other person's usefulness to the conspiracy.... Such statements include those that keep a coconspirator updated on the status of the business, motivate a coconspirator's continued participation, or provide background information on key conspiracy members.
United States v. Carson, 455 F.3d 336, 366-67 (D.C.Cir.2006) (internal quotation marks and citations omitted). Celis objects generally to the entire video, contending that "[a]ll conversations on the video are hearsay," Appellant Celis Br. 22, and he argues specifically that the following admitted statements were not made in furtherance of the conspiracy.
First, Celis claims that Giraldo's statements relating to Celis's debt to Valderama and the lost shipment of cocaine are inadmissible "past narratives" and were not made in furtherance of the conspiracy. Appellant Celis Br. 28. The district court did not clearly err here. In United States v. Perholtz, we held that a past narrative may be admissible if it is "part[ ] of continuing activity that was essential to" the conspiracy. 842 F.2d 343, 357 (D.C.Cir. 1998). It is plausible that Giraldo made his statements to keep Alvarez informed about the current status of the conspiracy, ensuring that all coconspirators had up-to-date information. Indeed, this is precisely the kind of example we envisioned in United States v. Carson. 455 F.3d at 366-67 (holding that statements that "updated [others] on the status of the business" were admissible).
Second, Celis argues that statements Giraldo made about his personal access to Ramirez, his knowledge of drug routes, and his history in the drug business were "grandstanding" and "mere exaggeration." Appellant Celis Br. 28-29. As we stated in Carson, if one's statement can be understood as enhancing one's usefulness to the conspiracy, it is admissible. See 455 F.3d at 366-67. We view these statements as Giraldo demonstrating how he can be a more effective member of the conspiracy and conclude there was no clear error in their admission.
Finally, Celis labels some conversations as "idle chatter." Appellant Celis Br. 28-29. These include statements made by Giraldo while Alvarez was persuading him to remain in the car so she could continue to record him, statements made by Giraldo while having a short telephone conversation, and Giraldo's description of Ramirez as "dangerous." Though these statements did not further the conspiracy, we agree with the government that any error in their admission was harmless. In view of the mountain of evidence concerning Celis's culpability, which we have already detailed, none of these statements were prejudicial. Likewise, we have carefully reviewed the remaining *844 statements made during this conversation and conclude that Celis's general objection to the recording lacks merit. Statements not specifically identified by Celis undeniably furthered the conspiracy. See, e.g., Video Tape Exhibit N-6 (May 22, 2003) at 10 ("First of all, was that merchandize [sic] going to New York or to Miami?"); id. at 11 ("How much was it sold for?").
The district court also did not clearly err by concluding that the conspiracy remained intact at the time of Giraldo's statements. By this point, Celis suggests, the conspiracy "was broken and no longer functioning" because Valderama had threatened to kill Celis in 2002 over an outstanding debt from an earlier drug shipment. Appellant Celis Br. 24. Though there was evidence that Valderama did threaten to kill Celis, the conspiracy remained alive. Indeed, the government introduced a recording of Celis and Giraldo from May 20, 2003, which demonstrates they were still in communication regarding the conspiracy. In addition, Alvarez testified that Giraldo had informed her on May 22, 2003 that Celis continued to attempt to sell Valderama's cocaine to pay off his outstanding debt. See Trial Tr. at 694, Jan. 18, 2007. Given this evidence, the district court did not clearly err by finding that the conspiracy remained intact at the time of the recording. Admitting the videotaped recording, therefore, was not an abuse of discretion.

V.
Appellants raise two challenges regarding the indictment. First, Giraldo argues the district court erred by denying his motion to sever the indictment. Next, Celis argues the evidence at trial impermissibly varied from the indictment. We reject each challenge.

A.
Giraldo asked the district court to sever the indictment so that he would be tried separately from Valderama. The district court denied the request. Federal Rule of Criminal Procedure 14 permits the district court to sever an indictment if "the joinder of offenses ... appears to prejudice a defendant." FED.R.CRIM.P. 14. The Supreme Court has instructed district courts to grant severance "only if there is a serious risk that a joint trial would compromise a specific trial right of one of the defendants, or prevent the jury from making a reliable judgment about guilt or innocence." Zafiro v. United States, 506 U.S. 534, 539, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993). District courts should grant severance sparingly because of the "strong interests favoring joint trials, particularly the desire to conserve the time of courts, prosecutors, witnesses, and jurors." United States v. Mardian, 546 F.2d 973, 979 (D.C.Cir.1976). We review the denial of a motion to sever for abuse of discretion, which we will not find "if the jury could reasonably compartmentalize the evidence introduced against each individual defendant." United States v. Mejia, 448 F.3d 436, 446 (D.C.Cir.2006) (internal quotation marks omitted).
Valderama was a member of the FARC. Giraldo was not. Giraldo claims he was prejudiced by the joint trial because the government introduced evidence relating to FARC atrocities that had nothing to do with him. If the indictment had been severed, Giraldo argues, the jury would have considered his guilt or innocence without hearing a word about the FARC. That may well be true, but it does not follow that the jury was incapable of fairly assessing Giraldo's guilt. We have found juries capable of determining the guilt or innocence of an individual tried alongside others when the prosecution presents "independent *845 and substantial" evidence regarding each defendant's culpability. United States v. Halliman, 923 F.2d 873, 884 (D.C.Cir.1991). At trial, the government offered ample evidence of Giraldo's personal involvement in the conspiracy. Indeed, the evidence against Giraldo involved far more than unproven allegations of an association with the FARC. See, e.g., Trial Tr. at 602, Jan. 18, 2007 (describing Giraldo's role in arranging a meeting between Alvarez and Ramirez); id. at 621 (describing Giraldo's role in informing Valderama that Celis's shipment had been confiscated); Trial Tr. at 1157, Jan. 25, 2007 (describing Giraldo's role in shipping 400 kilograms of cocaine to the United States); id. at 1164-65 (describing the plan to ship cocaine "via the routes [Giraldo] maintained to the United States"). The jury could assess his personal culpability because it heard a significant amount of evidence relating to his own unlawful acts quite apart from anything said about the FARC.
Moreover, the district court instructed the jury to base its evaluation of each defendant's guilt on his or her own conductnot that of the FARC:
[T]he FARC is not a defendant in this case, and the defendants are not on trial for having knowledge of, or being associated with, the FARC.... [T]he government must prove as to each defendant that he or she knowingly and willfully joined and participated in the conspiracy.
Trial Tr. at 2253, 2256, Feb. 7, 2007. This instruction fully addressed Giraldo's concern. Because the jury is "presumed to follow [its] instructions," Zafiro, 506 U.S. at 540, 113 S.Ct. 933, "these instructions cured any possible risk of prejudice," Carson, 455 F.3d at 375. The independent evidence of Giraldo's guilt and the court's instruction lead us to conclude that the jury could separate the evidence against Giraldo from the evidence against his co-defendants. The district court did not abuse its discretion by denying his motion to sever.

B.
Celis claims that his trial was unfair because the government offered evidence of multiple conspiracies, although the indictment charged him with only one. The government's evidence, he argues, described criminal activity beyond what was alleged in the indictment. If Celis were correct that the government presented evidence of multiple conspiracies, he may also be correct that the jury might well have conflated evidence of crimes for which he was not charged with evidence of the offenses for which he was indicted. Even so, "[a] variance between the allegations of the indictment and the proof at trial constitutes grounds for reversal only if the appellant proves (1) that the evidence at trial established facts materially variant from those alleged in the indictment, and (2) that the variance caused substantial prejudice." Tarantino, 846 F.2d at 1391. Even if we assume that the trial evidence varied from the indictment, Celis cannot prove prejudice, which requires a showing that the jury was "substantially likely" to consider evidence of a crime for which he was not indicted in its assessment of his guilt. Id.; see United States v. Gaviria, 116 F.3d 1498, 1533 (D.C.Cir.1997). Celis claims that the government's evidence of others' crimes was "intermingled with testimony regarding Celis, making it difficult to parcel out and separately consider." Appellant Celis Br. 17. We look to three factors to determine how difficult it was for a jury to separate allegations against multiple defendants.
First, the number of co-defendants is significant because jurors will be less likely to transfer guilt from one defendant *846 to another when there are only a few. See Gaviria, 116 F.3d at 1533. We have found that the trial of four co-defendants presented no possibility of spillover prejudice even when the government put on evidence that varied from the crimes charged in the indictment. See, e.g., id.; United States v. Mathis, 216 F.3d 18, 25 (D.C.Cir.2000). With only three co-defendants, the risk of spillover prejudice was not substantial, see Gaviria, 116 F.3d at 1533, and we conclude that the jury could have distinguished among the crimes and determined without great difficulty what evidence fit which defendant.
Second, "the danger of spillover prejudice is minimal when the Government presents tape recordings of individual defendants." Id. Recordings of telephone calls of Celis, Valderama, and Giraldo were put into evidence, as well as a video recording of Giraldo's conversation with Alvarez. When the government presents an audio or video recording of the defendant discussing criminal acts, the risk of prejudicial spillover is minimal because the jury has "no need to look beyond each defendant's own words in order to convict." United States v. Anderson, 39 F.3d 331, 348 (D.C.Cir.1994) (internal quotation marks omitted), rev'd in part on other grounds, 59 F.3d 1323 (D.C.Cir.1995) (en banc).
Third, we consider whether the district court eliminated any potential prejudice through a clarifying jury instruction. When the jury is "properly instructed that proof of several conspiracies is not proof of the single conspiracy charged, the risk of prejudicial error is greatly diminished, if not eliminated altogether." United States v. Flood, 965 F.2d 505, 509 (7th Cir.1992). Here, the court instructed the jury to acquit if it found the defendants had participated in a conspiracy other than that alleged in the indictment:
[I]f you find from all the evidence that one or more separate conspiracies existed, you must determine whether at least one of them is the single conspiracy that the indictment charges. If you should find that a particular defendant was a member of a separate conspiracy but not the one charged in the indictment, then you must acquit that defendant.
Trial Tr. at 2258, Feb. 7, 2007. We assume juries follow their instructions, see Zafiro, 506 U.S. at 539-41, 113 S.Ct. 933, and Celis raises no argument nor proffered evidence that would suggest to us that the jury did not heed the court's admonition. See United States v. Clarke, 24 F.3d 257, 264 (D.C.Cir.1994) ("To find reversible error, we would have to conclude that the jury disregarded the court's instructions."). This instruction, therefore, "cure[d] any risk of prejudice." Carson, 455 F.3d at 374-75.
In light of the small number of co-defendants, the audio recordings of each defendant, and the explicit jury instruction, we hold that any purported variance from the indictment was not prejudicial to Celis and does not warrant reversal.

VI.
We conclude by considering Valderama's remaining contentions that the evidence was insufficient to warrant a conviction, the trial was fundamentally unfair, and the district court abused its discretion in denying her motion for a new trial. None is persuasive.

A.
Putting to one side the videotapes and audio recordings she argues should never have been admitted into evidence and the Confrontation Clause errors she claims infected much of the trial, Valderama asserts that the remaining "untainted" *847 evidence was insufficient to convict her as a matter of law. Of course, we have just concluded that all of the "tainted" evidence cited by Valderama was properly admitted and that there were no Confrontation Clause errors. Because Valderama's argument proceeds from a flawed premise, we need not refute her hypothetical allegations of error. Thus, we consider only whether the properly admitted evidence was sufficient for "any rational trier of fact [to] have found the essential elements of the crime beyond a reasonable doubt." United States v. Arrington, 309 F.3d 40, 48 (D.C.Cir.2002) (internal quotation marks omitted). We have no difficulty concluding that the evidence supported the jury verdict against Valderama. The government presented detailed, eye-witness testimony that she coordinated the production, refining, and distribution of massive quantities of cocaine in connection with the indicted conspiracy. Likewise, the jury heard evidence that Valderama attended relevant meetings for the purpose of initiating and then executing the charged conspiracy.
To the extent that Celis and Giraldo have joined this argument, our conclusion applies equally to them. The jury heard uncontroverted evidence regarding their involvement in the conspiracy, including recordings of Celis and Giraldo discussing their criminal activities. Viewing the evidence in the light most favorable to the government, as we must, see United States v. Martinez, 476 F.3d 961, 968 (D.C.Cir.2007), there is no doubt that the evidence was sufficient to convict each appellant.

B.
Valderama argues that the totality of errors committed by the district court deprived her of a fair trial. This claim is nothing more than a restatement of every objection she raised before and during trial. Valderama contends that the aggregation of these errors "worked a grave injustice," depriving her of her constitutional right to a fair trial. Appellant Valderama Br. 38. Valderama directs our attention to Egan v. United States for the proposition that the cumulative effect of many errors can render a verdict reversible. 287 F. 958, 971 (D.C.Cir.1923); see United States v. Brown, 508 F.3d 1066, 1076 (D.C.Cir. 2007). In Egan, we noted that even though individual errors may not be sufficient to warrant reversal, the total effect of numerous small missteps may deprive a defendant of a fair trial. True enough, but Egan requires the defendant to make a showing of prejudice, see 287 F. at 971, which Valderama has not done.

C.
Finally, in two conclusory sentences, Valderama argues the district court abused its discretion by denying her motions requesting a new trial. See Appellant Valderama Br. 37. At sentencing, Valderama so moved in light of her discovery of the faint fax header on Valdez's statement to the Colombian authorities. See supra Part III. Additionally, Valderama moved for a new trial because Valdez made post-trial statements to DEA agents that purportedly contradicted his trial testimony. See Sentencing Tr. at 5-9, July 2, 2007. Valderama contended that these statements impeached Valdez's testimony.
We review a district court's decision to deny a motion for new trial for abuse of discretion. See United States v. Johnson, 519 F.3d 478, 487 (D.C.Cir.2008). To obtain a new trial because of newly discovered evidence, a defendant must satisfy five requirements:
(1) the evidence must have been discovered since the trial; (2) the party seeking the new trial must show diligence in the attempt to procure the newly discovered *848 evidence; (3) the evidence relied on must not be merely cumulative or impeaching; (4) it must be material to the issues involved; and (5) [it must be] of such nature that in a new trial it would probably produce an acquittal.
Id. (quoting United States v. Lafayette, 983 F.2d 1102, 1105 (D.C.Cir.1993)). This is a high bar to cross, and Valderama does not come close to reaching it. In light of the overwhelming evidence of guilt, we conclude that in a new trial these two pieces of evidence would not "probably produce an acquittal." See id.
Accordingly, we affirm the judgments of conviction.
NOTES
[1]  Appellants join each others' briefs. See FED. R.APP. P. 28(i). Valderama and Celis do so without qualification; Giraldo does so "except those contrary to his interests on appeal," Appellant Giraldo Br. 27. Celis purports to join the arguments in Valderama's and Giraldo's briefs but provides no explanation of how the incorporated contentions affect him individually. In view of our disposition we need not decide whether Celis thereby waived these contentions. Cf. United States v. Avilés-Colon, 536 F.3d 1, 27 n. 22 (1st Cir. 2008); see also N.Y. Rehabilitation Care Mgmt. v. NLRB, 506 F.3d 1070, 1076 (D.C.Cir.2007).
[2]  While Ramirez was indicted, he was never apprehended and remains a fugitive.
[3]  The Sixth Amendment provides, in relevant part: "In all criminal prosecutions, the accused shall enjoy the right ... to be confronted with the witnesses against him ... and to have the [a]ssistance of [c]ounsel for his defense." U.S. CONST. amend. VI.
[4]  The Fifth Amendment provides, in relevant part: "No person shall ... be deprived of life, liberty, or property, without due process of law." U.S. CONST. amend. V.
[5]  According to Giraldo, five of the protected witnesses were "so-called `insider' witnesses": "Alvarez" (the "know it all" witness), "Moreno" ("the `fly on the wall' witness, claiming to have been present at numerous meetings and conversations in which he was not participating"), "Valdez" ("`the dedicated soldier' who took advantage of a government-sponsored leniency program to prevent incarceration"), "Lopez" ("the `politically active' witness, whose work on behalf of the poor and down-trodden afforded him an opportunity to be in the right place, at the right time"), and "Jardinero" ("the `reluctant' witness, whose disdain for Mr. Giraldo and Ms. Valderama was palpable"). Appellant Giraldo Br. 4-5.
[6]  Criminal Rule 16 provides for disclosure by the prosecution or defense of statements, documents, reports, objects, and other items or information in particular circumstances, as well as for regulation of discovery by the district court. Names of witnesses are not listed as subject to disclosure. See FED. R.CRIM.P. 16.
[7]  In a similar vein, the United States Attorneys' Manual states that although disclosing information prior to trial might make the trial more efficient, "pretrial disclosure of a witness' identity or statement should not be made if there is, in the judgment of the prosecutor, any reason to believe that such disclosure would endanger the safety of the witness or any other person, or lead to efforts to obstruct justice," and suggests "applying for a protective order if discovery ... may create a risk of harm to the . . . witness." U.S. Attorneys' Manual § 9-6.200 (Nov.2000).
[8]  Valderama also claims that she was prevented from confronting hearsay statements by Moreno, but the only citations in her brief on this issue are to defense objections that were sustained.
[9]  The Jencks Act obligates the government to turn over "statements" of government witnesses. 18 U.S.C. § 3500(b). Unlike the government's Brady obligations, the government is not required to turn over Jencks material until after the witness has testified at trial. Id. Yet while the government may wait until after its witness has testified to turn over material, the act gives the district court discretion "to recess proceedings in the trial for such time as it may determine to be reasonably required for the examination of such statement by said defendant and his preparation for its use in the trial." Id. § 3500(c).
[10]  In addition to her motions for continuances to review Jencks Act material, Valderama also claims the district court should have granted a continuance during the testimony of Rodrigo Jardinero for entirely different reasons. As discussed supra, she claims the government misled her counsel into believing that Jardinero and Valderama had never met. She submits that counsel's surprise when Jardinero testified to knowing Valderama left her unprepared, so the court should have ordered a continuance. Once again, Valderama cannot demonstrate prejudice. As discussed supra, Valderama's counsel overcame any surprise and cross-examined Jardinero at length about the meeting at issue and his general credibility. We can find no prejudice in light of such exemplary cross-examination. See Kelley, 36 F.3d at 1126 (defendant not prejudiced by denial of motion for continuance when counsel presented "high quality" defense).
[11]  It is not obvious to us that discovery documents such as those at issue here would have come within the ambit of the relatively expansive order in Mosquera. Presumably, many of the documents produced in discovery would qualify as "original evidence."
