
597 F.3d 1329 (2010)
UNITED STATES of America, Appellee
v.
Alvaro Augustin MEJIA, also known as Edwin Renee Sapon Ruiz, Appellant.
No. 08-3097.
United States Court of Appeals, District of Columbia Circuit.
Argued February 19, 2010.
Decided March 30, 2010.
*1332 Carmen D. Hernandez, appointed by the court, argued the cause for the appellant.
Stephan E. Oestreicher Jr., Attorney, United States Department of Justice, argued the cause for the appellee. Lanny A. Breuer, Assistant Attorney General, Gary G. Grindler, Deputy Assistant Attorney General, and Brian M. Tomney, Attorney, were on brief. Teresa A. Wallbaum, Attorney, and Roy W. McLeese III, Assistant United States Attorney, entered appearances.
Before: HENDERSON and GARLAND, Circuit Judges, and EDWARDS, Senior Circuit Judge.
Opinion for the Court filed by Circuit Judge HENDERSON.
KAREN LeCRAFT HENDERSON, Circuit Judge:
Alvaro Augustin Mejia and four co-defendants were charged with a single count of conspiring to import five or more kilograms of cocaine into the United States after a United States Drug Enforcement Administration (DEA) sting operation caught them on tape plotting to transport and safeguard a 1,300 kilogram drug shipment through Guatemala. On appeal, Mejia challenges various aspects of his conviction and sentence. We affirm.

I.
In late 2005, the DEA initiated a Central American sting operation that ensnared Mejia and four fellow Guatemalan coconspirators: Jorge Ricardo Bardales-Bourdet (Bardales), Edgar Antonio Chiu Serrano (Serrano), Erik Donaire Constanza-Bran (Bran) and Juan Daniel Del Cid Morales (Morales). According to the evidence at trial, the DEA learned that Bardales was helping Colombian drug traffickers move cocaine through Guatemala with the help of corrupt Guatemalan law enforcement officials. In response, the DEA enlisted a pseudonymous confidential informant, "Augustine Cortez," to pose as a cocaine supplier and meet with Bardales. At their first meeting (also attended by Serrano, who was introduced as a Guatemalan law-enforcement officer), Cortez asked Bardales to arrange for security to transport a container of cocaine through Guatemala en route to the United States. Bardales agreed and proposed to charge Cortez one million dollars to move 3,000 kilograms. (Cortez surreptitiously recorded this and all subsequent meetings and telephone calls, transcripts of which were introduced by the government and described by Cortez at trial.)
In the weeks that followed the initial contact, Bran, who was Serrano's boss, followed up with Cortez numerous times to set up a meeting at which Bran planned to introduce Cortez to two Guatemalan law enforcement officials who would provide protection for the cocaine shipments: Mejia *1333 and the fourth codefendant, Morales. Meeting at a restaurant in San Salvador, El Salvador in July 2006, the informant Cortez told the four men assembled (Bardales, Bran, Morales and Mejia) that he intended to transport 1,300 "units" through their country. Meeting Tr., July 19, 2006 at 20. Bardales assured Cortez that Morales and Mejia would take care of transportation and security. See id. at 13 (identifying Morales and Mejia as "the ones in charge of everything that has to be done"). Although Mejia spoke little, he presented false identification and posed as "Edwin Rene Sapon-Ruiz," a high-level Guatemalan official with customs oversight authority. (Mejia was in fact a retired Guatemalan police officer.) Mejia said that Guatemalan law enforcement was "creat[ing] a new unit, DIPA [División de Protección de Puertos y Aeropuertos]," to handle narcotics and to "work[ ] ports and airports." Trial Tr., Feb. 27, 2008 (P.M.) at 61-62. Mejia suggested that he and Morales might be able to "control the commanders, the people who control[ ] DIPA." Id. at 62-63. At the end of the meeting, Cortez paid Morales $10,000 in advance.
Cortez met again with Bran, Morales and Mejia at the same restaurant in August 2006. (Bardales, who had been seriously injured in an automobile accident shortly before the meeting, did not attend.) According to Cortez, Bran had paperwork involving a "cover-up company" Bran controlled, and which could be used to stash the cocaine amidst legitimate cargospecifically, Christmas decorations.[1] Trial Tr., Feb. 28, 2008 (A.M.) at 11. Bran explained to Cortez how to ship the drugs to prevent detection. Again, Mejia said little.
The group met for a third and final time in September 2006. A few minutes into the meeting, Salvadoran police officers arrested all three men. Lead DEA Agent Stephen Fraga, who did not witness the arrest, arrived at the scene about ten minutes later. He testified that: one of the Salvadoran policemen handed him a bag of seized evidence for each of the arrested men and each bag contained a wallet; Mejia's wallet contained a folded piece of paper with a handwritten list of names and the word "DEA" handwritten on the side; both Mejia's and Morales's wallets contained semiautomatic handgun permits; and two handguns were seized from Bran's driver, who was not charged as a co-conspirator.
Mejia, Morales and Bran were handed over to DEA Agents Fraga and Jason Sandoval about ninety minutes after the arrest and were promptly taken aboard a DEA airplane bound for the United States. During the flight, Mejia signed a written waiver of rights and spoke to the DEA agents, who took notes but did not record the interview. According to the agents' testimony, Mejia confessed that he and Morales had been asked by Bran "to act as police officers ... to facilitate a cocaine transaction [by Cortez, who] ... obtained a container filled with cocaine in Colombia and was seeking protection for that cocaine once it arrived in Guatemala"; "he specifically represented himself as a different police officer to make money"; he "was aware that the container was to contain cocaine ... [and] was destined for the United States"; "he was knowledgeable of the topic of the stolen cocaine, and the prices of the stolen cocaine"; and "he had given thought to stealing the cocaine and reselling the cocaine in Guatemala for $4500 per kilogram." Trial Tr., Mar. 3, 2008 (P.M.) at 9-10, 97-101.
On September 20, 2007, Mejia and his four co-defendants were charged in a one-count *1334 superseding indictment with conspiring to import five or more kilograms of cocaine into the United States in violation of 21 U.S.C. §§ 952, 959, 960 and 963. Mejia, Morales and Bran all pleaded not guilty and the district court severed their cases for separate trials. (Serrano remains at large and Bardales eventually died from his auto accident injuries.) After Bran's trial resulted in a hung jury, he pleaded guilty and was sentenced to 144 months' imprisonment. In February 2008, shortly before Mejia's trial, the government offered Morales and him a wired Rule 11(c)(1)(C) nine-year plea agreement, which they rejected. Morales was convicted by a jury and sentenced to 220 months' imprisonment.[2] On March 8, 2008, after an eight-day trial, Mejia was also convicted. Because the conspiracy involved more than 150 kilograms of cocaine, Mejia's offense level was calculated at 38. Combined with his criminal history category of I, the advisory range of imprisonment was 235 to 293 months under the United States Sentencing Guidelines (Guidelines). See U.S.S.G. Ch. 5, Pt. A (sentencing table). The government recommended a below-Guidelines sentence of 210 months. Mejia asked for 60 months (one-half the 120-month statutory mandatory minimum), seeking an adjustment for his minor role in the offense, see U.S.S.G. § 3B1.2, as well as various discretionary departures, see id. § 5H1.4 (physical condition), id. § 5H1.5 (employment record), id. § 5H1.6 (family responsibilities), id. § 5H1.11 (military, civic, charitable and public service, employment-related contributions and record of good works), and id. § 5K2.20 (aberrant behavior). The district court found Mejia's account of the facts implausible[3] and declined to adjust his sentence based on his purportedly minor role; it then sentenced Mejia to 208 months' imprisonment. Mejia's sentenceslightly over seventeen yearswas nearly twice as long as the sentence proposed in the Rule 11(c)(1)(C) plea offer he rejected but more than two years fewer than the advisory range of 235 to 293 months.

II.
Mejia now appeals, asking the court to vacate his conviction or, in the alternative, to remand for resentencing. He contends that the court made a series of errors that, alone or together, entitle him to a new trial and sentence. His objections fall within four categories that we address in turn: the court's admissibility rulings, its jury instructions, the government's closing argument and the sentence imposed.

A.
Mejia contends that the district court erred in admitting various items and testimony into evidence. We review admissibility rulings for abuse of discretion. See United States v. Coumaris, 399 F.3d 343, 347 (D.C.Cir.2005).
*1335 The "DEA Note." We begin with Mejia's chain-of-custody objection. Citing Novak v. District of Columbia, 160 F.2d 588, 588-89 (D.C.Cir.1947), which reversed a conviction because of a gap in the chain of custody of certain physical evidence (the defendant's urine sample), Mejia contends that a similar gap as to evidence admitted against him likewise entitles him to a new trial.
The handwritten note with "DEA" and several names on it was admitted despite an undisputed break in the chain of custody. As noted earlier, shortly after Mejia (along with Morales, Bran and the informant Cortez) arrived at his third and final meeting, several Salvadoran police officers entered the restaurant where the three co-conspirators and Cortez were meeting and arrested them. DEA Agent Fraga did not witness the arrest because at the time he was in an automobile parked several blocks away from the scene. He testified that he arrived at the restaurant about ten minutes after the arrest, at which point he was given a bag from a Salvadoran police officer he presumed to be the leader of the arrest team. The bag contained Mejia's personal effects. The Salvadoran officer who seized Mejia's belongings did not testify and the government did not identify him; in fact, the government did not call any witness who took part in Mejia's arrest and the seizure of his property. Neither did it introduce a return or other official document listing the items seized from Mejia upon arrest. Agent Fraga testified that among the items included in the bag the Salvadoran officer gave him was Mejia's wallet and inside the wallet he found a folded, handwritten note with "DEA" and a list of names on it. The names included at least five agents stationed in the DEA's Guatemala City office. The paper did not include Mejia's name or signature and no handwriting or finger-print evidence was introduced to link Mejia to it. In short, Mejia's chain-of-custody objection to the admission of the listthat it was given to Agent Fraga by "[s]omeone who's not present here and we don't know what happened to it [before Agent Fraga obtained it]," Trial Tr., Mar. 3, 2008 (P.M.) at 102is fundamentally correct.
But was it nevertheless admissible? "It is generally recognized that tangible objects become admissible in evidence only when proof of their original acquisition and subsequent custody forges their connection with the accused and the criminal offense." Gass v. United States, 416 F.2d 767, 770 n. 8 (D.C.Cir.1969). Long ago we held that an unbroken chain of custody is a prerequisite to admissibility. See Novak v. District of Columbia, 160 F.2d 588, 588-89 (D.C.Cir.1947) (citing Smith v. United States, 157 F.2d 705 (D.C.Cir.1946)). In Novak, a police officer testified that he had obtained a urine sample from the defendant, labeled the bottle and delivered it to the laboratory for analysis; a lab chemist also testified as to the alcohol content of a urine sample in a bottle labeled with the defendant's name and confirming lab records were introduced. See id. at 588. The government did not establish, however, that the bottle the arresting officer labeled and initialed was the same one the lab chemist analyzed. See id. We concluded that the evidence was "missing a necessary link in the chain of identification" and reversed Novak's conviction. Id. at 589.
We have since retreated somewhat from Novak, holding that a challenge to the chain of custody goes to weight rather than admissibility. See United States v. Stewart, 104 F.3d 1377, 1383 (D.C.Cir. 1997) (evidence of delay in testing lab sample "went to the weight to be ascribed to the drug evidence by the jury, not its admissibility").[4] Indeed, we held in Stewart *1336 that the government's burden "only requires it to demonstrate that, `as a matter of reasonable probability,' possibilities of misidentification and adulteration have been eliminated." Id. (quoting United States v. Robinson, 447 F.2d 1215, 1220 (D.C.Cir.1971) (en banc)); see Fed.R.Evid. 901(a) ("The requirement of authentication or identification as a condition precedent to admissibility is satisfied by evidence sufficient to support a finding that the matter in question is what its proponent claims."); see also 2 McCormick on Evid. § 213 (6th ed. 2009) ("Cases decided under Rule 901 ... make it clear that a complete chain of custody need not always be proved ... [as t]he standard of proof requires only evidence from which the trier could reasonably believe that an item still is what the proponent claims it to be.") (internal footnotes omitted).
But Stewart involved circumstances in which there was in fact no break in the chain of custody. See Stewart, 104 F.3d at 1383 (citing United States v. Lane, 591 F.2d 961, 964 (D.C.Cir.1979)) ("Under the circumstances, because the evidence was at no point missing or accessible to unauthorized persons, the [twelve-day] delay in transferring the drugs from the vault at the Narcotics Branch to the DEA did not constitute a break in the chain of custody."). Similarly, in Lane, we found a "continuous chain of custody" for the drugs Lane sold to an undercover agent when they were immediately put in secure envelopes and, at trial, were "separately and uniformly identified by the undercover agent who made the purchases, the supervising control officers who received the purchased products from the undercover agent, and the DEA chemist who analyzed them." 591 F.2d at 965. Although we found that certain evidence "indicate[d] some chance for inadvertent misidentification and some opportunity for tampering," e.g., the control officer's inability at trial to locate her initials on one of the envelopes and her testimony that she occasionally took evidence home, we concluded that the continuous chain afforded "substantial protection against misidentification or adulteration." Id. at 964-65. And in the cases holding evidence admissible notwithstanding an interrupted chain there was nonetheless ample corroborative evidence as to its acquisition and subsequent custody. See, e.g., Robinson, 447 F.2d at 1220 (custody gap based on failure to testify by "middle link" in chain excused by defendant's stipulation as to movement of evidence between police officers and corroborative circumstances); Gass, 416 F.2d at 770 (government not required to present testimony of nurse who carried lab sample from clinician to pathologist because both clinician and pathologist testified, there was no indication sample had been tampered with and nurse enjoyed "presumption that individuals entrusted with grave responsibilities discharge them with care"). A break in the chain of custody, then, can be serious enough that the district court may abuse its discretion in admitting the evidence. See Novak, 160 F.2d at 589; see also 2 McCormick on Evid. § 213 ("If there is some specifically identified risk of misidentification or alteration, the proponent of the exhibit should produce evidence to overcome this risk or suffer exclusion."). We must decide whether the district court did so here.
*1337 The government asserts that the district court did not err because it was entitled to presume the "integrity of evidence routinely handled by government officials" and, although this presumption may be rebutted with a "minimal showing of ill will, bad faith, other evil motivation, or some evidence of tampering," Mejia made no such showing here. Lane, 591 F.2d at 962. While we agree with the proposition as a general matter, we do not believe it extends automatically to all government officials, including those of a foreign government. As the government acknowledges, "the record does not reveal what procedures the Salvadoran police used to preserve his wallet [or] whether the wallet was commingled with other evidence." Appellee's Br. at 46. Moreover, it is unclear to us how Mejia could have made even the minimal showing required of him, given his immediate transfer by air to the United States. Indeed, the government expressed doubt that "there's any way for anyone to be able to point out what happened in those ten minutes other than the Salvadoran police." Feb. 19, 2010 Oral Arg. Recording at 22:17.
On the one hand, the defect here was different from the ones in Lane and Stewart both of which involved an unbroken chain of custody but either an unexplained delay, see Stewart, 104 F.3d at 1383, or the possibility of misidentification and adulteration, see Lane, 591 F.2d at 965. Nor does this case involve an item of evidence transferred within a police department or from one hospital employee to another. Cf. United States v. Lott, 854 F.2d 244, 250 (7th Cir.1988) (rejecting chain of custody objection as to "lack of testimony concerning the transfer of exhibit 4 from the DEA field office to the DEA laboratory and the transfer of exhibit 5 from the Holiday Inn to the DEA field office or from the field office to the FBI laboratory"); Gass, 416 F.2d at 770. Here the first links in the chain, i.e., the seizure of the list and its transfer to Agent Fraga ten minutes later, were not established. See id. n. 8 (physical evidence admissible only on "proof of [its] original acquisition and subsequent custody [that] forges [its] connection with the accused"). Nothing in the record indicates the identity of the person (or persons) who seized the wallet or what was done with it before Agent Fraga took possession of it. On the other hand, there was substantial corroborative evidence tying the list to Mejia, to wit: Agent Fraga testified that he found it inside Mejia's wallet, which Mejia does not deny was his, see Feb. 19, 2010 Oral Arg. Recording at 17:12, and which also contained his identifications cards, Trial Tr., Mar. 3, 2008 (P.M.) at 116-19. Moreover, the brief (ten-minute) gap between Mejia's arrest and Fraga's taking possession of the list makes implausible that it was planted, tampered with or misidentified. See Fed. R.Evid. 901(a); Stewart, 104 F.3d at 1383 (citing Robinson, 447 F.2d at 1220); see, e.g., Robinson, 447 F.2d at 1219, 1221 (finding no probability of tampering and thus no error in admission of evidence based on stipulation and "corroborative circumstances contained in the record" where "middle link" officer in chain of custody was unavailable to testify due to heart attack); United States v. Cardenas, 864 F.2d 1528, 1532 (10th Cir.1989) ("The fact that [middle link in chain of custody] was not available to testify is not determinative of the admissibility of the cocaine since the whereabouts of the cocaine was accounted for from its original seizure ... until it was offered as evidence at trial.").
We conclude that the district court did not abuse its discretion in admitting the list. Even if admitting the list was error, however, it was harmless in light of its limited importance and the strength of the other evidence against Mejia. See *1338 Kotteakos v. United States, 328 U.S. 750, 765, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946); cf. United States v. Warren, 42 F.3d 647, 656 (D.C.Cir.1994) (erroneously excluded statement harmless error where "cumulative of other evidence heard by the jury" and "evidence of [defendant's] guilt was strong").
The Firearm Permit Evidence. The district court admitted over Mejia's objection a firearm permit found in Mejia's wallet as well as testimony that the police also seized a firearm permit from Morales and two handguns from Bran's driver. The government is correct that "this circuit has frequently recognized that guns and drugs go together in drug trafficking," United States v. McLendon, 378 F.3d 1109, 1113 (D.C.Cir.2004), and that evidence of seized guns is admissible to show a defendant's participation in the drug trade, see United States v. Jenkins, 928 F.2d 1175, 1180 (D.C.Cir.1991) ("Weapons are, in short, `tools of the trade' and the government introduced the bullets found in Jenkins' bedroom to prove that she was engaged in the trade." (quoting United States v. Payne, 805 F.2d 1062, 1065 (D.C.Cir.1986))).
But the probative value of a firearm permit possessed by a former police officer seems to us to be nil. Likewise, the probative value of testimony as to firearms carried by Bran's driverwho was not charged as a member of the conspiracy also seems negligible. In spite of the limited probative value, we need not decide whether the district court "grave[ly]" abused its discretion in admitting this evidence over Mejia's Rule 403 objection, see United States v. Douglas, 482 F.3d 591, 596 (D.C.Cir.2007), because, even assuming error, we find it to be harmless. Mejia does not identify any unfair prejudice associated with the admission of the permits or the testimony about the driver's guns. The jury was made aware of the undisputed fact that Mejia did not possess a gun at any of the meetings. Under these circumstances, and especially given his confession and the other strong evidence discussed above, we cannot say that the introduction of the gun evidence affected his substantial rights. See Kotteakos, 328 U.S. at 764-65, 66 S.Ct. 1239; cf. Warren, 42 F.3d at 656.
Other Evidentiary Rulings. We quickly dispense with Mejia's other assertions of error in evidentiary rulings. First, he maintains that the government erroneously failed to correct the false denial of its main witness, Cortez. This contention (which we review de novo, see United States v. O'Keefe, 128 F.3d 885, 893-94 (5th Cir.1997)), stems from another court's finding in an unrelated case that Cortez was "not entirely truthful." See Appellant's Br. at 31. Cortez had been cross-examined about that court's finding at co-defendant Bran's trial and had denied any knowledge of it. When again asked during cross-examination at Mejia's trial whether he was "aware of a federal judge ever making a finding that you were not entirely truthful," Cortez replied unequivocally: "I have never read or heard any judge, federal judge for that matter, ever saying that I haven't been truthful in any of the cases I have testified on behalf of the United States Government.... Or read about any judge doubting my truthfulness. I have never seen that before." Trial Tr., Feb. 29, 2008 (A.M.) at 63; see generally id. at 54-63.
Although the government "may not knowingly use ... false testimony[ ] to obtain a tainted conviction," including testimony that goes to the credibility of a witness, see Napue v. Illinois, 360 U.S. 264, 269-70, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959), Cortez made no false statement for the government to correct. There is no dispute that Cortez had no direct knowledge *1339 of the credibility finding in Smith, see Appellant's Br. at 32, so that his knowledge of it could have come only from his cross-examination in Bran's trial. And although Cortez denied having read or heard about the finding, he did not deny that he had been earlier questioned about it. See Trial Tr., Feb. 29, 2008 (A.M.) at 57 ("That question was asked to me previously.") Thus, we agree with the district court that, in context, Cortez testified truthfully as to his lack of personal knowledge. See June 20, 2008 Mem. and Order, Doc. No. 218 at 12 (rejecting Mejia's new trial motion because "[a]lthough Cortez's answers may appear to be disingenuous at first glance... [he] answered defense counsel's questions in a truthful manner since" he had no personal knowledge of other court's finding).
Citing Whitmore, 359 F.3d at 618, Mejia also contends the district court abused its discretion in sua sponte curtailing his cross-examination of Cortez regarding the same prior credibility finding. In Whitmore we held that it was error to deny the defendant the opportunity to cross-examine a witness regarding the witness's character for truthfulness. See 359 F.3d at 619-21. But the error in that case was that the district court had prohibited the entire line of cross-examination under Rule 403. See Whitmore, 359 F.3d at 621 ("We ... believe the district court erred in excluding the entire line of cross-examination" regarding prior untruthful testimony). Here, in contrast, after hearing extensive arguments and expressly relying on Whitmore, the court allowed Mejia to ask Cortez specific questions about the Smith credibility finding. Whitmore contemplates this precise procedure. 359 F.3d at 621 (district court should respond to "unfair prejudice or undue delay" concern not by excluding but by "limiting" cross-examination); see also Fed.R.Evid. 608(b) (character for truthfulness or untruthfulness may be inquired into on cross-examination if probative in "the discretion of the court").
Finally, Mejia complains that the district court erred in qualifying Carrillo Garcia, a Guatemalan police officer with fourteen years' experience, as an expert in drug trafficking because none of the cases Garcia participated in was prosecuted in the United States. But Garcia was not qualified as an expert in cocaine importation or prosecution in the United States but rather "in the field of drug-trafficking and transportation activities as they relate to Guatemala." See Trial Tr., Feb. 29, 2008 (P.M.) at 45-46. Moreover, Garcia had, in fact, testified in at least two U.S. prosecutions. See Trial Tr., Feb. 29, 2008 (P.M.) at 35 (Garcia testified a dozen times or more in Guatemala and twice in the United States). Accordingly, Mejia has not shown that the district court erred in qualifying Garcia as an expert. See Haarhuis v. Kunnan Enters., Ltd., 177 F.3d 1007, 1015 (D.C.Cir.1999) ("[T]he decision whether to qualify an expert witness is within the broad latitude of the trial court and is reviewed for abuse of discretion."). And because Garcia was properly qualified, Mejia's two hearsay objections to Garcia's testimony are without merit. See Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 592, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993) ("[A]n expert is permitted wide latitude to offer opinions, including those that are not based on firsthand knowledge or observation.").[5]


*1340 B.
Mejia next objects that the trial court improperly instructed the jury in two respects. Our review is de novo. See United States v. Orenuga, 430 F.3d 1158, 1166 (D.C.Cir.2005). First, Mejia argues that the district court's "reasonable doubt" instruction lessened the government's burden of proof and improperly shifted that burden to him.[6] But Mejia's argument is entirely foreclosed by United States v. Taylor, 997 F.2d 1551 (D.C.Cir.1993), where we rejected a similar challenge based on language drawn from the same pattern instruction, characterizing the instruction as "not in error." Id. at 1556. True, we recognized that other "circuits have criticized reasonable doubt instructions modeled on the Pattern Instruction" and noted "that the greatest wisdom may lie with [other circuits'] instruction to leave to juries the task of deliberating the meaning of reasonable doubt." Id. at 1557-58. But we also noted that none had in fact held the use of the instruction to be reversible error and likewise declined to do so. Id. at 1557.
Mejia acknowledges that Taylor "affirmed a conviction involving the same instruction at issue here," Appellant's Br. at 14, but attempts to distinguish it in several ways. For example, he asks us to attach significance to the fact that, unlike Taylor, who had unsuccessfully requested an alternative "reasonable doubt" instruction, Mejia requested that no charge be given. We decline to do so. "[T]he Constitution neither prohibits trial courts from defining reasonable doubt nor requires them to do so as a matter of course," Victor v. Nebraska, 511 U.S. 1, 5, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994), and Mejia offers no reason why the Constitution would apply differently simply because he preferred no instruction. He also argues that the instruction invaded the jury's province by providing that the jurors "must find him guilty" if firmly convinced of his guilt. Trial Tr., Mar. 5, 2008 (P.M.) at 32 (emphasis added); see Appellant's Br. at 13. In contrast, the Taylor instruction stated that it was the jury's "duty to find him guilty" if firmly convinced. Taylor, 997 F.2d at 1556 (emphasis added). But we have already found neither iteration more objectionable than the other. In United States v. Pierre, 974 F.2d 1355 (D.C.Cir.1992), we affirmed the instruction that the jury had a "duty" to return a guilty verdict if the government proved the elements of the offense beyond a reasonable doubt. Id. at 1357. We noted that, while an earlier case had reversed an instruction that the jury "must" find a defendant guilty, the error had resulted from the omission of the phrase "beyond a reasonable *1341 doubt." Id. (citing Billeci v. United States, 184 F.2d 394, 399 (D.C.Cir.1950)). We did "not think it significant that the district court used the word `must'" in Billeci. Id. In sum, the instruction was "not in error because there is no reasonable likelihood that the jury applied the challenged instruction in a way that violates the Constitution." Taylor, 997 F.2d at 1558.
Additionally, Mejia contends that the district court deprived him of due process of law when it instructed the jury: "You may infer but are not required to infer that a person intends the natural and probable consequences of acts knowingly done or knowingly omitted." Trial Tr., Mar. 5, 2008 (P.M.) at 48. The Supreme Court has distinguished between language that creates a "mandatory presumption" and language that allows a permissive inference. See Francis v. Franklin, 471 U.S. 307, 311, 105 S.Ct. 1965, 85 L.Ed.2d 344 (1985) (rejecting instruction that "[a] person of sound mind and discretion is presumed to intend the natural and probable consequences of his acts but the presumption may be rebutted"); see also Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979). The language here is permissive. Our sister circuits recognize the same distinction, consistently upholding similar instructions in specific intent crimes, including the crime of which Mejia was convicted.[7]See, e.g., United States v. Love, 767 F.2d 1052, 1059 (4th Cir.1985); United States v. Cotton, 770 F.2d 940, 946 (11th Cir.1985). Mejia's challenge to portions of the instructions therefore fails.

C.
Mejia contends that the government's closing argument included several statements unsupported by the evidence. Specifically, he objects to the government's contentions that (1) the co-conspirators needed Mejia because of his police connections (even though another conspirator, Morales, was also a retired Guatemalan police officer); (2) Mejia lived in Guatemala City at the time of the conspiracy (when the only record evidence was that he had lived there five or six years earlier); (3) Guatemalan police were essentially powerless to stop the gangs because Guatemala was emerging from a bloody civil war (based on a lack of record evidence regarding the civil war); and (4) DIPA was the Guatemalan "customs anti-narcotics agency" and Mejia was willing to use his connections there (based on a lack of supporting evidence).
A prosecutor errs in closing argument by making a statement unsupported by evidence, misstating evidence or misquoting testimony. See United States v. Watson, 171 F.3d 695, 699 (D.C.Cir.1999). After "comparing the witness[es]' testimony with the statements made by the prosecutor in closing arguments," id. at 700, 171 F.3d 695, we find no error as every statement *1342 was permissibly based on record evidence. First, contrary to Mejia's suggestion, the prosecutor never argued that "Mejia was brought into the conspiracy because he alone among the others had a law enforcement background." Appellant's Br. at 23 (emphasis added). Rather, the prosecutor's argument was consistent with the theory that the conspirators needed a) both Morales and Mejia because of their police backgrounds and b) Mejia specifically because of his extensive supervisory experience (of which there was ample record evidence). See Trial Tr., Mar. 5, 2008 (P.M.) at 15 (Mejia spent fifteen years with the Guatemalan police department "not only as a cop on the beat apparently, but as a supervisor, as someone with a sufficiently sophisticated position that he was planning major operations, and that's why .... they recruited him into the conspiracy").
Second, the only record evidence regarding Mejia's residence was the testimony of the sole defense witness, Francisco De Leon, that Mejia had lived in Guatemala City five or six years earlier, but "no longer lives there now." Trial Tr., Mar. 5, 2008 (A.M.) at 36. Considering that Mejia was in federal custody at the time of the witness's testimony, this statement is ambiguous and hardly stands for the proposition that Mejia was no longer a Guatemala City resident when arrested.[8] Third, the prosecutor's argument was not, contrary to Mejia's objection, about the relationship between Mejia and the Guatemalan civil war but instead about the powerlessness of the Guatemalan police, of which there was plenty of record evidence. See, e.g., Trial Tr., Feb. 29, 2008 (A.M.) at 88 ("Guatemala has a very fragile law enforcement system, and it's very easy to bring large quantities of drugs into Guatemala without really worrying about being caught."). Last, we disagree with Mejia's complaints as to the lack of evidence that DIPA was an anti-drug agency and that Mejia was willing to use police connections, as the record sufficiently supports both claims. See Trial Tr., Feb. 29, 2008 (P.M.) at 21 (DIPA's "main purpose... was to attack the narcotic activity at" Guatemala's seaports); see Meeting Tr., July 19, 2006 at 16 (Mejia's videotaped statements that DIPA's "commands are ours," and "[w]hat we have to control is the structure" of DIPA).
Mejia also challenges the prosecutor's embellishment in closing: "[W]e forget that the success of a drug trafficker is based upon a human weakness called addiction" and that drug dealers "make a lot of money by preying on that human weakness." Trial Tr., Mar. 5, 2008 (A.M.) at 71. We have held that a more detailed comment was improper. See United States v. Johnson, 231 F.3d 43, 47 (D.C.Cir.2000) (prosecutor "improperly suggested that the jury should convict the defendant in order to protect others from drugs" by arguing that "[j]ustice protects not only the person who is accused, but it also protects persons like those ... 400-plus individuals [whom] the crack cocaine [was] intended for"). We believe the statement here was harmless because it was isolated and the case was not close. See United States v. Hemphill, 514 F.3d 1350, 1361-62 (D.C.Cir.2008) ("A single misstatement in a lengthy argument ... is rarely a severe error."); Johnson, 231 F.3d at 49-50 (despite lack of specific curative instruction error harmless because, among other reasons, "great weight of the evidence strongly supports Johnson's conviction").


*1343 D.
Finally, Mejia challenges his sentence on multiple grounds. We review the district court's sentence for abuse of discretion, first ensuring that the court committed no significant procedural error and then ascertaining if the sentence is substantively reasonable. See Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007); United States v. Settles, 530 F.3d 920, 923 (D.C.Cir.2008).
Contrary to Mejia's first argument, his sentence is consistent with Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), which held that "[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt." Id. at 490, 120 S.Ct. 2348. The jury convicted Mejia of conspiring to import five kilograms or more of cocaine into the United States in violation of 21 U.S.C. § 960(a). The verdict triggered a statutory imprisonment range of ten years to life, with ten years being the mandatory minimum. See 21 U.S.C. § 960(b)(1)(B)(ii). Mejia argues that because the jury did not ascribe a specific amount of cocaine to Mejia personally, the statutory maximum should have been twenty years under 21 U.S.C. § 960(b)(3). But the sentence he received208 months, or a little over seventeen yearsis less than the statutory maximum Mejia himself urges. See Settles, 530 F.3d at 923 (sentencing court not constitutionally barred from finding facts by preponderance of evidence as long as "sentence does not exceed the statutory maximum for the crime of conviction" because "the Supreme Court has `never doubted the authority of a judge to exercise broad discretion in imposing a sentence within a statutory range'" (quoting United States v. Booker, 543 U.S. 220, 233, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005))).
Second, we do not agree that Mejia's sentence was unreasonable based on the district court's failure to grant a number of the adjustments and departures Mejia requestedincluding, most significantly, a multi-level adjustment for his allegedly minor role in the offense. See U.S.S.G. § 3B1.2. Although the district judge (who also presided over the trials of Bran and Morales) determined that "Mejia's role was the least of the three," he permissibly and reasonably concluded that no one in the conspiracy played a "minor" role. Sentencing Tr., Oct. 16, 2008 (A.M.) at 56-57, 70 (finding Mejia "was aware of the full plan," took "three trips to El Salvador for purposes of meetings to further this conspiracy" and "was to have the important role of a security function"). As for the discretionary departures, because the judge plainly recognized his authority to impose a below-Guidelines sentencehe gave one, after allhis decision was in accord with United States v. Booker. Insofar as Mejia contends that his sentence was substantively unreasonable, see Gall, 552 U.S. at 51, 128 S.Ct. 586, we do not agree. Indeed, it is hard to imagine how Mejia could make such a showing given that his sentence is two years below the range we ordinarily view as reasonable. See United States v. Dorcely, 454 F.3d 366, 376 (D.C.Cir.2006) ("We agree with our sister circuits that a sentence within a properly calculated Guidelines range is entitled to a rebuttable presumption of reasonableness."); see also United States v. George, 403 F.3d 470, 473 (7th Cir.2005) ("It is hard to conceive of below-range sentences that would be unreasonably high.").
Third, Mejia argues that his sentence resulted in an unwarranted disparity between himself and co-defendant Bran, in *1344 contravention of a statutory sentencing factor. See 18 U.S.C. § 3553(a)(6) (sentencing court must take account of "need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct"). It is true that Bran, whothe court determinedhad played a leadership role in the conspiracy, received only 144 months, a sentence more than five years shorter than Mejia's 208-month sentence. See Sentencing Tr., Oct. 16, 2008 (A.M.) at 69-70 ("Mr. Bran was more of the leader than these two were."). But Moralesthe third co-defendant, who, according to the district court, played a role closer to Mejia's than Bran'swas sentenced to 220 months, one year longer than Mejia.
We conclude that there was no error in the disparity between Mejia and Bran, which disparity is entirely explained by Bran's three-level acceptance-of-responsibility reduction for his having pleaded guilty after his jury hung, which lowered his advisory Guidelines range to 168-210 months. See U.S.S.G. § 3E1.1 (defendant who "clearly demonstrates acceptance of responsibility for his offense" is entitled to reduction); see, e.g., In re Sealed Case, 488 F.3d 1011, 1014 (D.C.Cir.2007) (affirming sentence based on plea agreement awarding defendant three-level reduction for acceptance of responsibility under § 3E1.1). Unlike Bran, Mejia never accepted responsibility. See Trial Tr., Oct. 16, 2008 at 53 (A.M.) (Mejia said, "[w]ith regard to the charges against me, I put my hand on my heart and with all mywith all sincerity I can tell you ... that I am innocent. I am totally innocent"); Sentencing Tr., Oct. 16, 2008 (A.M.) at 70-71 (court found "Mejia obviously has shown no remorse of any kind ... and he says that he was not aware that cocaine was involved, which I find to be unbelievable, I do not accept that"). Under these circumstances, Mejia's harsher sentence was not an abuse of discretion.
Fourth, we reject Mejia's claim of prosecutorial vindictiveness. His claim is premised on the fact that the sentence the government recommended following trial was nearly twice the length of the plea offer he rejected before trial. But there is nothing impermissible (or even unusual) with the prosecutor recommending a longer sentence after trial than before trial. Nor, as noted, is there anything out of the ordinary with the defendant's acceptance of responsibility factoring into the sentencing calculus. See U.S.S.G. § 3E1.1; United States v. Jones, 997 F.2d 1475, 1476 (D.C.Cir.1993) (en banc); see also Alabama v. Smith, 490 U.S. 794, 801-02, 109 S.Ct. 2201, 104 L.Ed.2d 865 (1989) (no presumption of vindictiveness for imposition of greater penalty by same judge following trial than after earlier guilty plea (subsequently withdrawn) because "after trial, the factors that may have indicated leniency as consideration for the guilty plea are no longer present").

III.
For the foregoing reasons, Mejia's conviction and sentence are affirmed.
So ordered.
NOTES
[1]  And thus giving unintended meaning to a "white Christmas."
[2]  Both Bran and Morales appealed to this Court. We affirmed Bran's conviction and sentence on October 29, 2009. See United States v. Constanza Bran, No. 08-3086, 2009 WL 4250087 (D.C.Cir. Oct. 29, 2009). Morales's appeal remains pending. See United States v. Morales, No. 08-3038 (D.C.Cir.).
[3]  The court found:

It is not plausible that he went to three meetings in another country and believed that this only involved moving Christmas goods for possible avoidance of Customs or tax requirements ... [as that] does not comport with the evidence at trial and is not in my view what an experienced police officer could possibly have believed in light of the circumstances that he was involved in and the discussions that were taking place.
Sentencing Tr., Oct 16, 2008 (A.M.) at 59.
[4]  The United States Supreme Court made the same point last year. See Melendez-Diaz v. Massachusetts, ___ U.S. ___, 129 S.Ct. 2527, 2532 n. 1, 174 L.Ed.2d 314 (2009) ("`[G]aps in the chain ... normally go to the weight of the evidence rather than its admissibility.'" (quoting United States v. Lott, 854 F.2d 244, 250 (7th Cir.1988))). The Court noted that the government's obligation to establish a chain of custody does not require it to call to the stand every witness who may have handled a piece of evidence as the government may decide "what steps in the chain of custody are so crucial as to require evidence." Id.
[5]  Mejia also challenges the admissibility of Agent Fraga's notes of his interview with Mejia, which notes were discussed during his cross-examination and on redirect. But Agent Fraga's notes were not admitted into evidence.
[6]  Over Mejia's objection, the court defined "reasonable doubt" as follows:

Proof beyond a reasonable doubt is proof that leaves you firmly convinced of the Defendant's guilt. There are very few things in this world that we know with absolute certainty, and in criminal cases, the law does not require proof that overcomes every possible doubt.
If, based on your consideration of the evidence you are firmly convinced that the Defendant is guilty of the crime charged, you must find him guilty. If, on the other hand, you think there is a real possibility that the Defendant is not guilty, you must give him the benefit of the doubt and find him not guilty.
Trial Tr., Mar. 5, 2008 (P.M.) at 32. The instruction is taken verbatim from the Federal Judicial Center's Pattern Criminal Jury Instruction 21 (Federal Judicial Ctr.1988), which has been described as "clear, straightforward, and accurate." Victor v. Nebraska, 511 U.S. 1, 26-27, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994) (Ginsburg, J. concurring in part and in judgment) ("This model instruction surpasses others I have seen in stating the reasonable doubt standard succinctly and comprehensibly.").
[7]  We have also upheld an instruction containing similar language in a case involving a specific intent crime. See United States v. Moore, 435 F.2d 113, 115-16 & n. 2 (D.C.Cir. 1970) ("It may be inferred that one intends the natural and probable consequences of his act, but you are not required to so infer"). Although we found no plain error in Moore, we did note that the challenged instruction "may be misleading" in a specific intent case and that it "should not have" been given. Id. at 116 & n. 5. But the court's principal concern was that the instruction omitted the phrase "knowingly done or knowingly omitted." Id. Here, the instruction included the knowledge component. See Trial Tr., Mar. 5, 2008 (P.M.) at 48 ("You may infer but are not required to infer that a person intends the natural and probable consequences of acts knowingly done or knowingly omitted.") (emphasis added).
[8]  Indeed, even on appeal, Mejia does not assert that the statement was wrong, simply that "[t]here also was no evidence in the record that Mejia lived in Guatemala City during the time of the offense." Appellant's Br. at 25.
