
519 F.3d 98 (2008)
UNITED STATES of America, Appellee,
v.
Duong-Cam TRAN, Defendant-Appellant.
No. 05-5644-CR.
United States Court of Appeals, Second Circuit.
Argued: May 1, 2007.
Decided: March 10, 2008.
*99 *100 Bruce R. Bryan, Bryan Law Firm, Syracuse, NY, for Defendant-Appellant (James P. Harrington, Harrington & Mahoney, Buffalo, NY, on the brief).
Joseph Karaszewski, Assistant United States Attorney, Buffalo, New York for Appellee (Stephan J. Baczynski, Assistant United States Attorney, and Terrance P. Flynn, United States Attorney, on the brief).
Before: SACK, SOTOMAYOR, HALL, Circuit Judges.
HALL, Circuit Judge.
Defendant-Appellant Duong-Cam Tran appeals a final judgment of conviction in the United States District Court for the Western District of New York (Arcara, C.J.) of knowingly importing into the United States 500 grams or more of a mixture or substance containing methamphetamine, 21 U.S.C. §§ 952(a), 960(b)(1)(H), and knowingly possessing with the intent to distribute a mixture containing methamphetamine, *101 id. § 841(a)(1). The district court sentenced Tran principally to 235 months' imprisonment. For the following reasons, we AFFIRM the conviction and sentence.

BACKGROUND

I. The Offense
Defendant-Appellant Duong-Cam Tran is a Canadian citizen and resident of Toronto, Canada. Born in 1958 in North Vietnam of Chinese ancestry, Tran spent many years in refugee camps in Hong Kong and China and speaks "some English" with an accent. He owns a small mattress manufacturing company.
On October 1, 2003, Tran telephoned an office of Thrifty Car Rental in Toronto and inquired into renting a vehicle for a planned trip to a casino in upstate New York. According to Tran, his own car was in disrepair. The rental agent suggested a Chrysler Pacifica. Tran hesitated because he disliked Chrysler vehicles, but the agent prevailed upon him to visit the rental agency and inspect the car. The next day, sometime between noon and 2 p.m., Tran arrived at Thrifty Car Rental to inspect the Chrysler Pacifica. He approved of the vehicle and signed a rental agreement, but he did not immediately assume possession of the vehicle. Instead, Tran returned to his factory for the afternoon. Meanwhile, the Chrysler Pacifica remained unattended in the Thrifty Car Rental parking lot, secured by its door locks and a steering wheel lock.
At approximately 5 p.m., Tran returned to Thrifty Car Rental and assumed possession of the rental vehicle. He drove to a shopping mall, and he then drove to a bar, where he ate and drank until midnight. After leaving the bar, Tran again returned to his factory. Although he planned to sleep for only a few hours, he instead slept until approximately 9 a.m. In preparation for his trip, he then packed a T-shirt, a jacket, and a brush, as well as $1,000 (USD) and $300 (Canadian). Although Tran had no idea where the Seneca Niagara Casino was located, he took no directions with him. He also apparently had no specific plans for returning home other than he expected to stay "one day" or, luck permitting, "longer."
Tran left Toronto for the Peace Bridge border crossing, driving alone in the rental car. When Tran reached the Peace Bridge, a United States Customs officer inspected his citizenship card and asked him about his destination. The officer later testified that, when asked where he was headed, Tran "became somewhat nervous. . . . [H]e began sweating, he gripped the steering wheel. He became a little fidgety in the vehicle as in somewhat moving around, looking around." The officer referred Tran to the secondary inspection area.
At the secondary inspection area, two other officers asked Tran to complete a customs declaration form while they searched his car. During the inspection, the officers found a screwdriver and a gas can in the vehicle. Meanwhile, one of the officers recalled an intelligence report that suggested "there [could be] hidden compartments on the . . . Pacifica." After confirming the substance of this intelligence report with a special agent, the officer physically inspected the vehicle's headliner, or interior roof lining, with his hands. Upon discovering that the headliner "felt very inconsistent with what a headliner should feel like," the officer then tested the density of the headliner using a density-measuring device known as a "buster." The device confirmed that the headliner density was unusual. At that point, the officer began removing the headliner, *102 which, as he later testified "came down very easily."
As the liner loosened, a bag slipped out from the space between the liner and the roof. The bag contained four smaller vacuum-sealed bags, each of which held several even smaller baggies. These smaller baggies contained what appeared to be pink and green pills. When Tran saw the bags emerging from the headliner, he yelled something to the effect of "what's going on" or "what's happening." The officers seized the bags of pills as evidence, arrested Tran, and began to question him. Tran repeatedly denied knowledge of the bags or the pills within them.

II. DEA Handling and Analysis of the Pills
Shortly thereafter, DEA agents arrived at the Peace Bridge to take custody of the pills, which the Customs officers had sealed in evidence bags. The agents removed the pills from the four bags and separated them into evidence bags by color. The sorting produced a bag of pink pills and two bags of green pills. While sorting the pills, the agents did not track which pills came from each of the original four bags (or, for that matter, which came from each of the smaller baggies therein).
The three evidence bags were sent to a laboratory for chemical analysis. There, the chemist first counted the pills, finding a total of 40,790 pills weighing 10.243 kilograms: 16,278 pink pills in one bag, 14,342 green pills in another, and 10,170 green pills in the last. He then removed twenty-nine pills from each of the three bags. Initial screening showed that the pills in each group contained either methylenedioxymethamphetamine ("MDMA," commonly known as "ecstacy") or methamphetamine. After grinding up each of the three piles of twenty-nine pills into three corresponding piles of powder, the chemist performed further tests. According to those tests, the first pile contained 28% MDMA and 5.6% d-methamphetamine; the second 15% MDMA and 6.9% d-methamphetamine; and the third 28% MDMA and 5.9% d-methamphetamine. At trial, the chemist testified that in his opinion, the results of these tests performed on the samples of pills accurately reflected the amount and percentage of MDMA and d-methamphetamine in all of the pills that had been seized.

III. Tran's Trial
Following Tran's arrest, a grand jury in the Western District of New York charged him with knowingly importing into the United States 500 grams or more of a mixture or substance containing methamphetamine, in violation of 21 U.S.C. §§ 952(a), 960(b)(1)(H). The grand jury also charged Tran with knowingly possessing with intent to distribute a mixture containing methamphetamine, in violation of 21 U.S.C. § 841(a)(1).
At trial, Tran maintained his innocence and testified, inter alia, that he was an unwitting courier with no knowledge that his rental vehicle contained drugs. In its jury instructions, the district court explained what the jury must consider in deciding whether Tran had knowledge of the drugs in the car:
It is obviously impossible to prove directly the operation of the Defendant's mind. But a wise and intelligent consideration of all the facts and circumstances . . . may enable you to infer what the Defendant's state of mind was. . . .
For example, if a Defendant was a sole occupant of an apartment, it's reasonable to conclude the Defendant knew about the items in the apartment. The Defendant's behavior may also indicate *103 knowledge. Nervousness in the presence of drugs or flight from the site at which the authorities identified drugs may indicate that the Defendant knew that the materials in question were narcotics.

(Sept. 29, 2004 Trial Tr. at 90:83-84 (emphases added).) With the exception of this passage, the district court's instructions to the jury largely comported with the model jury instructions. See Leonard B. Sand et al., Modern Federal Jury Instructions: Criminal § 3-56.01. At no point did the district court instruct the jury that it could infer knowledge from the defendant's sole occupancy of the vehicle.
The jury convicted Tran on both counts. In September 2005, the district court accepted the Guidelines calculation of the Probation Office and sentenced Tran to 235 months' incarceration, which was at the bottom of the applicable Guidelines range, as well as five years' supervised release and a special assessment of $200.

DISCUSSION
Tran appeals his conviction and sentence on several grounds. First, he challenges two of the district court's jury instructions. Second, he argues that the evidence was insufficient to support the jury verdict. Third, he claims that his sentence was unreasonable.

I. The Jury Instructions
Tran challenges two of the district court's instructions to the jury: (1) an instruction relating to the reasonable inferences that can be drawn from a defendant's sole occupancy of a vehicle; and (2) an instruction on the relevance of a defendant's nervousness to the element of knowledge.
A. Sole Occupancy of a Vehicle
In his brief, Tran states that the district court instructed the jury that "if the defendant was the sole occupant of a . . . a[sic] vehicle, it is reasonable to conclude that the defendant knew about items in the vehicle." (App. Br. 26 (ellipsis in original) (emphases removed).) Tran observes that the pills at issue here were hidden beneath a vehicle's headliner and argues that the district court's jury instruction was therefore erroneous. For support, he cites to the doctrine, adopted by the several circuits and the model jury instructions, that when contraband is found in a vehicle's hidden compartments, "[p]ossession of or control over [the] vehicle [cannot], standing alone, suffice to prove guilty knowledge." United States v. Anchondo-Sandoval, 910 F.2d 1234, 1236 (5th Cir.1990); see also United States v. Jackson, 55 F.3d 1219, 1226 (6th Cir.1995) ("In `hidden compartment' cases, courts have generally required additional evidence indicating knowledge  `circumstances evidencing a consciousness of guilt on the part of the defendant.'" (quoting United States v. Diaz-Carreon, 915 F.2d 951, 954 (5th Cir. 1990)) (emphasis omitted)); United States v. Stanley, 24 F.3d 1314, 1319-20 (11th Cir.1994) (same); Diaz-Carreon, 915 F.2d at 954 ("[C]ontrol of the vehicle . . . does not support an inference of guilty knowledge; it is at least a fair assumption that a third party might have concealed the controlled substances in the vehicle with the intent to use the unwitting defendant as the carrier in a smuggling enterprise."); Sand, Modern Federal Jury Instructions: Criminal Form 56-8 cmt. ("In [hidden compartment] cases, most courts will require further evidence [beyond sole occupancy].").
This challenge fails, however, because it is based on a serious misrepresentation of the record: The district court did not, in fact, give the instruction about which Tran *104 complains.[1] Because Tran does not challenge the instructions actually given to the jury, we find no reversible error.
B. Nervousness
Tran contends that the district court committed error by instructing that "[n]ervousness in the presence of drugs . . . may indicate that the Defendant knew that the materials in question were narcotics." Tran argues that this instruction assumes that the "materials in question" are visible to the occupant of the vehicle and that this assumption does not obtain in hidden compartment cases.
The argument is unpersuasive. Even where drugs are hidden and therefore not immediately visible to the occupant or others, the possibility of discovery may cause an individual with knowledge of the drugs to respond with nervousness to a law enforcement officer's presence. As several Circuits have recognized, "nervousness" is one type of evidence that, when considered alongside the defendant's sole occupancy of a vehicle, can support an inference that the defendant knew about the drugs in the hidden compartment. E.g., United States v. Palomino, 100 F.3d 446, 451 (6th Cir.1996) (holding that a jury could have inferred defendant's knowledge of drugs in a hidden compartment as a result of defendant's "control and possession of the vehicle" in addition to other factors including "his nervousness"); Diaz-Carreon, 915 F.2d at 954 (noting, in a hidden compartment case, that "[n]ervous behavior at an inspection station frequently constitutes persuasive evidence of guilty knowledge").
Tran would have a stronger claim of error had the district court instructed the jury that nervousness alone was a sufficient basis for finding knowledge, because "[i]n the absence of facts which suggest that the defendant's nervousness or anxiety derives from an underlying consciousness of criminal behavior, evidence of nervousness is insufficient to support a finding of guilty knowledge." Diaz-Carreon, 915 F.2d at 954. A review of the record, however, shows that the district court's instruction did not convey such a message. Read in full, the district court instructed the jury that:
The Defendant's behavior may also indicate knowledge. Nervousness in the presence of drugs or flight from the site at which the authorities identified drugs may indicate that the Defendant knew that the materials in question were narcotics. Also, the possession of a large quantity of drugs may indicate that the Defendant knew what he had in his possession.
These examples are neither exhaustive nor are they conclusive. It is up to you, based upon all the evidence, to determine whether the Defendant knew that he possessed narcotic drugs.
(Sept. 29, 2004 Trial Tr. at 90:84.) These instructions do not suggest that the jury could find knowledge based on nervousness alone. Instead, they accurately inform the jury that nervousness is one type of behavior, among others, that is relevant *105 to determining whether Tran knew about the drugs. The instructions that were given adequately conveyed the law to the jury. United States v. Schultz, 333 F.3d 393, 413-14 (2d Cir.2003) ("[N]o jury instruction is ever perfect. . . . [W]e review the court's instructions to determine whether considered as a whole, the instructions adequately communicated the essential ideas to the jury." (internal quotation marks and brackets omitted)). There was no error.

II. Sufficiency of the Evidence
Tran argues that the Government presented insufficient evidence to support conviction. In particular, Tran contends that the jury could not have found facts sufficient to establish (1) that Tran knew about the pills, and (2) that the substance contained a sufficient amount of methamphetamine to support Tran's conviction for an offense requiring proof of "500 grams or more of a mixture or substance containing a detectable amount of methamphetamine," 21 U.S.C. § 960(b)(1)(H).
A. Standard of Review
In raising "an appellate challenge to the sufficiency of the evidence supporting a conviction," the defendant "faces a heavy burden, because we must review the evidence in the light most favorable to the government, drawing all reasonable inferences in its favor." United States v. Gaskin, 364 F.3d 438, 459 (2d Cir.2004) (internal quotation marks omitted). "Reversal is warranted only if no rational factfinder could have found the crimes charged proved beyond a reasonable doubt." Id. at 459-60.
B. Tran's Knowledge
We agree with the other courts to have addressed the issue that a defendant's sole occupancy of a vehicle cannot alone suffice to prove knowledge of contraband found hidden in the vehicle; corroborating evidence, such as nervousness, a false statement, or suspicious circumstances, is necessary to prove this element. Anchondo-Sandoval, 910 F.2d at 1236 (Fifth Circuit) ("Possession of or control over [the] vehicle [cannot], standing alone, suffice to prove guilty knowledge."); Jackson, 55 F.3d at 1226 (Sixth Circuit) (same); Stanley, 24 F.3d at 1319-20 (Eleventh Circuit) (same). Here, the Government introduced evidence of nervousness and suspicious circumstances. On the question of nervousness, the officer who first intercepted Tran testified that when he asked Tran about his destination, Tran "began sweating" and "gripped the steering wheel." Tran "became a little fidgety in the vehicle" and began "moving around, looking around." Although Tran points out, and the officer acknowledged, that it is not unusual for individuals to become nervous at a border crossing, the jury reasonably could have found that Tran's nervousness surpassed that level and thus reflected consciousness of guilt rather than ordinary anxiety upon interacting with law enforcement. In addition to evidence of nervousness, moreover, the Government introduced evidence of suspicious circumstances. For example, Tran said that he had never visited Seneca Niagara Casino and rarely traveled to Buffalo, but he had no directions for getting to the casino. And while Tran intended to stay for a day or longer, he did not bring a change of clothing or any toiletries other than a brush.
Furthermore, Tran lost "his right to have sufficiency assessed on the basis of the government's presentation alone" when he testified on his own behalf. United States v. Aulicino, 44 F.3d 1102, 1114 (2d Cir.1995). Although "a verdict of guilty cannot properly be based solely on *106 the defendant's denial of the charges," id. at 1114-15, because the jury is entitled to disbelieve the defendant's attempts at exculpatory explanation, United States v. Stanley, 928 F.2d 575, 577 (2d Cir.1991), a testifying defendant might inadvertently "add weight to the government's case," Aulicino, 44 F.3d at 1114 (collecting cases). When Tran testified at trial and stated that he did not know about the contraband in the vehicle, he placed his own credibility in issue. A reasonable jury could have found Tran's explanation incredible, as this jury obviously did. That finding would have been a relevant factor in the jury's determination of whether Tran knew that he was transporting controlled substances.
Because, in addition to Tran's occupancy of the vehicle, the Government introduced corroborating evidence of nervousness and suspicious circumstances, and because the jury considered and rejected Tran's own testimony denying knowledge of the drugs that were found, sufficient evidence supports the jury's finding that Tran knew that those drugs were in the vehicle.
C. Drug Amount
Tran also argues that insufficient evidence supports the finding that he possessed "500 grams or more of methamphetamine," as required to prove a violation of 21 U.S.C. §§ 952(a), 960(b)(1)(H). He contends that the chemist's use of sampling left the jury without a legitimate basis from which it could infer that each of the 40,790 pills  and not just some  contained methamphetamine. Tran claims that because the chemist treated indiscriminately pills "contained in numerous bags, some green and others pink, some bearing the `R' logo and others not," the powder mixtures became tainted. (App. Br. 18-19.) As a result, there remains the possibility that some of the pills contained only MDMA, and that others, amounting to a total of less than 500 grams, contained methamphetamine. On this basis, Tran urges that we reverse his conviction or at least remand for resentencing on the more lenient assumption that each pill contained only MDMA, not methamphetamine.
As with Tran's inaccurate challenge to the jury instructions, part of this challenge rests on a material misrepresentation of the record. Tran claims that some of the pills were marked with the "R" logo and others were not, but the DEA chemist explicitly testified that every pill bore the logo. Tran identifies no other ways in which the pills should have been differentiated. Because each powder mixture tested by the DEA chemist was thus formed from pills that were nearly identical in appearance, the chemist was simply employing a sampling technique to determine the chemical makeup of all of the pills. Although the Government must prove the quantity of drugs through "specific evidence," such as "drug records, admissions or live testimony," United States v. Shonubi, 998 F.2d 84, 89 (2d Cir.1993), sampling is a permissible method of proof, United States v. Maceo, 873 F.2d 1, 6-7 (1st Cir.1989) (holding that sufficient evidence supported the finding of drug quantity where a DEA chemist tested 16 of 227 identical vials, then extrapolated from those results to determine the total amount of crack cocaine contained in all the vials together). Based on the evidence about the sampling technique that was introduced at trial, as well as the chemist's opinion that all of the pills contained the same substances in approximately the same proportions, a reasonable jury could find that at least 500 grams of the total 10.2 kilograms of pills found in Tran's rental vehicle were a "mixture or substance containing a detectable amount of *107 methamphetamine," 21 U.S.C. § 960(b)(1)(H).

III. Sentencing Challenges
Tran argues his sentence is unreasonable because (1) his status as a Vietnam War refugee and his lack of education merit leniency, (2) he presents a low risk of recidivism because of his age, (3) incarceration will impose a severe hardship on his family, and (4) no evidence of any other criminal conduct was introduced, making his offense aberrational.
We review sentencing decisions for reasonableness using "an abuse-of-discretion standard." Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 597, 169 L.Ed.2d 445 (2007); see also United States v. Fernandez, 443 F.3d 19, 27 (2d Cir.2006) (defining reasonableness review as asking "whether the sentencing judge exceeded the bounds of allowable discretion, committed an error of law in the course of exercising discretion, or made a clearly erroneous finding of fact" (alterations and internal quotation marks omitted)). Under this standard, Tran's challenge to his sentence fails. Although Tran points to several factors identified in his submissions to the district court that he believes justified a lower sentence, he has not shown that the district court neglected to consider any of them in reaching its decision. In fact, the district court informed Tran that it had "considered the factors that [he] ha[d] set forth" as well as "the factors set forth in 18 U.S.C. § 3553(a)." The court, nevertheless, ruled that it would not give a shorter sentence because "the sentence imposed is necessary and reasonable and appropriate to address the nature of and the seriousness of the offense[,][t]he criminal history and the characteristics of the defendant[, and] to serve the overall objective of punishment, general deterrence, incapacitation and rehabilitation."
The record makes clear that the district court considered all of Tran's arguments, the applicable Guidelines range, and the factors enumerated in § 3553(a). Tran has failed to identify any way in which the district court "exceeded the bounds of allowable discretion, committed an error of law in the course of exercising discretion, or made a clearly erroneous finding of fact." Fernandez, 443 F.3d at 27 (2d Cir. 2006) (alterations and internal quotation marks omitted). His sentence is therefore affirmed.

CONCLUSION
For the reasons stated, the judgment of conviction and sentence are hereby AFFIRMED.
NOTES
[1]  The erroneously quoted jury instruction was not the only material misrepresentation of the record contained in Tran's brief; Tran's attorneys also inaccurately stated that some of the seized pills bore an "R" logo while others did not. Such "oversights" are inconsistent with the duties that Tran's attorney owes to both Tran and this Court.

Though responsibility for these misrepresentations lies with Tran's attorneys, we are constrained to note that the Government failed to notice and point out these same errors. We remind both parties that vigorous testing of an adversary's position not only strengthens one's own claims but also facilitates our review of the issues.
