
583 F.3d 196 (2009)
UNITED STATES of America
v.
Dylan C. STARNES, Appellant.
United States of America
v.
Cleve-Allan George, Appellant.
Nos. 07-3341, 08-1691.
United States Court of Appeals, Third Circuit.
Argued December 11, 2008.
Filed: September 24, 2009.
*202 Todd G. Scher (Argued), Marc D. Seitles, Miami, FL, for Appellant, Dylan C. Starnes.
Darren John-Baptiste (Argued), The Practice, PLLC, Charlotte Amalie, St. Thomas, VI, for Appellant, Cleve-Allan George.
Anna T. Katselas (Argued), United States Department of Justice, Environmental & Natural Resources Division, Washington, DC, for Appellee, United States of America.
Before: FISHER, JORDAN and STAPLETON, Circuit Judges.

OPINION OF THE COURT
FISHER, Circuit Judge.
Cleve-Allan George and Dylan C. Starnes appeal from judgments of conviction and sentence entered against them following a jury trial in the United States District Court for the District of the Virgin Islands. Although these appeals have not been formally consolidated, we resolve them together because they arise from a common set of facts. For the reasons set forth below, we will affirm the judgments.

I. Background
In 1999, the Virgin Islands Housing Authority (VIHA) received a HOPE VI grant from the United States Department of Housing and Urban Development (HUD) for the demolition of the Donoe Housing Community, a low-income public residential community located on St. Thomas, U.S. Virgin Islands. The following year, VIHA issued an invitation for bids on the Donoe demolition project. The invitation for bids included the project's specifications  which provided, among other things, that work on the project was to be "performed in strict accordance with all federal, state and local regulations and ordinances"  and a report detailing a 1996 asbestos survey that Induchem Environmental Services had conducted at Donoe, which revealed the presence of friable asbestos-containing materials in the ceilings of eighty-six of the community's eighty-eight structures, as well as nonfriable asbestos-containing materials throughout the structures.[1]
VIHA eventually awarded the demolition contract to Alvin Williams Trucking & Equipment Rental, Inc. That company, with the consent of VIHA, subcontracted the asbestos-abatement portion of the project to the Virgin Islands Asbestos Removal Company (VIARCO), a company owned by George. VIARCO's bid for the subcontract specified that George would be the general manager of the asbestos-abatement project and listed his credentials, which included prior experience managing similar asbestos-abatement projects, the completion of comprehensive training courses for "asbestos workers" and "asbestos contractors/supervisors," familiarity with all federal regulations relating to asbestos, and all-around "competen[ce] in all aspects of ... asbestos abatement." VIARCO's bid also referenced the applicable regulations promulgated by the EPA and the Occupational Safety and Health *203 Administration (OSHA) and indicated that VIARCO had "joined forces" with Environmental Contracting Company (ECC), a company run by Starnes.
Starnes had extensive experience in many aspects of asbestos abatement, having even taught courses on the subject. As he personally informed VIHA after George brought him on board, among his various areas of responsibility on the Donoe project was oversight of air-quality monitoring. To this end, Starnes recruited Thrideo Sukhram, a former student, to collect air samples at the Donoe site. Starnes also contacted Carlos Carcamo, who had previously worked for Starnes as a course instructor, and offered him the job of project manager. Carcamo promptly accepted the position and, at Starnes's request, set about recruiting a work crew for the Donoe project. When some of those workers arrived in St. Thomas, Starnes met them at the airport and took them to the Donoe site, where he explained to them the work they would be doing on the project and promised them each a $2,000 bonus if the project was completed on time.
Work on the Donoe project was slated to begin on January 2, 2001, but did not get under way in earnest until January 10, 2001. George and Starnes directed Carcamo to instruct the work crew to use a "pressure washer" to dislodge asbestos-containing materials from the site's structures. This removal method, although time-efficient, generated a substantial amount of debris-filled wastewater, which the crew pumped into toilets and bathtubs. But those fixtures rapidly clogged, causing wastewater to pour out and accumulate on the buildings' balconies. In response, George constructed a drainage system out of PVC pipes, which permitted the wastewater to flow off the balconies and down to the ground. When the wastewater evaporated, it left a dusty white residue clinging to the facades of the buildings and the surrounding sidewalks and grass.
On January 24, 2001, VIHA sent a noncompliance notice to George's attention. Under OSHA rules regulating occupational exposure to asbestos in the construction industry, 29 C.F.R. § 1926.1101, VIARCO was obligated to monitor airborne concentrations of asbestos by collecting and analyzing air samples from the Donoe site, and the notice sent by VIHA indicated that the company had failed to file daily reports detailing the results of its air monitoring, as required by the project specifications. The following day, twelve air-monitoring reports  each corresponding with a work day between January 9, 2001 and January 25, 2001, and each signed by Starnes, attesting that he had analyzed air samples collected at the Donoe site  were delivered to VIHA.
On January 31, 2001, an air-quality specialist with the Virgin Islands Department of Planning and Natural Resources (DPNR) visited the Donoe site and observed the deplorable conditions there, including liquid seeping from a trailer used to store removed asbestos-containing material and unprotected workers covered in white powder. He soon returned to the site accompanied by an OSHA inspector and saw workers using shovels to remove chunks of dry asbestos-containing ceiling material from apartments, causing visible emissions to emanate from the material. On February 9, 2001, after the assistant director of DPNR also inspected the Donoe site and saw that conditions were essentially unchanged, DPNR issued a stop-work order, shutting down the project. DPNR then referred the matter to the EPA for further investigation.
On March 27, 2002, Agent Justus Derx of the EPA's Criminal Investigation Division executed a search warrant at *204 Starnes's office in Chamblee, Georgia, during which he seized copies of the twelve air-monitoring reports that were transmitted to VIHA. The layered fax-header information on the copies indicated that George had faxed blank air-monitoring report forms to Starnes in Florida on January 25, 2001 and that Starnes faxed the completed forms back to George approximately seventeen minutes later.
On February 6, 2003, a grand jury in the District of the Virgin Islands returned a sixteen-count indictment against George and Starnes. Counts One through Four of the indictment charged the defendants with knowingly violating EPA work-practice standards for the handling and disposal of regulated asbestos-containing material, 40 C.F.R. §§ 61.145, 61.150, subjecting them to criminal liability under the Clean Air Act, 42 U.S.C. §§ 7412 and 7413(c)(1). Counts Five through Sixteen charged them with knowingly and willfully making materially false, fictitious or fraudulent statements and representations in a matter within the jurisdiction of the executive branch of the United States by transmitting twelve falsified air-monitoring reports to VIHA, in violation of 18 U.S.C. § 1001(a).[2]
Both defendants pleaded not guilty to all charges, and were tried together to a jury in June 2005. At trial, the government introduced evidence that Starnes flew from St. Thomas to Atlanta, Georgia on January 9, 2001, and from Atlanta to Tampa, Florida on January 24, 2001. Sukhram testified that before Starnes left St. Thomas he gave Sukhram a few air-monitoring devices, each of which was essentially an air pump attached to a filter cassette.[3] Sukhram testified that Starnes taught him how to activate the air-monitoring devices and how to insert and remove the cassettes. Armed with this basic understanding of the devices, Sukhram continued, he set up the devices, removed the cassettes on a daily basis, labeled and dated them, and then passed them on to George, who was responsible for sending them to Starnes for analysis. When Sukhram soon ran out of cassettes, George alerted Starnes, who then told Sukhram to reuse the old cassettes (even though, as the evidence showed, each cassette could only be used once). Sukhram testified that he never saw any indication that the cassettes were analyzed but that Starnes nonetheless instructed him to complete a number of air-monitoring reports as if the observed results fell within legal limits.
The jury also heard testimony from David Dugan, a regional technical coordinator with the EPA's National Enforcement Investigation Center. Dugan testified that in February 2002 he took samples of suspected asbestos-containing material from ceilings in Building 31, a structure at the Donoe site which had yet to be demolished. The evidence showed that the samples collected by Dugan contained asbestos concentrations ranging from 4.1 to 6 percent. Both defendants' attorneys objected to Dugan's testimony on relevance grounds, arguing that it should be stricken because Dugan took the samples approximately a year after the conduct charged in the indictment, from a building in which VIARCO did not work. Starnes's attorney also objected on the ground that any probative value the testimony might have was substantially outweighed by the danger of *205 unfair prejudice. The District Court, after consideration, ultimately overruled those objections.
At the conclusion of the trial, each defendant moved under Federal Rule of Criminal Procedure 29 for a judgment of acquittal on all counts. The District Court denied George's motion in its entirety and denied Starnes's motion as to all counts except Count Four. Following deliberations, the jury found George and Starnes guilty on all counts the District Court permitted it to consider.
The United States Probation Office prepared a presentence investigation report (PSR) for each defendant. For both defendants, the Probation Office began with a base offense level of eight under U.S.S.G. § 2Q1.2 and recommended a six-level enhancement under U.S.S.G. § 2Q1.2(b)(1)(A), a four-level enhancement under U.S.S.G. § 3B1.1(a), and a two-level enhancement under U.S.S.G. § 3B1.3. In addition, the Probation Office recommended for Starnes a four-level enhancement under U.S.S.G. § 2Q1.2(b)(4). For George, this resulted in a total offense level of twenty, which, combined with George's criminal history category of I, yielded an advisory Guidelines range of thirty-three to forty-one months of imprisonment. For Starnes, the resulting total offense level of twenty-four, combined with his criminal history category of I, yielded an advisory Guidelines range of fifty-one to sixty-three months of imprisonment.
Starnes's sentencing hearing was held first, on July 27, 2007. The District Court largely adopted the PSR prepared for Starnes, but rejected the Probation Office's recommendation that it enhance his base offense level by four levels under U.S.S.G. § 2Q1.2(b)(4), resulting in a total offense level of twenty and an advisory Guidelines range of thirty-three to forty-one months. The District Court sentenced Starnes to thirty-three months of imprisonment, three years of supervised release, and a special assessment of $1,600.
George's sentencing hearing was held on February 26, 2008. The District Court found the PSR prepared for George to be factually and legally accurate, and its calculations to be appropriate and correct. While noting the government's position that George's acts were more egregious than those of Starnes, the District Court nonetheless imposed on George the same sentence that it had imposed on Starnes.
These appeals followed. The District Court had subject matter jurisdiction under 48 U.S.C. § 1612(a) and 18 U.S.C. § 3231. We have jurisdiction under 28 U.S.C. §§ 1291, 1294(3) and 18 U.S.C. § 3742(a).

II. Discussion
George and Starnes raise several challenges to their convictions. Specifically, Starnes contends that the District Court should have granted his motion for judgment of acquittal in full because the evidence presented at trial was insufficient to support his convictions on both the Clean Air Act counts and the false-statement counts. George likewise contends that the District Court erred in denying his motion for judgment of acquittal on the false-statement counts.[4] Both defendants challenge the District Court's decision to admit the testimony of David Dugan. Each defendant also attacks the District Court's determination of his sentence.


*206 A. Challenges to the Sufficiency of the Evidence
We turn first to the defendants' challenges to the sufficiency of the evidence supporting their respective convictions.
We exercise plenary review over a district court's grant or denial of a motion for judgment of acquittal based on the sufficiency of the evidence, applying the same standard as the district court. United States v. Brodie, 403 F.3d 123, 133 (3d Cir.2005). In reviewing a sufficiency-of-the-evidence claim, therefore, we must "examine the totality of the evidence, both direct and circumstantial," and "interpret the evidence in the light most favorable to the government as the verdict winner." United States v. Miller, 527 F.3d 54, 60, 62 (3d Cir.2008) (citations and internal quotation marks omitted). We must uphold the jury's verdict if there is substantial evidence from which a rational trier of fact could find the essential elements of the crime beyond a reasonable doubt. Id. at 60 (quoting United States v. Brown, 3 F.3d 673, 680 (3d Cir.1993)); United States v. Greenidge, 495 F.3d 85, 100 (3d Cir.2007). "The burden on a defendant who raises a challenge to the sufficiency of the evidence is extremely high." United States v. Iglesias, 535 F.3d 150, 155 (3d Cir.2008) (internal quotation marks omitted); accord United States v. Hodge, 321 F.3d 429, 439 (3d Cir.2003) ("Our review of the sufficiency of the evidence after a guilty verdict is `highly deferential.'" (quoting United States v. Hart, 273 F.3d 363, 371 (3d Cir. 2001))).

1. Counts One Through Three  Convictions for Violations of the Clean Air Act
Starnes argues that the District Court erred in denying his motion for judgment of acquittal on Counts One through Three because the evidence presented at trial was insufficient to permit the jury to conclude beyond a reasonable doubt that he was an "owner or operator" of the Donoe asbestos-abatement project within the meaning of the Clean Air Act. We disagree.
Under the Clean Air Act, an "owner or operator of a demolition or renovation activity" is subject to criminal liability for knowingly violating the EPA work-practice standards for the handling and disposal of regulated asbestos-containing material. See 42 U.S.C. § 7413(c)(1); 40 C.F.R. §§ 61.145, 61.150. In this regard, the EPA defines the term "owner or operator of a demolition or renovation activity" as "any person who owns, leases, operates, controls, or supervises the facility being demolished or renovated or ... the demolition or renovation operation, or both." 40 C.F.R. § 61.141. We have previously explained, albeit in the related context of a civil enforcement action under 42 U.S.C. § 7413(b), that "a non-owner can still be liable as an `operator'" if he or she has "significant or substantial or real control and supervision of a project." United States v. Anthony Dell'Aquilla, Enters. & Subsidiaries, 150 F.3d 329, 333 (3d Cir. 1998) (characterizing as "axiomatic" the availability of operator liability under the Clean Air Act). We see no reason the same should not hold true in the present context of a criminal prosecution under 42 U.S.C. § 7413(c)(1). Cf. United States v. DiPentino, 242 F.3d 1090, 1096 (9th Cir. 2001) (upholding the conviction of a nonowner defendant under 42 U.S.C. § 7413(c)(1) where the evidence established that he "had significant or substantial or real control and supervision" over an asbestos-abatement project and that he knowingly violated 40 C.F.R. § 61.145).
Our review of the record in this case reveals substantial evidence by which a rational juror could conclude that Starnes *207 exercised significant control and supervision over the Donoe asbestos-abatement project. For instance, the evidence showed that Starnes: (1) recruited Sukhram to collect air samples at the Donoe site, gave him rudimentary direction on the use of the air-monitoring devices, and instructed him to falsify some air-monitoring reports; (2) recruited Carcamo to be the manager of the project, told him to assemble a crew to work on the project, and directed him to instruct the crew to use a "pressure washer" to strip asbestos-containing materials from the Donoe site's structures; and (3) met several workers at the airport and took them to the Donoe site, where he explained to them the work they would be doing on the project and promised them each a bonus if the project was completed on time.
This evidence, viewed in the light most favorable to the government and in the context of the totality of the evidence in the record, supports a finding that Starnes was an operator of the Donoe project within the meaning of the Clean Air Act. We will therefore affirm the District Court's denial of his motion for judgment of acquittal on Counts One through Three.[5]

2. Counts Five Through Sixteen  Convictions for Violations of 18 U.S.C. § 1001(a)
George and Starnes contend that the District Court erred in denying their motions for judgment of acquittal on Counts Five through Sixteen, which charged them with violating 18 U.S.C. § 1001(a) by knowingly and willfully transmitting twelve falsified air-monitoring reports to VIHA.[6] Specifically, both defendants assert that the evidence supporting their respective convictions on these counts was insufficient to establish falsity or federal-government jurisdiction, necessary elements of a § 1001(a) violation. George also claims that there was insufficient evidence to prove that he had the requisite mens rea. Again, we disagree.

a. Falsity
Both defendants argue that no rational juror could have found beyond a reasonable doubt that the air-monitoring reports were actually false because the government failed to adduce any evidence that airborne asbestos fibers were found at the Donoe site on the relevant days in concentrations exceeding the permissible *208 exposure limits set by OSHA. See 29 C.F.R. § 1926.1101(c). This argument is without merit. For one thing, it rests on the faulty premise that the defendants were charged with, and convicted of, falsely representing the amounts of airborne asbestos found in air samples taken at the site. To the contrary, the crux of the government's case on the false-statement counts was that the reports falsely represented that Starnes had analyzed the air samples in the first place  to the extent any were even collected  when in fact he had not, a proposition that Starnes does not contest and that George concedes in his appellate brief.
Even if we were to recharacterize this argument to focus on the proper theory underpinning the government's case, it would still fail. The record reflects that there was ample evidence to establish that Starnes did not analyze the samples, despite the presence of his signature on each of the twelve reports attesting that he had done so. For example, the government introduced evidence demonstrating that Starnes could not have analyzed the samples without having physical access to the filter cassettes from the air-monitoring devices but that he was in the continental United States from January 9, 2001 through January 26, 2001  that is, during the period in which he ostensibly analyzed the air samples described in the reports  and that no packages were sent to him after January 11, 2001. We have no difficulty concluding that there was sufficient evidence of falsity.

b. Federal-Government Jurisdiction
Both defendants also argue that the evidence at trial was insufficient to establish that the air-monitoring reports pertained to a matter "within the jurisdiction" of the executive branch of the federal government because the reports were sent to VIHA, not to a federal agency. This argument is also without merit.
It is well settled that a false statement or representation may pertain to a matter "within the jurisdiction" of the executive branch for purposes of § 1001(a) even if it was not made to an agency (or other component) of the executive branch. See United States v. Waters, 457 F.2d 805, 805-06 (3d Cir.1972); see also, e.g., United States v. Shafer, 199 F.3d 826, 828-29 (6th Cir.1999); United States v. Petullo, 709 F.2d 1178, 1180 (7th Cir.1983); United States v. Candella, 487 F.2d 1223, 1227 (2d Cir.1973); Ebeling v. United States, 248 F.2d 429, 434 (8th Cir.1957). Indeed, it is enough that the statement or representation pertain to a matter in which the executive branch has "the power to exercise authority." United States v. Rodgers, 466 U.S. 475, 479, 104 S.Ct. 1942, 80 L.Ed.2d 492 (1984); see United States v. Atalig, 502 F.3d 1063, 1067 (9th Cir.2007).
The evidence presented at trial  including the uncontroverted testimony of Monique Farrell, a VIHA official  established that HUD, an agency within the executive branch, provided the funding for the Donoe project to VIHA and had the power to exercise authority over the project, had it chosen to do so. "[I]t is the existence of federal supervisory authority that is important, not necessarily its exercise." Petullo, 709 F.2d at 1180; see United States v. Canel, 708 F.2d 894, 897-98 (3d Cir.1983). We are satisfied that the record contains substantial evidence from which a rational juror could find that the false representations in the air-monitoring reports submitted to VIHA were made within the jurisdiction of HUD.

c. "Knowingly and Willfully"
George alone challenges the sufficiency of the evidence to establish that he "possessed the requisite mens rea, specific *209 intent ... to violate § 1001(a)." Before we evaluate this factual challenge we must consider the soundness of the legal proposition on which it is premised, namely that the statutory terms "knowingly and willfully" required the government to prove that George acted with "specific intent."
To support that proposition, George relies exclusively on a dictum in United States v. Barr, 963 F.2d 641, 645 (3d Cir. 1992), that "[a] conviction under § 1001 requires ... [proof of] specific intent." But Barr does nothing to give context to the phrase "specific intent" and George gives no indication of what, exactly, he believes that phrase means in this context. The government, for its part, agrees that it must prove "specific intent" and likewise cites to Barr, although it takes the additional step of attempting to put some flesh on the bones left bare by that case (if not color on the flesh) by pointing to United States v. Curran, 20 F.3d 560, 567 (3d Cir.1994), where we addressed, in passing, the "requisite intent" that the government must prove under § 1001.
"Specific intent" is usually distinguished from "general intent." United States v. Bailey, 444 U.S. 394, 403, 100 S.Ct. 624, 62 L.Ed.2d 575 (1980). As most commonly understood, a general-intent crime is one that requires "proof of knowledge with respect to the actus reus of the crime," Carter v. United States, 530 U.S. 255, 269, 120 S.Ct. 2159, 147 L.Ed.2d 203 (2000), while a specific-intent crime, in contrast, is "one whose definition requires a special mens rea above and beyond that which is required for the actus reus of the crime," United States v. Dollar Bank Money Mkt. Account No. XXXXXXXXXX, 980 F.2d 233, 237 (3d Cir.1992). Both concepts are somewhat elusive, with "specific intent" being particularly susceptible to a wide variety of meanings. See generally 1 W. LaFave & A. Scott, Substantive Criminal Law § 5.2(e) (2d ed. 2003 & Supp. 2008) (discussing various meanings attributed to the phrases "general intent" and "specific intent"). While the "traditional dichotomy of general versus specific intent" is a venerable one, in many situations it can be more perplexing than helpful. Dixon v. United States, 548 U.S. 1, 7, 126 S.Ct. 2437, 165 L.Ed.2d 299 (2006) (citing Bailey, 444 U.S. at 403-04, 100 S.Ct. 624); cf. Liparota v. United States, 471 U.S. 419, 423 n. 5, 105 S.Ct. 2084, 85 L.Ed.2d 434 (1985) (recognizing that "the mental element in criminal law encompasses more than the two possibilities of `specific' and `general' intent"); United States v. Hernandez-Hernandez, 519 F.3d 1236, 1239 (10th Cir.2008) (decrying "opaque common law labels [like `general' and `specific' intent] that sometimes blur the line between distinct mental elements"). This is doubly true where, as here, the criminal statute in question does not use either phrase.
Congress defined the crime at issue here, § 1001(a), to punish defendants who act "knowingly and willfully." It is this mental state, not an amorphous "specific intent," that the government was required to prove beyond a reasonable doubt. See Dixon, 548 U.S. at 7, 126 S.Ct. 2437 (observing that "`[t]he definition of the elements of a criminal offense is entrusted to the legislature, particularly in the case of federal crimes, which are solely creatures of statute'" (quoting Liparota, 471 U.S. at 424, 105 S.Ct. 2084)); United States v. Hudson, 11 U.S. (7 Cranch) 32, 3 L.Ed. 259 (1812). While use of the phrase "specific intent" as a shorthand descriptor for the statute's express "knowingly and willfully" requirement is not necessarily inappropriate, it tends to obscure the meaning of the statutory terms. Cf. Fla. State Conference of NAACP v. Browning, 522 F.3d 1153, 1167 (11th Cir.2008) ("Categories and labels are helpful, but only to a point, and *210 they too often tend to obfuscate instead of illuminate."). "Few areas of criminal law pose more difficulty than the proper definition of the mens rea required for any particular crime." Bailey, 444 U.S. at 403, 100 S.Ct. 624. We see little reason to needlessly complicate our interpretation of § 1001(a) by maintaining an insubstantial extra layer of terminology atop the explicit statutory language.
The question, then, is, What does "knowingly and willfully," as used in § 1001(a), mean? The statute does not define either term but, of the two terms, "knowingly" is the less abstruse. In general, "knowingly" requires the government to prove that a criminal defendant had "knowledge of the facts that constitute the offense." Bryan v. United States, 524 U.S. 184, 193, 118 S.Ct. 1939, 141 L.Ed.2d 197 (1998); see United States v. Hayden, 64 F.3d 126, 130 (3d Cir.1995).
"Willfully," on the other hand, is a "notoriously slippery term," a "chameleon word" that "takes color from the text in which it appears." United States v. Ladish Malting Co., 135 F.3d 484, 487-88 (7th Cir.1998); see Bryan, 524 U.S. at 191 & n. 12, 118 S.Ct. 1939; cf. Bryan A. Garner, A Dictionary of Modern Legal Usage 145 (2d ed. 1995) ("`In any closely reasoned problem, whether legal or nonlegal, chameleon-hued words are a peril both to clear thought and to lucid expression.'" (quoting Wesley N. Hohfeld, Fundamental Legal Conceptions 35 (1919) (reprint 1966))).[7] The cases delineate at least three levels of interpretation of the term. See, e.g., Bryan, 524 U.S. at 191-95, 118 S.Ct. 1939; United States v. Kay, 513 F.3d 432, 447-48 (5th Cir.2007). In some contexts, "willfully" may denote "`an act which is intentional, or knowing, or voluntary, as distinguished from accidental.'" Bryan, 524 U.S. at 191 n. 12, 118 S.Ct. 1939 (quoting United States v. Murdock, 290 U.S. 389, 394, 54 S.Ct. 223, 78 L.Ed. 381 (1933)). But when "willfully" is used in a criminal statute, and particularly where the term is used in conjunction with "knowingly," as it is in § 1001(a), it usually requires the government to prove that the defendant acted "not merely `voluntarily,' but with a `bad purpose,'" that is, with knowledge that his conduct was, in some general sense, "unlawful." Id. at 192-93 & n. 13, 118 S.Ct. 1939 (quoting Ratzlaf v. United States, 510 U.S. 135, 137, 114 S.Ct. 655, 126 L.Ed.2d 615 (1994) and Felton v. United States, 96 U.S. 699, 702, 24 L.Ed. 875 (1877)); see Kay, 513 F.3d at 447-48; Hayden, 64 F.3d at 130; see also Third Circuit Model Criminal Jury Instructions § 5.05 (providing that "willfully" requires the government to prove beyond a reasonable doubt that a defendant "knew that [his or her] conduct was unlawful and intended to do something that the law forbids"); cf. Safeco Ins. Co. of Am. v. Burr, 551 U.S. 47, 60, 127 S.Ct. 2201, 167 L.Ed.2d 1045 (2007) ("[O]n the criminal *211 side of the law, where the paired modifiers [`knowingly' and `willfully'] are often found, see, e.g., 18 U.S.C. § 1001 ..., `willfully' typically narrows the otherwise sufficient intent, making the government prove something extra."). And in some rare instances involving highly technical statutes that present the danger of ensnaring individuals engaged in apparently innocent conduct, such as the federal criminal tax and antistructuring provisions, "willfully" has been read to require proof that the defendant actually knew of the specific law prohibiting the conduct. See Bryan, 524 U.S. at 194-95, 118 S.Ct. 1939 (discussing, among other cases, Ratzlaf, 510 U.S. at 138, 149, 114 S.Ct. 655 (antistructuring statutes) and Cheek v. United States, 498 U.S. 192, 199-201, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991) (criminal tax statutes)); Kay, 513 F.3d at 448, 450 (explaining that under the "strictest level of interpretation of criminal willfulness"  that reserved for "complex" statutes  "a defendant must know the specific law he is violating in order to act willfully").
Our decision in Curran, cited by the government, is instructive. Curran was convicted on charges of causing election campaign treasurers to submit false contribution reports to the Federal Election Commission. Because Curran's conduct "did not fall directly within the scope of section 1001"  he did not make the false representations himself, but caused the campaign treasurers to do so  the government could not "proceed[] directly" under § 1001 and instead prosecuted Curran under that section "in tandem with" 18 U.S.C. § 2(b), which provides that a person who "willfully causes" another to commit a criminal act is liable as a principal. Curran, 20 F.3d at 567. Relying in part on the Supreme Court's decision in Ratzlaf, we held that the strictest interpretation of criminal willfulness governed tandem violations of §§ 1001 and 2(b) in the "federal election law context." Curran, 20 F.3d at 569.
Because the mens rea required for a tandem § 2(b) violation encompasses (and goes beyond) that required for a direct violation of the underlying criminal statute with which § 2(b) is used, in reaching our conclusion in Curran we necessarily touched on the meaning of § 1001's "knowingly and willfully" requirement. Importantly for our current purposes, we explained,
"To establish knowing and willful conduct in the making of a false statement [under § 1001], the government must show that a defendant `acted deliberately and with knowledge that the representation was false.' ... [T]he government must prove not only that the statement was false, but that the accused knew it to be false."
Id. at 567 (citations omitted). But that showing, while a necessary one, may not always be sufficient to satisfy § 1001's "knowingly and willfully" requirement; thus, we also stressed in Curran that "the government is required to show that the misrepresentation was not made innocently or inadvertently." Id. This reading of the statutory text comports with the generally understood meaning of "knowingly" and with the intermediate level of interpretation of "willfully" articulated by the Supreme Court in Bryan  that is, knowledge of the general unlawfulness of the conduct at issue  which we believe adequately demarcates the boundary between innocent and unlawful conduct in this context. See Bryan, 524 U.S. at 195 & n. 23, 118 S.Ct. 1939 (explaining that "requiring only knowledge that the conduct is unlawful," as opposed to specific "knowledge of the law," is "fully consistent" with protecting "law-abiding citizens who might inadvertently violate the law" and "individuals *212 engaged in apparently innocent activity"); Kay, 513 F.3d at 447-48; cf. United States v. Whab, 355 F.3d 155, 162 (2d Cir.2004) (holding that "it was not `plain error' for the District Court to fail to instruct the jury that `willfully' under § 1001 required something more than that the defendant have been aware of the generally unlawful nature of his conduct").[8] To the extent that George's brief can be read to argue that the government was required to prove that he actually knew of § 1001(a), we reject that argument.
The record in this case contains sufficient evidence to convince a rational juror beyond a reasonable doubt that George acted deliberately and with knowledge that the representations contained in the air-monitoring reports  that Starnes had analyzed air samples taken at the Donoe site on the relevant days  were false and that he was aware, at least in a general sense, that his conduct was unlawful. The noncompliance notice sent by VIHA to George on January 24, 2001  the notice that precipitated the events culminating in the filing of the falsified reports  restated in unequivocal terms that a period of no longer than twenty-four hours was permitted between the "collection of air samples" from the site and the transmission of accurate results to VIHA. In addition, the government adduced evidence showing that George was an experienced contractor who had worked as a "General Manager" on several asbestos-abatement projects in the Virgin Islands prior to bidding on the subcontract for asbestos abatement on the Donoe project; that in securing that subcontract he had represented that he was "competent in all aspects of ... asbestos abatement" and "all the contents of the Code [of] Federal Regulations as they relate to ... [a]sbestos, and the removal procedure and practices for reducing the hazard thereof"; and that, over the years, he had completed a substantial number of comprehensive training courses for "asbestos workers" and "asbestos contractors/supervisors" that covered air-monitoring requirements. And trial testimony indicated that George was responsible for collecting the filter cassettes from Sukhram during the period when Starnes was in the continental United States and for sending the cassettes to Starnes for analysis, but that George did not send any packages to Starnes after January 11, 2001.
This evidence, viewed in the light most favorable to the government and in the context of the totality of the evidence in the record, dispels any doubt that George was sufficiently informed of the intricacies of air-monitoring procedures to recognize that Starnes could not analyze any air samples from the Donoe site without physical access to the filter cassettes and that George knew that Starnes did not have such access during the relevant period of time, and thus would *213 permit a rational juror to reasonably infer that the representations to the contrary contained in the air-monitoring reports were necessarily false. This evidence also supports a reasonable inference that George was aware that transmitting falsified air-monitoring reports to VIHA was unlawful. Accordingly, we reject George's contention that the evidence was insufficient to satisfy § 1001(a)'s mens rea requirement. See Iglesias, 535 F.3d at 156 ("[T]he government may defeat a sufficiency-of-the-evidence challenge on circumstantial evidence alone."); cf. Ratzlaf, 510 U.S. at 149 n. 19, 114 S.Ct. 655 ("A jury may, of course, find the requisite knowledge on defendant's part by drawing reasonable inferences from the evidence of defendant's conduct."); Am. Commc'ns Ass'n v. Douds, 339 U.S. 382, 411, 70 S.Ct. 674, 94 L.Ed. 925 (1950) ("[C]ourts and juries every day pass upon knowledge, belief and intent  the state of men's minds  having before them no more than evidence of their words and conduct, from which, in ordinary human experience, mental condition may be inferred."); United States v. Bank of New Eng., N.A., 821 F.2d 844, 854 (1st Cir.1987) ("Willfulness can rarely be proven by direct evidence, since it is a state of mind; it is usually established by drawing reasonable inferences from the available facts.").[9]

B. Challenges to the Admission of David Dugan's Testimony
George and Starnes next challenge the District Court's decision to admit David Dugan's testimony concerning the samples of ceiling materials that he collected in February 2002 from Donoe Building 31, which were subsequently revealed to contain unacceptably high levels of friable asbestos. We review a trial court's decision to admit or exclude evidence for abuse *214 of discretion. United States v. Kemp, 500 F.3d 257, 295 (3d Cir.2007); see Old Chief v. United States, 519 U.S. 172, 174 n. 1, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997). The "[a]dmission of evidence is an abuse of discretion if the district court's action was arbitrary, fanciful or clearly unreasonable," and "[w]e will not disturb a trial court's exercise of discretion unless no reasonable person would adopt the district court's view." Ansell v. Green Acres Contracting Co., 347 F.3d 515, 519 (3d Cir. 2003) (internal quotation marks omitted); see United States v. Frazier, 469 F.3d 85, 87-88 (3d Cir.2006); United States v. Universal Rehab. Servs. (PA), Inc., 205 F.3d 657, 665 (3d Cir.2000) (en banc).
The District Court determined that Dugan's testimony concerning the samples from Building 31 was relevant because it tended to prove that dangerous levels of friable asbestos likewise were present in the Donoe buildings worked on by VIARCO in January 2001. The defendants contend that this determination amounted to an abuse of discretion because Dugan collected the samples from a building in which they did not work and at a point in time too distant from the events at issue. We disagree.
Under the Federal Rules of Evidence, evidence is admissible only to the extent that it is relevant. Fed.R.Evid. 402. "`Relevant evidence' means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." Fed.R.Evid. 401; see Gibson v. Mayor & Council of Wilmington, 355 F.3d 215, 232 (3d Cir.2004) ("[E]vidence is irrelevant only when its has no tendency to prove a consequential fact." (internal quotation marks omitted)). Rule 401 does not raise a high standard. Kemp, 500 F.3d at 295; Hurley v. Atl. City Police Dep't, 174 F.3d 95, 109-110 (3d Cir.1999).
The government supported the introduction of Dugan's testimony by demonstrating that the ceilings in all of the Donoe buildings were made of the same materials and that no structural changes or significant renovations were made to them after the Induchem survey was conducted in 1996. Given this predicate showing, there is no question that the testimony could give rise to a reasonable inference that the buildings worked on by VIARCO contained dangerous levels of friable asbestos in January 2001. See Ansell, 347 F.3d at 525 (explaining that a trial court's determination whether "evidence is too remote to be relevant ... must be based on the potential the evidence has for giving rise to reasonable inferences of fact which are `of consequence to the determination of the action'" (quoting Fed.R.Evid. 401)). This is so even if the materials used in those buildings did not perfectly correspond with the materials used in Building 31, because any dissimilarities would "affect the weight of the evidence ... not its admissibility." Stecyk v. Bell Helicopter Textron, Inc., 295 F.3d 408, 412 (3d Cir.2002); see Ansell, 347 F.3d at 525 ("The passage of time and purportedly changed circumstances were proper issues for counsel to argue to the jury, and for the jury to consider in weighing the evidence."); cf. Arcade Co. v. Boxwell, 41 App. D.C. 213, 223-24 (D.C.Cir.1913) (concluding that testimony offered to prove "conditions of moisture, darkness, and excessive cold" in a cold storage room on June 1, 1911, although based on an inspection that occurred more than a year later, was admissible).
We also reject Starnes's argument that the District Court should have excluded Dugan's testimony under Federal Rule of Evidence 403 because the testimony "could not but have influenced the jury *215... into declaring guilt" based on the "deplorable conditions" in Building 31. Rule 403 provides that even relevant evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice. Fed.R.Evid. 403. Starnes ignores that relevant evidence is excludable under Rule 403 if its probative value is substantially outweighed by the danger of unfair prejudice, not just prejudice. Goodman v. Pa. Tpk. Comm'n, 293 F.3d 655, 670 (3d Cir.2002) ("`[T]he prejudice against which [Rule 403] guards is unfair prejudice  prejudice of the sort which clouds impartial scrutiny and reasoned evaluation of the facts, which inhibits neutral application of principles of law to the facts as found.'" (quoting Wagenmann v. Adams, 829 F.2d 196, 217 (1st Cir.1987))); see Old Chief, 519 U.S. at 180, 117 S.Ct. 644. And unfair prejudice "does not simply mean damage to the opponent's cause. If it did, most relevant evidence would be deemed [unfairly] prejudicial.... [T]he fact that probative evidence helps one side prove its case obviously is not grounds for excluding it under Rule 403." Goodman, 293 F.3d at 670 (internal quotation marks omitted). While Dugan's testimony may have hurt Starnes's case, Starnes has not demonstrated that it carried a risk of unfair prejudice, much less that the District Court abused its broad discretion in determining that any such risk did not substantially outweigh the testimony's probative value.

C. Challenges to the Defendants' Sentences
George and Starnes also raise various challenges to the District Court's determination of their respective sentences. We readily dispatch these challenges.
We review a district court's sentencing decisions for reasonableness under "a deferential abuse-of-discretion standard." Gall v. United States, 552 U.S. 38, 128 S.Ct. 586, 591, 169 L.Ed.2d 445 (2007); see United States v. Tomko, 562 F.3d 558, 564-68 (3d Cir.2009) (en banc). In this regard, "our role is two-fold." United States v. Wise, 515 F.3d 207, 217 (3d Cir.2008). "We must first ensure that the district court committed no significant procedural error in arriving at its decision" and, if it has not, "we then review the substantive reasonableness of the sentence." Id. at 217-18 (citing Gall, 128 S.Ct. at 597); see Tomko, 562 F.3d at 567. A district court commits significant procedural error  and thus abuses its discretion  when, for example, it bases its calculation of the advisory Guidelines range on a clearly erroneous finding of fact or an erroneous legal conclusion. See Tomko, 562 F.3d at 567-68; Wise, 515 F.3d at 217-18. "A [factual] finding is clearly erroneous when although there is evidence to support it, the reviewing body on the entire evidence is left with the definite and firm conviction that a mistake has been committed." Wise, 515 F.3d at 218 (internal quotation marks omitted); see United States v. Grier, 475 F.3d 556, 570 (3d Cir.2007) (en banc). In addition, "[t]o be procedurally reasonable, a sentence must reflect a district court's meaningful consideration of the factors set forth at 18 U.S.C. § 3553(a)." United States v. Lessner, 498 F.3d 185, 203 (3d Cir.2007). "At both [the procedural and substantive] stages of our review, the party challenging the sentence has the burden of demonstrating unreasonableness." Tomko, 562 F.3d at 567 (citing United States v. Cooper, 437 F.3d 324, 332 (3d Cir.2006)); see United States v. Howe, 543 F.3d 128, 132 (3d Cir.2008).

1. Sentencing Enhancements
George and Starnes both argue that the District Court committed significant procedural error by including certain sentencing *216 enhancements in its calculation of their respective advisory Guidelines ranges. In sentencing each defendant, the District Court imposed a six-level enhancement under U.S.S.G. § 2Q1.2(b)(1)(A) for an offense resulting "in an ongoing, continuous, or repetitive discharge, release, or emission of a hazardous or toxic substance or pesticide into the environment," a four-level enhancement under U.S.S.G. § 3B1.1(a) for being "an organizer or leader of a criminal activity that involved five or more participants or was otherwise extensive," and a two-level enhancement under U.S.S.G. § 3B1.3 for abuse of a position of trust.
George cursorily asserts that "the District Court failed [to] make sufficient findings by a preponderance of the evidence to support the [three] sentencing enhancements made with respect to" him. But he declines to elaborate in any meaningful way on this assertion and does not point to any specific deficiencies in the District Court's findings of fact or to any case law germane to the enhancements he disputes. We are skeptical that George's skeletal argument suffices to raise an issue for our review. Cf. United States v. Hoffecker, 530 F.3d 137, 163 (3d Cir.2008) ("A skeletal `argument,' really nothing more than an assertion, does not preserve a claim. Especially not when the brief presents a passel of other arguments, as defendant's did. Judges are not like pigs, hunting for truffles buried in briefs." (internal quotation marks omitted) (quoting United States v. Dunkel, 927 F.2d 955, 956 (7th Cir.1991))).
In any event, insofar as George contends that the District Court altogether failed to make findings of fact with respect to the enhancements, he is simply incorrect. To the extent he means to argue that the District Court imposed the enhancements based on clearly erroneous factual findings, our review of the record in his case  including the jury's verdict, the facts necessarily implied by that verdict, the undisputed facts set out in the PSR, and the statements made by the District Court at the sentencing hearing  does not leave us "with the definite and firm conviction that a mistake has been committed." Wise, 515 F.3d at 218 (internal quotation marks omitted). Either way, even setting aside the inadequacy of George's briefing in this regard, we conclude that he has not met his burden to demonstrate that the District Court committed significant procedural error when it included the three enhancements in its calculation of his advisory Guidelines range. See Tomko, 562 F.3d at 567.
Starnes's arguments concerning the enhancements made by the District Court to his base offense level are marginally more specific; he likewise fails to meet his burden to show that the District Court committed significant procedural error by imposing the enhancements. Starnes initially contends that the District Court erred by enhancing his base offense level by four levels under U.S.S.G. § 3B1.1(a) because the District Court's predicate factual finding that he "involved" Carcamo in the criminal activity at Donoe was inadequate to justify treating Carcamo as a culpable "participant" within the meaning of that section. But a "participant" under § 3B1.1 "is a person who is criminally responsible for the commission of the offense, [who] need not have been convicted," U.S.S.G. § 3B1.1 cmt. n. 1, and, while the District Court surely could have discussed this point more thoroughly, we are satisfied that its finding concerning Carcamo's involvement entails such criminal responsibility.
In addition, Starnes argues that the District Court's factual finding that he was an "organizer" of the criminal activity at Donoe for purposes of § 3B1.1 was clearly *217 erroneous because he was "not the general contractor" but only a "consultant" and "advisor" to George. This argument is misplaced. The District Court's statements at the sentencing hearing, while succinct, indicate that it properly gave no weight to Starnes's formal job title in assessing whether he should be characterized as an organizer, see U.S.S.G. § 3B1.1 cmt. n. 4, and also that it made this finding after evaluating the evidence in the record in light of the other pertinent considerations identified in § 3B1.1 and the Application Notes accompanying that section. See United States v. Helbling, 209 F.3d 226, 243 (3d Cir.2000). After reviewing the record, we see no clear error in this finding.
Starnes also contends that the District Court erred by enhancing his base offense level by two levels under U.S.S.G. § 3B1.3 because he did not hold a position of trust as contemplated by that section. In deciding whether a defendant holds a position of trust, a court must consider: "(1) whether the position allows the defendant to commit a difficult-to-detect wrong; (2) the degree of authority which the position vests in [the] defendant vis-á-vis the object of the wrongful act; and (3) whether there has been reliance on the integrity of the person occupying the position." United States v. Pardo, 25 F.3d 1187, 1192 (3d Cir.1994); see United States v. Dullum, 560 F.3d 133, 140 (3d Cir.2009); United States v. Lieberman, 971 F.2d 989, 993 (3d Cir.1992) ("[T]he primary trait that distinguishes a person in a position of trust from one who is not is the extent to which the position provides the freedom to commit a difficult-to-detect wrong." (internal quotation marks omitted)). "These factors should be considered in light of the guiding rationale of the section  to punish `insiders' who abuse their positions rather than those who take advantage of an available opportunity." Pardo, 25 F.3d at 1192; accord Dullum, 560 F.3d at 140.
In this case, Starnes had significant authority over the manner in which work was performed at the Donoe site, including central responsibility for air monitoring. He was subject to very little, if any, supervision in exercising his authority and had substantial "managerial discretion," see U.S.S.G. § 3B1.3 cmt. n. 1, which facilitated his crimes and made them difficult to detect. And there is no question that VIHA relied on him to accurately monitor and honestly report the levels of asbestos in the air at the Donoe site. Cf. United States v. Snook, 366 F.3d 439, 445-46 (7th Cir.2004); United States v. Turner, 102 F.3d 1350, 1360 (4th Cir.1996). On these facts, we conclude that the District Court correctly determined that Starnes was in a position of trust.[10]

2. Meaningful Consideration of the 18 U.S.C. § 3553(a) Factors
Both defendants also argue, albeit somewhat perfunctorily, that the District Court committed significant procedural error by failing to give meaningful consideration to the sentencing factors set forth in 18 U.S.C. § 3553(a).[11] We disagree.
*218 While a sentencing court must consider all of the § 3553(a) factors, it does not have to discuss and make findings as to each factor so long as the record otherwise makes clear that it took the factors into account. See Tomko, 562 F.3d at 568; see also United States v. Lofink, 564 F.3d 232, 238 n. 13 (3d Cir.2009); Lessner, 498 F.3d at 203. "Nor must the [sentencing] court consider arguments that clearly lack merit." Lessner, 498 F.3d at 203.
In each case now before us, the record demonstrates that the District Court listened to each argument concerning sentencing and then gave meaningful consideration to the § 3553(a) factors in imposing a within-Guidelines sentence. "[W]hen a judge decides simply to apply the Guidelines to a particular case, doing so will not necessarily require lengthy explanation." Rita v. United States, 551 U.S. 338, 356, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007). In sentencing George, the District Court necessarily considered the "sentencing range established for ... the applicable category of offense committed by the applicable category of defendant," 18 U.S.C. § 3553(a)(4), when it explicitly adopted the PSR prepared in his case, including the Probation Office's calculation of his advisory Guidelines range. See Lessner, 498 F.3d at 203. The District Court also heard testimony from several members of George's family and acknowledged the "good things" they said on his behalf, but discounted such mitigating considerations in light of the nature and circumstances of George's offenses  which it emphasized could "result in serious injury and death"  and the need for his sentence to reflect the seriousness of those offenses and to afford adequate deterrence. See 18 U.S.C. § 3553(a)(1), (a)(2)(A)-(B).
At Starnes's sentencing hearing, the District Court likewise demonstrated its consideration of the applicable advisory Guidelines range when it rejected the Probation Office's recommendation in the PSR to enhance Starnes's base offense level by four levels under U.S.S.G. § 2Q1.2(b)(4)  leading it to calculate a lower advisory Guidelines range than that proposed by the Probation Office  but otherwise adopted the PSR. See 18 U.S.C. § 3553(a)(4). The District Court also touched on the nature and circumstances *219 of Starnes's offenses, noting the "danger... [Starnes's actions] pose[d] to the health of the community and the people of the Virgin Islands," see id. § 3553(a)(1), and indicated its belief that the sentence it imposed on Starnes was necessary to reflect the seriousness of those offenses, id. § 3553(a)(2)(A), to promote respect for the law, id., and to deter others from committing similar crimes, id. § 3553(a)(2)(B). Given the "straightforward, conceptually simple arguments" both defendants made at sentencing, we believe that the District Court's statement of reasons in each case, "though brief, was legally sufficient." Rita, 551 U.S. at 356, 127 S.Ct. 2456; accord United States v. Stinson, 574 F.3d 244, 248 (3d Cir.2009); Tomko, 562 F.3d at 569.[12]

III. Conclusion
For the foregoing reasons, we will affirm the judgments of conviction and sentence entered against George and Starnes.
NOTES
[1]  The Environmental Protection Agency (EPA) differentiates between asbestos-containing materials that are "friable"  meaning materials that "contain[] more than 1 percent asbestos ... that, when dry, can be crumbled, pulverized, or reduced to powder by hand pressure"  and materials that are "nonfriable"  those that "contain[] more than 1 percent asbestos ... that, when dry, cannot be crumbled, pulverized, or reduced to powder by hand pressure." 40 C.F.R. § 61.141. Friable asbestos-containing material and certain categories of nonfriable asbestos-containing material that has become friable or is likely to become friable are considered "[r]egulated asbestos-containing material." Id.
[2]  Each count of the indictment also charged both defendants with aiding and abetting in the commission of the underlying substantive offense. See 18 U.S.C. § 2.
[3]  As we understand it, the pump pulls air through the filter cassette, collecting an air sample, and the cassette is then removed and sent to a lab for analysis within twenty-four hours of collection.
[4]  George does not challenge the sufficiency of the evidence underpinning his conviction on the Clean Air Act counts.
[5]  Because we conclude that there was sufficient evidence to sustain Starnes's convictions on Counts One through Three as a principal, we need not address his contention that the evidence was insufficient to sustain his convictions on the same counts as an aider and abettor. See Griffin v. United States, 502 U.S. 46, 56-57, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991); cf. United States v. Frorup, 963 F.2d 41, 44 (3d Cir.1992) ("Inasmuch as the evidence was sufficient for us to uphold the verdict based on the theory of aiding and abetting, we need not [evaluate the evidence under the alternate theory presented]."); cf. also United States v. Hodge, 211 F.3d 74, 77 (3d Cir.2000) (explaining that 18 U.S.C. § 2 "take[s] the view that an aider and abettor should be treated like any other principal"). In any event, the record contains sufficient evidence to sustain Starnes's convictions on these counts under an aider and abettor theory as well.
[6]  18 U.S.C. § 1001(a) provides, in pertinent part:

"Except as otherwise provided in this section, whoever, in any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States, knowingly and willfully 
...
(2) makes any materially false, fictitious, or fraudulent statement or representation; or
(3) makes or uses any false writing or document knowing the same to contain any materially false, fictitious, or fraudulent statement or entry;
shall be fined under this title, imprisoned not more than 5 years or ... both."
[7]  As we have previously observed, the interpretive difficulties posed by the word "willfully" are well-illustrated by a notable exchange that took place between Judge Learned Hand and Herbert Wechsler, the Reporter for the Model Penal Code, during which Judge Hand made plain his feelings on the utility of the term: "`[Wilfully is] a very dreadful word.... It's an awful word! It is one of the most troublesome words in a statute that I know. If I were to have the index purged, `wilful' would lead all the rest in spite of its being at the end of the alphabet.'" United States v. Hayden, 64 F.3d 126, 129 n. 5 (3d Cir.1995) (quoting ALI Proceedings 160 (1955), quoted in Model Penal Code and Commentaries § 2.02, at 249 n. 47 (Official Draft and Revised Comments 1985)); cf. Rex Wine Corp. v. Dunigan, 224 F.2d 93, 95 (2d Cir.1955) (Hand, J.) (noting of the word "willful" that "[i]t must be owned that about that adjective there always gathers an unhappy cloud of uncertainty"). We could not agree more.
[8]  We note that this interpretation of § 1001(a)'s "knowingly and willfully" requirement is consistent with cases holding that the government need not prove that a defendant knew that the false statement or representation was within the jurisdiction of the federal government. See United States v. Yermian, 468 U.S. 63, 75, 104 S.Ct. 2936, 82 L.Ed.2d 53 (1984); United States v. Leo, 941 F.2d 181, 190 (3d Cir.1991); see also United States v. Curran, 20 F.3d 560, 567 (3d Cir. 1994) ("[A § 1001] defendant need not be aware of the jurisdictional fact that the false statement or concealment is within the statutory authority of a specific government agency."); cf. United States v. Gumbs, 283 F.3d 128, 131 (3d Cir.2002) ("[T]he Supreme Court has held that a defendant generally need not be aware of the existence of a jurisdictional element to be guilty of a federal offense." (citing United States v. Feola, 420 U.S. 671, 672-73, 95 S.Ct. 1255, 43 L.Ed.2d 541 (1975) and Yermian, 468 U.S. at 75, 104 S.Ct. 2936)).
[9]  Insofar as George's brief could be read as contending that the evidence of his conduct was insufficient to satisfy § 1001(a)'s actus reus element because "the air-monitoring results were delivered by Starnes," we also reject that contention. The fax headers on the copies of the falsified reports seized by Agent Derx show that George faxed blank air-monitoring report forms to Starnes in Florida on January 25, 2001  the day after VIHA sent the noncompliance notice to George's attention  and that Starnes faxed the completed reports back to George approximately seventeen minutes later. Monique Farrell testified that the falsified air-monitoring reports were delivered to VIHA later that same day. A rational juror could infer from this evidence that George transmitted, or arranged for the transmission of, the falsified records to VIHA. And while Farrell also testified that she could not recall exactly who delivered the falsified reports to VIHA, that testimony does not, as George would have it, establish that he did not do so, and "[t]he evidence does not need to be inconsistent with every conclusion save that of guilt if it does establish a case from which the jury can find the defendant guilty beyond a reasonable doubt." Gov't of V.I. v. Williams, 739 F.2d 936, 940 (3d Cir.1984) (internal quotation marks omitted); see Holland v. United States, 348 U.S. 121, 140, 75 S.Ct. 127, 99 L.Ed. 150 (1954) ("Admittedly, circumstantial evidence may in some cases point to a wholly incorrect result. Yet this is equally true of testimonial evidence. In both instances, a jury is asked to weigh the chances that the evidence correctly points to guilt against the possibility of inaccuracy or ambiguous inference. In both, the jury must use its experience with people and events in weighing the probabilities. If the jury is convinced beyond a reasonable doubt, we can require no more."); United States v. Glantzman, 447 F.2d 199, 201 n. 9 (3d Cir.1971) ("To warrant a conviction on circumstantial evidence the facts and circumstances established by such evidence must be of such a character as to produce a moral certainty beyond a reasonable doubt, but need not be absolutely incompatible with innocence.").

Also, given our conclusion that the evidence was sufficient to sustain the defendants' convictions on the false-statement counts as principals, we need not address their contentions that the evidence was insufficient to prove the government's alternative theories of liability under 18 U.S.C. § 2. See Griffin, 502 U.S. at 56-57, 112 S.Ct. 466; Frorup, 963 F.2d at 44.
[10]  To the extent that Starnes's brief can be read to challenge the District Court's finding that he abused his position of trust, we conclude that the District Court did not clearly err in making that finding. Cf. United States v. Dullum, 560 F.3d 133, 140 (3d Cir.2009) (explaining that whether a defendant occupied a position of trust is a legal question that is reviewed de novo, but that whether a defendant abused a position of trust is a factual question that is reviewed for clear error (citing United States v. Hart, 273 F.3d 363, 376 (3d Cir.2001))).
[11]  The factors set forth in 18 U.S.C. § 3553(a) are:

(1) the nature and circumstances of the offense and the history and characteristics of the defendant;
(2) the need for the sentence imposed 
(A) to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense;
(B) to afford adequate deterrence to criminal conduct;
(C) to protect the public from further crimes of the defendant; and
(D) to provide the defendant with needed educational or vocational training, medical care, or other correctional treatment in the most effective manner;
(3) the kinds of sentences available;
(4) the kinds of sentence and the sentencing range established for 
(A) the applicable category of offense committed by the applicable category of defendant as set forth in the guidelines 
(i) issued by the Sentencing Commission..., subject to any amendments made to such guidelines by act of Congress ...; and
(ii) that, except as provided in section 3742(g), are in effect on the date the defendant is sentenced; ...
(5) any pertinent policy statement 
(A) issued by the Sentencing Commission..., subject to any amendments made to such policy statement by act of Congress...; and
(B) that, except as provided in section 3742(g), is in effect on the date the defendant is sentenced[;]
(6) the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct; and
(7) the need to provide restitution to any victims of the offense.
[12]  Starnes also argues that the District Court committed significant procedural error by "fail[ing] to elicit fully articulated objections following imposition of sentence," pointing to a supervisory rule announced by the Court of Appeals for the Eleventh Circuit in United States v. Jones, 899 F.2d 1097, 1102-03 (11th Cir.1990). But we have never adopted such a supervisory rule and, in light of our precedents, we doubt the propriety of doing so. See, e.g., United States v. Sevilla, 541 F.3d 226, 231 (3d Cir.2008) ("`[A]n objection to the reasonableness of the final sentence will be preserved if, during sentencing proceedings, the defendant properly raised a meritorious factual or legal issue relating to one or more of the factors enumerated in 18 U.S.C. § 3553(a).'" (quoting United States v. Grier, 475 F.3d 556, 571 & n. 11 (3d Cir.2007) (en banc))). In any event, we have no occasion here to evaluate the need for such a rule, because the record clearly indicates that the District Court afforded fair opportunity to Starnes's attorney to raise further objections at the conclusion of the sentencing hearing, but that he had none.

In addition, we note that neither George nor Starnes challenges the substantive reasonableness of his sentence, and we discern no substantive error related to either defendant's sentence.
