
529 F.3d 470 (2008)
UNITED STATES of America, Appellee,
v.
Herby LEGROS, Defendant-Appellant.
Docket No. 05-2828-cr.
United States Court of Appeals, Second Circuit.
Submitted: February 22, 2008.
Decided: June 17, 2008.
*472 Vivian Shevitz, South Salem, NY, for Appellant.
Roslynn R. Mauskopf, United States Attorney for the Eastern District of New York, Peter A. Norling, Jo Ann M. Navickas, Assistant United States Attorneys, Brooklyn, NY, for Appellee.
Before: JACOBS, Chief Judge, CALABRESI, and SACK, Circuit Judges.
SACK, Circuit Judge:
Defendant Herby Legros appeals from a judgment of conviction of the United States District Court for the Eastern District of New York (Joanna Seybert, Judge) sentencing him principally to a term of imprisonment of 120 months for being a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1). Legros appeals his sentence only. We conclude that it is procedurally "unreasonable" because the district court's findings of fact, as stated on the record, do not support a four-level enhancement under U.S.S.G. § 2K2.1(b)(6) for possessing a firearm in connection with another felony offense.[1] We therefore vacate the judgment and remand for resentencing. At resentencing, the district court may either recalculate the applicable Guidelines range without the enhancement or make additional factual findings that sufficiently support the enhancement. The judgment below is in all other respects affirmed.

BACKGROUND
On November 1, 2003, police responded to a series of "911" calls reporting multiple shots fired in the street of a residential area of West Babylon, Suffolk County, New York. Two police officers arrived on the scene almost immediately, spotted three men in the vicinity, and approached them. One of them (later identified as Legros) ran. One of the officers pursued him. During the chase, Legros tossed a handgun to the ground. He was arrested by the officer. The gun he discarded was later matched to spent shell casings and one expended bullet recovered from the scene of the reported gunshots.
Legros was indicted on one count of being a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1). Following a jury trial, he was convicted of the offense.
Prior to sentencing the United States Probation Office prepared a presentence investigation report ("PSR") calculating a sentencing range under the United States Sentencing Guidelines of 110 to 137 months. According to the PSR, the Probation Office arrived at that range by assessing a base offense level of 20, U.S.S.G. § 2K2.1(a)(4)(A); a two-level enhancement because the firearm was stolen, id. § 2K2.1(b)(4)(A); a four-level enhancement because the firearm was possessed in connection with another felony offense, id. § 2K2.1(b)(6); and a criminal history category of V. The maximum sentence permitted by statute, however, was 120 months, ten months above the bottom of the applicable Guidelines range. See 18 U.S.C. § 924(a)(2).
The four-level enhancement under U.S.S.G. § 2K2.1(b)(6) is central to this appeal. Without the enhancement, the applicable Guidelines range would have been 77 to 96 months.
According to the PSR, the enhancement was based on the assertion that Legros *473 had committed "aggravated assault" by shooting at one Christopher Passius in retaliation for Passius's testimony against two fellow gang members who had been convicted in state court of manslaughter for beating to death a member of a rival gang. The government argued that the enhancement was proper because Legros had "discharged the charged firearm at Christopher Passius in retaliation for what [Legros] believed was Passius's betrayal of fellow `Bloods' members through Passius's cooperation with Suffolk County law enforcement at trial." Letter from Special Assistant U.S. Attorney Sondra M. Mendelson to the district court dated Mar. 31, 2005, at 4.
Legros challenged the enhancement. He argued that there was no evidence that he was in a gang or that he had shot at Passius or anyone else.
At the sentencing hearing, the government introduced evidence intended to support the enhancement. The police had taken a statement of one Jermaine Bullock, who said he had seen Legros fire a weapon. Although Bullock himself did not testify,[2] Detective Christopher Loeffler, who had taken Bullock's statement, read Bullock's statement to the court. The district court found Bullock's hearsay statement reliable and admitted it. In relevant part, Loeffler said that Bullock told him:
When I was looking up the street, I saw a guy with a hood and I heard a few shots. At first I took cover, but then I tried to mediate the crisis between Chris and Herb. Herb was firing in the air. Police told me they found a bullet hole in Chris's car. I don't know how that got there.
Sentencing Transcript, May 20, 2005 ("Sentencing Tr."), at 38 (emphasis added).
At the conclusion of the hearing, the court imposed a term of imprisonment of 120 months, which was the maximum permitted by statute and within the range of 110 to 137 months recommended in the PSR based in part on the four-level enhancement. The court said that "there is proof adduced at th[e] hearing that the defendant was the individual who fired the gun in the air." Id. at 73. Noting also that the shooting occurred in a residential neighborhood, the court found that such conduct "amounts to reckless endangerment." Id. Alternatively, the court found that the enhancement was applicable on the basis relied upon in the PSR: that Legros had possessed the gun in the course of committing an aggravated assault.
Legros appeals.

DISCUSSION

I. Standard of Review
[T]he appellate court . . . must first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the [18 U.S.C.] § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence  including an explanation for any deviation from the Guidelines range. Assuming that the district court's sentencing decision is procedurally sound, the appellate court should then consider the substantive reasonableness of the sentence imposed. . . .
Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 597, 169 L.Ed.2d 445 (2007). We review sentences for reasonableness *474 under an abuse-of-discretion standard. United States v. Cutler, 520 F.3d 136, 156 (2d Cir.2008). The abuse-of-discretion standard incorporates de novo review of questions of law (including interpretation of the Guidelines) and clear-error review of questions of fact. Cutler, 520 F.3d at 157; see also United States v. Richardson, 521 F.3d 149, 156 (2d Cir.2008).

II. Enhancement Under U.S.S.G. § 2K2.1(b)(6)
Legros argues that there is insufficient evidence to support a four-level enhancement on the ground that he "used or possessed any firearm . . . in connection with another felony offense." U.S.S.G. § 2K2.1(b)(6). According to the applicable Guidelines' commentary, this enhancement applies "if the firearm . . . facilitated, or had the potential of facilitating, another felony offense." U.S.S.G. § 2K2.1 application note 14(A). The commentary defines "another felony offense" as "any [f]ederal, state, or local offense," other than the offense of conviction, "punishable by imprisonment for a term exceeding one year, regardless of whether the criminal charge was brought, or a conviction obtained." Id., application note 14(C).
The government bears the burden of proving by a preponderance of the evidence that the defendant committed another felony offense. United States v. Spurgeon, 117 F.3d 641, 643 (2d Cir.1997) (per curiam). Each element of the underlying felony offense must be established. See United States v. Betts, 509 F.3d 441, 445 (8th Cir.2007). Although we do not require that the district court state each element on the record and declare it proved by a preponderance of the evidence, like other "facts disputed in connection with sentencing, the [district] court is required to make findings sufficient to permit appellate review." United States v. Thompson, 76 F.3d 442, 456 (2d Cir.1996).

A. Reckless Endangerment
We begin with the district court's finding that Legros's possession of the gun was in connection with his commission of the crime of reckless endangerment. In New York, there are two degrees of reckless endangerment. "A person is guilty of reckless endangerment in the second degree," a misdemeanor, "when he recklessly engages in conduct which creates a substantial risk of serious physical injury to another person." N.Y. Penal Law § 120.20. "A person is guilty of reckless endangerment in the first degree," a felony, "when, under circumstances evincing a depraved indifference to human life, he recklessly engages in conduct which creates a grave risk of death to another person." Id. § 120.25. Under New York law, depraved indifference to human life is a "culpable mental state." People v. Feingold, 7 N.Y.3d 288, 294, 819 N.Y.S.2d 691, 695, 852 N.E.2d 1163, 1167 (2006).
Reflecting wickedness, evil or inhumanity, as manifested by brutal, heinous and despicable acts, depraved indifference is embodied in conduct that is so wanton, so deficient in a moral sense of concern, so devoid of regard of the life or lives of others, and so blameworthy as to render the actor as culpable as one whose conscious objective is to kill. Quintessential examples are firing into a crowd; driving an automobile along a crowded sidewalk at high speed; opening the lion's cage at the zoo; placing a time bomb in a public place; poisoning a well from which people are accustomed to draw water; opening a drawbridge as a train is about to pass over it and dropping stones from an overpass onto a busy highway.
People v. Suarez, 6 N.Y.3d 202, 214, 811 N.Y.S.2d 267, 276, 844 N.E.2d 721, 730 *475 (2005) (per curiam) (internal quotation marks, citations, and footnote omitted).
For a defendant to be subject to the four-level enhancement under U.S.S.G. § 2K2.1(b)(6), he must have possessed a firearm in connection with another felony offense. In this case, then, it would have been insufficient support for the enhancement for the district court to find that Legros recklessly engaged in conduct creating a substantial risk of serious physical injury to another person, because that would support only second-degree reckless endangerment, a misdemeanor. An enhancement for reckless endangerment could be imposed only if the district court properly found that his conduct created a "grave risk of death" and that he acted with a mens rea of "depraved indifference to human life." See N.Y. Penal Law § 120.25.
In explaining its decision to impose the four-level enhancement, the district court made no mention of a "grave risk" or "depraved indifference." The court said:
[T]here is proof adduced at th[e] hearing that the defendant was the individual who fired the gun in the air. That amounts to reckless endangerment. The court heard testimony with respect to the fact that it was a neighborhood. And the statement is confirmed by the admission of Germaine [sic] Bullock's statement into evidence.
Sentencing Tr. at 73. There was sufficient evidence to support the district court's finding that, in the course of the incident in question, Legros fired the gun in the air, as described by Bullock, and that he did so in a residential area. But these facts, standing alone, are not sufficient to support a finding of felony reckless endangerment. See People v. Davis, 72 N.Y.2d 32, 36-37, 530 N.Y.S.2d 529, 531, 526 N.E.2d 20, 22 (1988) (shooting pistol into the air does not constitute reckless endangerment in the first degree) (citing People v. Richardson, 97 A.D.2d 693, 694, 468 N.Y.S.2d 114, 115 (1st Dep't 1983)). Shooting a gun into the air in a residential area is of course risky. But nothing in the record indicates that the district court found such conduct created a "grave risk of death" and that Legros acted with a mens rea of "depraved indifference to human life." See N.Y. Penal Law § 120.25.
We need not decide whether there is evidence in the record to support such findings. Without a further explanation from the district court, we cannot affirm its judgment in this respect on this ground. See United States v. Sindima, 488 F.3d 81, 88 (2d Cir.2007); United States v. Dupre, 462 F.3d 131, 146 (2d Cir.2006), cert. denied, ___ U.S. ___, 127 S.Ct. 1026, 166 L.Ed.2d 773 (2007).[3]

B. Aggravated Assault
The district court's decision as to the propriety of the enhancement was also based on the alternative theory that the "[ ]other felony" in connection with which Legros possessed the gun was an aggravated assault. Although there is no crime of "aggravated assault" in New York, Legros would be guilty of attempted assault in the first degree, a felony, if, as alleged by the government and in the PSR, Legros fired one or more shots at Passius.[4] "A *476 person is guilty of assault in the first degree when . . . [w]ith intent to cause serious physical injury to another person, he causes such injury to such person or to a third person by means of a deadly weapon or a dangerous instrument." N.Y. Penal Law § 120.10(1). "A person is guilty of an attempt to commit a crime when, with intent to commit a crime, he engages in conduct which tends to effect the commission of such crime." Id. § 110.00.
As was the case with respect to the court's treatment of reckless endangerment, the court did not mention the essential elements of the offense or identify facts in the record that satisfied them. The court said:
The last basis that the court finds the enhancement is applicable is with respect to the aggravated assault. The temporal connection is strong in terms of the defendant's apprehension and the events preceding his arrest. There is sufficient circumstantial evidence that the defendant was wearing a black-hooded sweatshirt, and that also is confirmed as the defendant being the shooter when we have the statement of Mr. Bullock which has been admitted and thoroughly corroborates the circumstances involved in this case.
Sentencing Tr. at 73. Indeed, as was the case with the reckless endangerment theory, the evidence was sufficient to support a finding that Legros was "the shooter." But the district court identified no facts to support a finding that Legros intended to cause serious injury or engaged in conduct which tends to effect such injury. Shooting a gun "in the air," as Legros's conduct was described by the only eyewitness statement introduced at sentencing, is insufficient to support a finding of attempted first-degree assault. See People v. Leonardo, 89 A.D.2d 214, 215-16, 455 N.Y.S.2d 434, 435-36 (4th Dep't 1982) (finding evidence insufficient to support intent to cause serious physical injury where defendant aims gun at tree), aff'd, 60 N.Y.2d 683, 455 N.E.2d 1261, 468 N.Y.S.2d 466 (1983); see also United States v. Pimentel, 346 F.3d 285, 298 (2d Cir.2003) (stating that under New York law of attempts, defendant must engage in conduct that comes "dangerously near" commission of the completed crime, and that "[i]n the context of attempted murder prosecutions . . . the Government must establish that the defendant pointed a weapon at a victim and was about to kill him with it" (emphasis added)), cert. denied, 543 U.S. 955, 125 S.Ct. 451, 160 L.Ed.2d 316 (2004). In enhancing Legros's sentence on the basis of aggravated assault, the district court did not explain what evidence it relied upon in finding, if it did so find, that Legros aimed and shot at Passius.[5]
We cannot say that there is insufficient evidence to support the enhancement on this basis. The record on appeal does not include a full transcript of Legros's trial, and the district court is, of course, more familiar with the facts of and proceedings in this case than are we. But, as with the reckless endangerment theory, we are unable to affirm a finding of felony assault without a more detailed explanation by the district court identifying the facts in the record that would support such a finding. See United States v. Carter, 489 F.3d 528, 540 (2d Cir.2007), cert. denied, ___ U.S. ___, 128 S.Ct. 1066, 169 L.Ed.2d 814 *477 (2008). We therefore vacate the judgment and remand for resentencing.[6]

III. Remaining Arguments
Legros makes several other arguments challenging his sentence. We find them to be without merit.
First, Legros argues that under the Fifth and Sixth Amendments his sentence cannot be enhanced under U.S.S.G. § 2K2.1(b)(6) based on his commission of a separate felony offense unless the elements of that offense are proved to a jury beyond a reasonable doubt. We recently rejected that argument. In United States v. Martinez, 525 F.3d 211, 214-15 (2d Cir. 2008) (per curiam), we adopted the Third Circuit's holding in United States v. Grier, 475 F.3d 556 (3d Cir.) (en banc), cert. denied, ___ U.S. ___, 128 S.Ct. 106, 169 L.Ed.2d 77 (2007): "Facts relevant to application of the Guidelines  whether or not they constitute a `separate offense'  do not. . . constitute `elements' of a `crime' under the rationale of [Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000),] and do not implicate the rights to a jury trial and proof beyond a reasonable doubt." Id. at 567-68.
Second, Legros argues that the district court was "swayed" in its sentencing decision by evidence that he says was improperly admitted: that he was a member of a gang. Appellant's Br. at 23. We need not decide whether any such evidence was improperly admitted because the district judge explicitly stated in the course of the sentencing that she made no finding as to whether Legros's conduct was gang-related.
Legros also argues that Bullock's statement, read into the record by Detective Loeffler, is unreliable. Although Bullock did not personally testify, hearsay testimony is permitted in sentencing hearings and the district court did not abuse its discretion in finding the hearsay reliable. See United States v. Martinez, 413 F.3d 239, 242-44 (2d Cir.2005), cert. denied, 546 U.S. 1117, 126 S.Ct. 1086, 163 L.Ed.2d 902 (2006).
Finally, Legros argues that the district court failed to consider the sentencing factors enumerated in 18 U.S.C. § 3553(a) and failed to treat the Guidelines as advisory. Although the district judge asked for argument on where within the Guidelines range she should sentence Legros, she also invited counsel to make any argument she should consider after reviewing the Guidelines range. In fact, the district judge specifically discussed the section 3553(a) factors, stated that she had considered them all, and stated *478 that the sentence was not imposed "as a result simply of the guidelines." Sentencing Tr. at 80. "[W]e presume, in the absence of record evidence suggesting otherwise, that a sentencing judge has faithfully discharged her duty to consider the statutory factors." United States v. Fernandez, 443 F.3d 19, 30 (2d Cir.), cert. denied, ___ U.S. ___, 127 S.Ct. 192, 166 L.Ed.2d 143 (2006). Overall, the record in this case reflects that the district court considered the section 3553(a) factors and did not consider itself bound by the Guidelines range. See United States v. Brown, 514 F.3d 256, 270 (2d Cir.2008).

CONCLUSION
For the foregoing reasons, the judgment of the district court is vacated and the case remanded to the district court for further proceedings.
NOTES
[1]  Although the relevant enhancement was U.S.S.G. § 2K2.1(b)(5) at the time Legros was sentenced, subsection (b)(5) was subsequently renumbered (b)(6) without substantive change. See U.S.S.G. Supp. to App. C, amend. 691 (eff. Nov. 1, 2006). Throughout this opinion we cite to the enhancement as U.S.S.G. § 2K2.1 (b)(6).
[2]  Another police detective testified that after a diligent search, he was unable to locate Bullock to subpoena him for the sentencing hearing.
[3]  The government argues that the plain-error standard of review applies because Legros did not object to the district court's reckless endangerment finding. See Fed.R.Crim.P. 52(b). While Legros did not use the terms "grave risk" and "depraved indifference," we think that his argument to the district court challenging the propriety of imposing the enhancement based on the theory that the other felony was the crime of reckless endangerment was sufficient to raise the issue.
[4]  According to the PSR, no one was injured as a result of Legros's conduct.
[5]  Although a police officer testified that an expended bullet matched to Legros's gun was found within a vehicle parked in the vicinity of the shooting, and Bullock said that the police told him they found a bullet hole in Passius's car, the record on appeal does not indicate whether Passius was in or near the car when the gun was discharged.
[6]  Upon review of the record, we find a possible third basis that the district court may have relied on for the section 2K2.1(b)(6) enhancement: criminal possession of stolen property. See N.Y. Penal Law § 165.45(4). Neither the defendant nor the government raised an argument to challenge or defend the enhancement on that basis. The district court, however, made no finding that Legros knew the firearm was stolen, an essential element of felony possession of stolen property under New York law. See Krause v. Bennett, 887 F.2d 362, 370 (2d Cir. 1989). Because the PSR states that the weapon had been stolen nearly a decade before the offense of conviction, the district court could not, without more, infer Legros's knowledge from the fact of his unlawful possession. See People v. Davis, 163 A.D.2d 826, 827, 558 N.Y.S.2d 358, 360 (4th Dep't) (mem.), appeal denied, 76 N.Y.2d 939, 564 N.E.2d 678, 563 N.Y.S.2d 68 (1990); People v. Sturgis, 122 A.D.2d 535, 535, 504 N.Y.S.2d 899, 899 (4th Dep't 1986) (mem.), aff'd, 69 N.Y.2d 816, 506 N.E.2d 532, 513 N.Y.S.2d 961 (1987). As was the case with the other two possible grounds for a felony offense enhancement, we are unable to affirm a finding of felony possession of stolen property without a fuller explanation from the district court identifying the record evidence to support such a finding.
