
656 F.3d 147 (2011)
UNITED STATES of America, Appellee,
v.
Gerald AUMAIS, Defendant-Appellant.
Docket No. 10-3160-cr.
United States Court of Appeals, Second Circuit.
Argued: June 15, 2011.
Decided: September 8, 2011.
*148 Gene V. Primomo, Assistant Federal Public Defender (Molly Corbett, on the brief), for Lisa Peebles, Federal Public Defender, Albany, New York, for Defendant-Appellant.
Paul D. Silver, Assistant United States Attorney (Elizabeth Horsman, Assistant United States Attorney, on the brief), for Richard S. Hartunian, United States Attorney for the Northern District of New York, for Appellee.
Before: JACOBS, Chief Judge, WINTER and McLAUGHLIN, Circuit Judges.
DENNIS JACOBS, Chief Judge:
Gerald Aumais ("Aumais") appeals from an Amended Judgment of Conviction entered on August 3, 2010 in the United States District Court for the Northern District of New York (Sharpe, J.). Aumais pleaded guilty to transporting and possessing child pornography in violation of 18 U.S.C. § 2252A(a)(1), and (a)(5)(B). The district court sentenced Aumais to 121 months' imprisonment and ordered him, pursuant to 18 U.S.C. § 2259, to pay $48,483 in restitution to finance future counseling costs of "Amy" (a pseudonym), one of the victims depicted in the images and videos. Aumais challenges the restitution order on the ground that his possession was not a proximate cause of Amy's loss. Aumais also argues that the district court committed procedural and substantive error in sentencing him to 121 months' imprisonment. We conclude that: based on the facts in this case, Aumais' possession of Amy's images was not a substantial factor in causing her loss; and that the *149 district court committed no procedural or substantive error in imposing the sentence of imprisonment. Affirmed in part and reversed in part.

Background
Aumais attempted to enter the United States from Canada at the Fort Covington, New York Port of Entry in November 2008, where he was referred for secondary inspection. A search of his car revealed a cache of DVDs and other electronic devices that stored thousands of still images of child pornography and over one hundred such videos. Aumais told border agents that he owned all of the electronic media located in the car and admitted to downloading the child pornography from a peer-to-peer network.
He was charged with: (1) transporting child pornography in foreign commerce, in violation of 18 U.S.C. § 2252A(a)(1); and (2) possessing child pornography that had been transported in foreign commerce, in violation of 18 U.S.C. § 2252A(a)(5)(B). On February 4, 2009, Aumais entered a plea of guilty, without a written plea agreement, to both counts of the indictment.

A.
Aumais' Presentence Investigation Report ("PSR") reflected a base offense level of 22.[1] The offense level was increased two levels because some of the images were of pre-pubescent minors, see U.S.S.G. § 2G2.2(b)(2); four levels because the material contained sadistic images, see U.S.S.G. § 2G2.2(b)(4); two levels because the offense involved use of a computer, see U.S.S.G. § 2G2.2(b)(6); and five levels based upon the number of images in Aumais' possession, see U.S.S.G. § 2G2.2 (b)(7)(D). Aumais' offense level was reduced three levels for his early acceptance of responsibility, see U.S.S.G. § 3E1.1(a)(b). With a total offense level of thirty-two and a Criminal History Category of I, the recommended Guidelines range was 121 to 151 months' imprisonment.
The PSR identified a victim known as "Amy," who sought $3.3 million in restitution pursuant to 18 U.S.C. § 2259. Her Victim Impact Statement explained that she was unable to forget the abuse she suffered at the hands of the uncle (who took the pictures) because the "disgusting images of what he did to [her] are still out there on the internet." She said she lives in fear that she will be recognized in the pictures that remain on the internet and will be "humiliated all over again."
The district court found that Aumais was a pedophile, that he presented a danger to children (although the court credited a polygraph result indicating that he had never gone beyond viewing images), and that he was responsible for harm caused to the children in the images. The district court found that a sentence of 121-months' imprisonment (the low-end of the Guidelines range) was appropriate in view of all the 18 U.S.C. § 3553(a) factors. Accordingly, the district court imposed a sentence of 121 months' imprisonment on *150 Count 1 and 120-months' imprisonment on Count 2, to run concurrently, and a five-year term of supervised release. The district court bifurcated the issue of restitution and referred the matter to a magistrate judge for consideration.

B.
On December 22, 2009, Magistrate Judge David Homer conducted an evidentiary hearing on restitution. The only witness to testify, Government witness Dr. Joyanna Silberg, had evaluated Amy at the request of Amy's attorney, James Marsh, on June 11-12, 2008, July 29, 2008, and November 10, 2008. Dr. Silberg recounted that Amy had been sexually abused by her uncle between the ages of 4 and about 7 or 8, that Amy underwent treatment after suffering the abuse, and that the treatment allowed Amy to "function[] pretty well normally" until she learned that her image was being traded on the internet, after which she experienced a fear "of being at parties, fear of being in public gatherings," and had difficulty coping "with her life because of her sense of pervasive helplessness" about the fact that people were viewing her image. Government Appendix 30-31.
Amy discovered that her images were on the internet when she received victim notifications from The National Center for Missing and Exploited Children ("NCMEC"), which compares images of child pornography, identifies those depicted within, and then notifies the victim every time someone is arrested who is found to possess that victim's image. Knowledge that her images were still being viewed caused emotional and psychological problems: she bit her nails to the point of bleeding, took to alcohol, and could not finish college. Dr. Silberg concluded that Amy was a direct victim of Aumais' conduct and that "Mr. Aumais represent[ed] one component of the damages, because Mr. Aumais is one of the individuals arrested for having looked at her picture and possessing it." See Government Appendix 41-43.
Finally, although Dr. Silberg's contact with Amy was evaluative rather than therapeutic, she recommended that Amy receive therapy once a week from a professional trained in the effects of sexual abuse and trauma on people in Amy's age group. Dr. Silberg opined that Amy might need three courses of inpatient treatment throughout her life to deal with her alcoholism.
On January 13, 2010, the magistrate judge issued a Report and Recommendation that Aumais should be ordered to pay Amy $48,483 in restitution. United States v. Aumais, No. 08-CR-711, 2010 WL 3033821, at *9 (N.D.N.Y. Jan. 13, 2010) ("Aumais I"). The court determined that in order to recover restitution, Amy must show that Aumais' possession of her images proximately caused her harm. Id. at *2. If so, Amy could be entitled to payments for future medical costs "if those expenses can be reasonably estimated." Id. at *3 (citing United States v. Pearson, 570 F.3d 480, 486-87 (2d Cir.2009) (per curiam)). The magistrate judge observed, however, that the issue of "whether a defendant convicted only as a consumer of child pornography may be liable for restitution under § 2259 to a child victim" remained "unaddressed by the Second Circuit." Id.
According to the Report and Recommendation, "[t]here is no question that consumers, such as Aumais, contribute to the exploitation of child victims, such as Amy, depicted in the child pornography they possess." Id. at *4. The court recognized that "the uncle's horrific acts of sexual abuse, production of the images, and distribution of those images to others unquestionably constituted the principal cause of the losses identified by Amy." Id. *151 at *5. At the same time (it was concluded), "if the harm caused by Aumais' possession of Amy's images caused substantial harm to Amy, proximate cause has been demonstrated even if the conduct of others similar to that of Aumais caused equal or greater harm." Id.
Based on Amy's Victim Impact Statement and Dr. Silberg's testimony, the magistrate judge found that, although Amy had neither contact with Aumais nor knowledge of his existence, his possession of her images exacerbated the harm (originally caused by her uncle) by creating a market for distribution, and by inflicting the humiliation of knowing that the images are out there being exploited by a group of consumers, of whom Aumais was one. Id. at *6. Although Aumais may be among hundreds or thousands of such others, it was found that Amy's harm was not thereby obviated or diminished; rather, "it exacerbate[d] the harm by confirming how expansive has become the number of individuals exploiting Amy's images." Id.
The findings as to damages are thorough and discriminating, as follows. Where "a party is responsible for exacerbating a pre-existing condition, damages are generally limited to that attributable to the exacerbation and not the original injury." Id. at *7. The Government failed to prove by a preponderance of evidence that Aumais proximately caused harm that resulted in Amy's difficulties maintaining employment. Id. But the Government did prove by a preponderance of evidence that Aumais caused the need for weekly counseling sessions in the next five years and monthly counseling sessions for five years thereafter. Id. at *8-9. Discounting future counseling costs to present value, the magistrate judge found that the Government proved by a preponderance of evidence that Amy is entitled to $48,483. Id. at *9.
As to joint and several liability, the magistrate judge found that Aumais should be liable for the full amount and that it was "a matter for administration by the government" to prevent excess recovery. Id.
The district court adopted Magistrate Judge Homer's Report and Recommendation, and entered judgment on August 3, 2010. United States v. Aumais, No. 08-CR-711, 2010 WL 3034730 (N.D.N.Y. Aug. 3, 2010) ("Aumais II").

Discussion
"We review an order of restitution `deferentially, and we will reverse only for abuse of discretion. To identify such abuse, we must conclude that a challenged ruling rests on an error of law, a clearly erroneous finding of fact, or otherwise cannot be located within the range of permissible decisions.'" Pearson, 570 F.3d at 486 (quoting United States v. Boccagna, 450 F.3d 107, 113 (2d Cir.2006)).
We review a district court's sentencing decision for reasonableness. See United States v. Booker, 543 U.S. 220, 260-62, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). We review the sentence for substantive reasonableness under a "deferential abuse-of-discretion standard." United States v. Cavera, 550 F.3d 180, 189 (2d Cir.2008) (en banc). The Court "will not substitute [its] own judgment for the district court's"; rather, a district court's sentence may be set aside "only in exceptional cases where [its] decision cannot be located within the range of permissible decisions." Id. (internal quotation marks omitted).

I.
As Magistrate Judge Homer observed, this Circuit has yet to address the issue of "whether a defendant convicted only as a consumer of child pornography may be *152 liable for restitution under [18 U.S.C.] § 2259 to a child victim."[2]Aumais I, 2010 WL 3033821, at *3.
Section 2259 mandates a district court to order a defendant to pay a "victim," defined as an "individual harmed as a result of a commission of a crime under this chapter," 18 U.S.C. § 2259(c), "the full amount of the victim's losses," id. § 2259(b)(1). The victim's losses include:
any costs incurred by the victim for 
(A) medical services relating to physical, psychiatric, or psychological care;
(B) physical and occupational therapy or rehabilitation;
(C) necessary transportation, temporary housing, and child care expenses;
(D) lost income;
(E) attorneys' fees, as well as other costs incurred; and
(F) any other losses suffered by the victim as a proximate result of the offense.
Id. § 2259(b)(3)(A)-(F). "An order of restitution under [§ 2259] shall be issued and enforced in accordance with section 3664 in the same manner as an order under section 3663A." Id. § 2259(b)(2). Under 18 U.S.C. § 3664(e), "[t]he burden of demonstrating the amount of the loss sustained by a victim as a result of the offense shall be on ... the Government." So it was for the Government to establish that Amy is a victim who was harmed as a result of Aumais' possession of her images.

A.
The United States Supreme Court has recognized that the distribution of child pornography is "intrinsically related to the sexual abuse of children" because, inter alia, "the materials produced are a permanent record of the children's participation and the harm to the child is exacerbated by their circulation." New York v. Ferber, 458 U.S. 747, 759, 102 S.Ct. 3348, 73 L.Ed.2d 1113 (1982); see also United States v. McDaniel, 631 F.3d 1204, 1208 (11th Cir.2011). "Because the child's actions are reduced to a recording, the pornography may haunt [the child] in future years, long after the original misdeed took place." Ferber, 458 U.S. at 759 n. 10, 102 S.Ct. 3348 (internal quotation marks omitted).
We conclude that Amy is a victim as defined by § 2259(c).

B.
A circuit split has opened as to whether the Government must show that a victim's losses (identified in 18 U.S.C. § 2259(b)(3)(A)-(F)) were proximately caused by the defendant's actions, or whether it is enough to show causation more generally. And within those circuits holding that a showing of proximate cause is required, some rely on the text of the statute and others on general rules of criminal and tort law.
Of the circuits that have reached the causation issue, most have held that the text of § 2259 requires a showing of proximate cause. See McDaniel, 631 F.3d at 1209; United States v. Laney, 189 F.3d 954, 965 (9th Cir.1999); United States v. Crandon, 173 F.3d 122, 125 (3d Cir.1999). These circuits have read the last phrase of § 2259(b)(3)(F) (see supra at 152)  "suffered by the victim as a proximate result of the offense"  to apply to all the types of loss in § 2259(b)(3). As the court in McDaniel observed:
"When several words are followed by a clause which is applicable as much to *153 the first and other words as to the last, the natural construction of the language demands that the clause be read as applicable to all." Porto Rico Ry., Light & Power Co. v. Mor, 253 U.S. 345, 348, 40 S.Ct. 516, 64 L.Ed. 944 (1920). The phrase "as a proximate result of the offense" is equally applicable to medical costs, lost income, and attorneys' fees as it is to "any other losses." Because the language of the statute is plain, our inquiry ends here.
631 F.3d at 1209 (internal citation omitted). The D.C. Circuit, likewise holding that § 2259 requires a finding of proximate cause, based its ruling on "traditional principles of tort and criminal law and on § 2259(c)'s definition of `victim' as an individual harmed `as a result' of the defendant's offense." United States v. Monzel, 641 F.3d 528, 535 (D.C.Cir.2011). After reciting the "bedrock rule of both tort and criminal law that a defendant is only liable for harms he proximately caused," the court concluded that "nothing in the text or structure of § 2259 leads us to conclude that Congress intended to negate the ordinary requirement of proximate cause." Id. at 535-36 (footnote omitted).
The only circuit to hold that a finding of proximate cause is not required, the Fifth Circuit, read the phrase "as a proximate result of the offense" in § 2259(b)(3)(F) to apply only to that "catchall" provision, as opposed to all of the loss provisions set forth in § 2259(b)(3):
The structure and language of § 2259(b)(3) impose a proximate causation requirement only on miscellaneous "other losses" for which a victim seeks restitution. As a general proposition, it makes sense that Congress would impose an additional restriction on the catchall category of "other losses" that does not apply to the defined categories. By construction, Congress knew the kinds of expenses necessary for restitution under subsections A through E; equally definitionally, it could not anticipate what victims would propose under the open-ended subsection F.
In re Amy Unknown, 636 F.3d 190, 198 (5th Cir.2011). The Fifth Circuit also relied on the manifestation of a "congressional purpose to award broad restitution" to justify its limitation of proximate cause only to the loss identified in subsection F. Id. at 199.
We agree with the majority of circuits and hold that under § 2259, a victim's losses must be proximately caused by the defendant's offense. We endorse the D.C. Circuit's reasoning in Monzel: proximate cause is a deeply rooted principle in both tort and criminal law that Congress did not abrogate when it drafted § 2259. See Monzel, 641 F.3d at 535-36; United States v. U.S. Gypsum Co., 438 U.S. 422, 437, 98 S.Ct. 2864, 57 L.Ed.2d 854 (1978) ("Congress [is] presumed to have legislated against the background of our traditional legal concepts which render [proximate cause] a critical factor, and absence of contrary direction" here "[is] taken as satisfaction [of] widely accepted definitions, not as a departure from them." (quoting Morissette v. United States, 342 U.S. 246, 263, 72 S.Ct. 240, 96 L.Ed. 288 (1952)) (internal quotation marks omitted)); see also Hemi Group, LLC v. City of New York, ___ U.S. ___, 130 S.Ct. 983, 989, 175 L.Ed.2d 943 (2010) ("[P]roximate cause thus requires `some direct relation between the injury asserted and the injurious conduct alleged.'" (quoting Holmes v. Sec. Investor Prot. Corp., 503 U.S. 258, 268, 112 S.Ct. 1311, 117 L.Ed.2d 532 (1992))). The text of § 2259 cross-references the Victim and Witness Protection Act of 1982, 18 U.S.C. §§ 1512-1515, 3663-3664, and the Mandatory Victims Restitution Act of 1996 ("MVRA"), 18 U.S.C. §§ 3663A, 3613A, both of which define "victim" as "a person directly and proximately *154 harmed as a result of the commission of an offense for which restitution may be ordered," §§ 3663(a)(2), 3663A(a)(2).
"Proximate cause" labels "generically the judicial tools used to limit a person's responsibility for the consequences of that person's own acts. At bottom, the notion of proximate cause reflects `ideas of what justice demands, or of what is administratively possible and convenient.'" Holmes, 503 U.S. at 268, 112 S.Ct. 1311 (quoting W. Keeton, D. Dobbs, R. Keeton, & D. Owen, Prosser and Keeton on Law of Torts § 41, at 264 (5th ed. 1984)). Proximate cause demands "some direct relation between the injury asserted and the injurious conduct alleged." Id.
The magistrate judge based his finding of proximate cause on the following facts, taken from Amy's Victim Impact Statement and Dr. Silberg's testimony: Amy "suffered understandable trauma from the abuse of her uncle ... [and t]he fact that the images of that abuse exist and remain in circulation exacerbates the harm"; the viewers of Amy's images contribute to the "humiliation and degradation" that Amy suffers and "constitute an independent component of harm which exacerbates the trauma initiated by the uncle and generates a need for continuing therapy"; Amy's abuse was memorialized in pictures that continue to be circulated, so that she "can never regard [her] victimization as terminated or as a past event to which [she] must adjust"; and Aumais' viewing of Amy's images "leaves Amy and similar victims with feelings that they will never be safe, of helplessness, and of constant fear that they will be recognized from those images by friends and strangers." Aumais I, 2010 WL 3033821, at *6. Moreover, the magistrate judge found that "even though there may be hundreds or thousands of others who, like Aumais, have possessed and used Amy's images and thereby contributed to her harm, Aumais' conduct remains a substantial cause of that harm" because it "exacerbates the harm by confirming how expansive has become the number of individuals exploiting Amy's images." Id.
We review a district court's findings of fact for clear error, but we review de novo a "district court's application of th[e] facts to draw conclusions of law, including a finding of liability." Travellers Int'l, A.G. v. Trans World Airlines, 41 F.3d 1570, 1575 (2d Cir.1994). So called mixed questions of law and fact are also reviewed de novo. Id. While the magistrate judge's findings of fact are supported by evidence, we disagree that those facts establish a causal connection between Aumais' possession of Amy's images and Amy's losses.
The magistrate judge found that "Amy had no direct contact with Aumais nor even knew of his existence." Aumais I, 2010 WL 3033821, at *6. Amy's Victim Impact Statement makes no mention of Aumais (or any other possessor of her images for that matter). Moreover, Dr. Silberg's evaluation of Amy, upon which the doctor's testimony was based, took place on June 11-12, 2008, July 29, 2008, and November 10, 2008, whereas Aumais was not arrested at the border until November 16, 2008. While Dr. Silberg may describe generally what Amy suffers from knowing that people possess her images, Dr. Silberg cannot speak to the impact on Amy caused by this defendant. As the Ninth Circuit held in rejecting another of Amy's claims:
[T]he government's evidence showed only that [the defendant] participated in the audience of persons who viewed the images of Amy.... While this may be sufficient to establish that [the defendant's] actions were one cause of the generalized harm Amy ... suffered due *155 to the circulation of [her] images on the internet, it is not sufficient to show that they were a proximate cause of any particular losses.
United States v. Kennedy, 643 F.3d 1251, 1264 (9th Cir.2011). Here, in the absence of evidence linking Aumais' possession to any loss suffered by Amy, we cannot agree with the magistrate judge's conclusion that "Aumais' conduct remains a substantial cause of [Amy's] harm." Aumais I, 2010 WL 3033821, at *6.
This opinion does not categorically foreclose payment of restitution to victims of child pornography from a defendant who possesses their pornographic images. We have no basis for rejecting Dr. Silberg's findings that Amy has suffered greatly and will require counseling well into the future. But where the Victim Impact Statement and the psychological evaluation were drafted before the defendant was even arrested  or might as well have been  we hold as a matter of law that the victim's loss was not proximately caused by a defendant's possession of the victim's image.

C.
A proximate cause of injury can be expected to lend itself more easily to assessment and allocation than a cause that is generalized or inchoate. Our conclusion  that Aumais' conduct was not a proximate cause of Amy's injury  is thus confirmed by the baffling and intractable issue that this case would otherwise present in terms of damages and joint and several liability.[3]
With respect to the amount of restitution, the district court ordered Aumais to pay $48,483 to cover Amy's future counseling costs. Aumais I, 2010 WL 3033821, at *8-9. But, as the magistrate judge determined, "[t]he harm from the uncle's abuse and that from possession of the images of the abuse by others are closely related for purposes of counseling and cannot be separate[d] to allocate costs between them as it appears that Amy will require counseling for both." Id. at *8. If Amy's future counseling costs are thus partly caused by her uncle's abuse, then Aumais cannot be responsible for all of those losses  a problem under the wording of § 2259, which mandates that Aumais make restitution for the full amount of Amy's losses caused as a result of Aumais' possession. This difficulty is illustrated by the disparate amounts of restitution ordered throughout the country, ranging from $3,000, see United States v. Mather, 1:09-CR-412, 2010 WL 5173029, at *5-6 (E.D.Cal. Dec. 13, 2010), to $3,680,153, see United States v. Staples, 09-14017-CR, 2009 WL 2827204, at *1 (S.D.Fla. Sept. 2, 2009).
A restitution award to Amy in this case would raise issues as to joint and several liability. As of the date of the restitution hearing, Amy had sought restitution in over 250 cases around the country. Aumais I, 2010 WL 3033821, at *5. In one such case, United States v. Faxon, 689 F.Supp.2d 1344, 1346, 1353 (S.D.Fla.2010), Amy's lawyer estimated that as of January 2010, Amy had received approximately *156 $170,000 from restitution orders and settlements.
In United States v. Nucci, 364 F.3d 419 (2d Cir.2004), we held that a victim may not recover more than his or her actual loss. There, we observed that "the relevant sections of the MVRA," id. at 423, do not in themselves prevent double-recovery in the criminal context.[4] However, recognizing that "[a]t common law, joint and several liability does not permit double recovery," we declined to "read[ ] the statute to provide recovery in excess of the amount of the loss," and accordingly applied the common law rule. Id.
Section 2259(b)(4)(B) provides that "[a] court may not decline to issue an order under this section because of  (i) the economic circumstances of the defendant; or (ii) the fact that a victim has, or is entitled to, receive compensation for his or her injuries from the proceeds of insurance or any other source." Our holding in Nucci indicates that because Amy may already have been fully compensated by others for the loss found in this case, there would be "no legal basis to permit an award that allows a victim to recover more than his due." Nucci, 364 F.3d at 424. It is in any event likely that the collection of a restitution award would need to be carefully monitored to ensure that total payments by all defendants did not exceed what Amy has been awarded for future counseling costs. The need for such monitoring would pose significant practical difficulties. As an initial matter, it is not entirely clear what government body, if any, is responsible for tracking payments that may involve defendants in numerous jurisdictions across the country. In addition, determining what amount Amy has received would entail collecting data about hundreds of cases, ascertaining what money has actually been paid, and determining what losses that money was intended to cover.
Finally, as discussed above, § 2259(b)(2)  dealing with the enforcement of the restitution order  cross references § 3664. Section 3664(h) implies that joint and several liability may be imposed only when a single district judge is dealing with multiple defendants in a single case (or indictment); so it would seem that the law does not contemplate apportionment of liability among defendants in different cases, before different judges, in different jurisdictions around the country.[5]

II.
Aumais argues that the district court committed procedural and substantive errors in sentencing Aumais to 121 months' imprisonment  the bottom of the Guidelines range. As to procedural reasonableness, Aumais contends that the district court treated the Sentencing Guidelines as mandatory and presumptively reasonable. This argument is refuted by the record. The district court conducted *157 an "individualized assessment" of the sentence warranted by § 3553(a) "based on the facts presented," Gall v. United States, 552 U.S. 38, 50, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), and concluded that "nothing below the minimum of the advisory guideline [and] nothing above the minimum of the advisory guideline range is necessary in light of the various factors that are at play here." Government Appendix at 22-23.
As to substantive reasonableness, Aumais principally relies on our recent decision in United States v. Dorvee, 616 F.3d 174 (2d Cir.2010), to support his argument that the sentence was greater than necessary to serve the purposes of sentencing. This argument, too, is without merit.
Dorvee observed that U.S.S.G. § 2G2.2, the Guideline at issue here, can, "unless applied with great care, ... lead to unreasonable sentences that are inconsistent with what § 3553 requires" because the enhancements in that Guideline "routinely result in Guidelines projections near or exceeding the statutory maximum, even in run-of-the-mill cases." 616 F.3d at 184, 186. The various child pornography enhancements applied in Dorvee resulted in a Guidelines range that, at the low end, was twenty-two months longer than the statutory maximum. Id. at 180. The Guidelines range calculated in this case (121-151 months) was well short of the statutory maximum, which was thirty years (had the district court chosen to impose consecutive sentences). Moreover, the district court found that 121 months imprisonment was "sufficient, but not greater than necessary" to comply with the purposes of § 3553(a), id. at 182 (quoting United States v. Samas, 561 F.3d 108, 110 (2d Cir.2009)), given the violent nature of the images, the number of them, and other considerations. The sentence is substantively reasonable.

CONCLUSION
For the foregoing reasons, the amended judgment of conviction is affirmed in part and reversed in part.
NOTES
[1]  Aumais sought a two-level reduction, pursuant to U.S.S.G. § 2G2.2(b)(1), on the ground that his conduct was limited to the receipt or solicitation of child pornography. The PSR had scored an additional two levels based upon a statement Aumais allegedly made at the time of his arrest that he traded in child pornography. The district court held a brief evidentiary hearing to resolve the factual dispute. The Government called Immigration and Customs Enforcement Officer Tim Losito, who testified that, at the time of his arrest, Aumais stated that he traded in child pornography. Based on this testimony and on the volume of pornographic images in Aumais' possession while he was ostensibly on a one-week business trip, the district court found that Aumais had traded in some materials and denied Aumais' request for a two-point reduction.
[2]  In United States v. Pearson, we considered whether a restitution order pursuant to 18 U.S.C. § 2259 may include an amount for estimated future medical expenses; but the defendant had produced child pornography and had had direct contact with the two child victims. 570 F.3d at 482, 486-87.
[3]  We note one additional issue (on top of the issues discussed in this section). In Aumais II, 2010 WL 3034730, at *1, the district court adopted the magistrate judge's Report and Recommendation and ordered that an Amended Judgment be issued. However, in the Amended Judgment, the district court did not check the box indicating that Aumais' liability was joint and several with other defendants. See Government Appendix 64-65. While it is settled that "where there is a direct conflict between an unambiguous oral pronouncement of sentence and the written judgment... the oral pronouncement, as correctly reported, must control," United States v. Marquez, 506 F.2d 620, 622 (2d Cir.1974) (internal quotation marks omitted), it is unclear whether this is true with respect to restitution orders.
[4]  In Nucci, we observed

Section 3664(f)(1)(A) requires the district court to order restitution in the full amount of the victim's losses and does not mention what the order should provide when multiple defendants are responsible for the same loss. Section 3664(h) provides that, where there are multiple defendants, the district court may order each defendant to pay the full amount or order that liability be apportioned to reflect each defendant's contribution to the loss. Section 3664(j)(2) does limit restitution that would result in an overpayment to the victim, but only where compensatory damages are later recovered by the victim in a "civil" proceeding.
Id. (footnote omitted).
[5]  In fact, two other circuits have observed, in unpublished opinions, that joint and several liability is not permissible under § 3664(h) regarding defendants in separate cases. See Monzel, 641 F.3d at 539 (citing United States v. McGlown, 380 Fed.Appx. 487, 490-91 (6th Cir.2010); United States v. Channita, 9 Fed. Appx. 274, 274-75 (4th Cir.2001)).
