
554 F.3d 64 (2009)
UNITED STATES of America, Appellee,
v.
Stefan IRVING, Defendant-Appellant.
Docket No. 07-1312.
United States Court of Appeals, Second Circuit.
Argued: May 30, 2008.
Final briefs submitted November 13, 2008.
Decided: January 28, 2009.
*67 Katherine Polk Failla, Assistant United States Attorney, New York, N.Y. (Michael J. Garcia, United States Attorney for the Southern District of New York, Stephen A. Miller, Assistant United States Attorney, New York, NY, on the brief), for Appellee.
Cheryl J. Sturm, Chadds Ford, PA, for Defendant-Appellant.
Before: KEARSE, SACK, and RAGGI, Circuit Judges.
KEARSE, Circuit Judge:
This case returns to us on the appeal of defendant Stefan Irving from an order of the United States District Court for the Southern District of New York, Lewis A. Kaplan, Judge, entered on remand following a decision of this Court which (a) upheld Irving's convictions, (b) postponed consideration of his sentencing challenges, and (c) remanded to the district court pursuant to United States v. Crosby, 397 F.3d 103 (2d Cir.2005) ("Crosby"), cert. denied, 549 U.S. 915, 127 S.Ct. 260, 166 L.Ed.2d 202 (2006), for consideration of resentencing in light of United States v. Booker, 543 U.S. 220, 244, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). Irving was convicted, following a jury trial, on two counts of traveling outside the United States with intent to engage in a sexual act with a minor, in violation of 18 U.S.C. § 2423(b) (counts 1 and 2); one count of aggravated sexual abuse, to wit, traveling outside the United States with intent to engage in a sexual act with a minor under the age of 12 years, in violation of 18 U.S.C. § 2241(c) (count 3); *68 one count of knowingly receiving child pornography, in violation of 18 U.S.C. § 2252A(a)(2)(B) (count 4); and one count of knowingly possessing child pornography, in violation of 18 U.S.C. § 2252A(a)(5)(B) (count 5). He was sentenced principally to concurrent 262-month prison terms on each count, to be followed by two concurrent five-year terms of supervised release on counts 3 and 4 and, concurrently, three concurrent three-year terms of supervised release on counts 1, 2, and 5; he was ordered to pay a $200,000 fine. On the Crosby remand, the district court declined to resentence Irving.
On this appeal, Irving contends that his sentence is unreasonable, asserting that the district court (a) applied the wrong sections of the United States Sentencing Guidelines (1998) ("Guidelines") in calculating the base offense levels for his crimes, (b) improperly increased his offense level on the ground of vulnerability of his victims, and (c) failed to consider, as required by 18 U.S.C. § 3553(a)(6), the need to avoid unwarranted sentencing disparities. In addition, in response to a request from this Court to address a double jeopardy question, Irving contends that his conviction on either count 4 or count 5 should be vacated on the ground that receipt of child pornography and possession of child pornography are the same crime for purposes of double jeopardy, and that his conviction on both counts thus violates the Double Jeopardy Clause.
For the reasons that follow, we reject all of Irving's contentions and affirm the order of the district court.

I. BACKGROUND
Irving is a formerly-licensed pediatrician who was convicted in 1983 of attempted sexual abuse of a seven-year-old boy. See generally United States v. Irving, 452 F.3d 110, 114 (2d Cir.2006) ("Irving II"), superseding, on rehearing, United States v. Irving, 432 F.3d 401 (2d Cir.2005) ("Irving I"). In the late 1990s, Irving became a target of a federal investigation into individuals suspected of traveling to Mexico for the purpose of engaging in sexual acts with children. The present prosecution centered on Irving's travel to Mexico in 1998 and to Honduras in 1999 and his later receipt and possession of child pornography.

A. The Evidence at Irving's Trial

The evidence presented at Irving's trial is discussed in Irving II, familiarity with which is assumed. Addressing Irving's initial appeal from the judgment of conviction, our description of the evidence with regard to his Mexico trip included the following:
In May 1998 Irving traveled to Acapulco, Mexico to visit Castillo Vista del Mar, a guest house that served as a place where men from the United States could have sexual relations with Mexican boys. When defendant visited, seven or eight boys ranging in age from eight to 20 years old were residing there. Irving learned of Castillo Vista del Mar from Robert Deckerits then manager, and a friend from the 1970s.
Decker testified that prior to visiting, Irving asked if specific boyswhom he knew from previous visitswould be there. Decker said Irving specifically asked about an eight-year-old boy. Decker testified further that he saw Irving fondle some of the boys who lived at the guest house while swimming with them. He also stated he saw defendant go upstairs to his bedroom at various times with different boys. Decker said that during Irving's visit the two of them discussed a previous trip to Honduras that Irving had taken, trips to the *69 beaches he took while there, and the boys he met. One of the boys at the guest house when Irving visited, Jesus Santiago Percastegui, corroborated relevant portions of Decker's testimony. Although unable to identify Irving in court, this witness stated that he saw "Esteban" (the name by which he knew Irving) at the beach caressing two other boys that lived at the guest house and twice go upstairs to his room with them.
Decker admitted while he was in Mexico he experienced financial difficulties, and that Irving gave him ATM cards, connected to an account he funded, up until Decker's September 2000 arrest. Irving gave Decker over $5,000 in support over the years. The two men also communicated regularly. Irving provided Decker with Internet web addresses of sites containing child pornography and on one occasion gave him images of boys engaged in sex acts with each other, with men, or by themselves. Irving told Decker he preferred prepubescent boys, under the age of 11, and that he preferred oral sex or fondling.

452 F.3d at 114-15 (emphases added).
On Irving's return to the United States from Mexico, a customs search of his luggage turned up, inter alia, computer diskettes containing "[i]mages of child erotica." Id. at 115. As to Irving's 1999 trip to Honduras, his personal journal described, inter alia, "details [of] his activities while there, particularly his luring of a 12-year-old boy back to his hotel with him and the sexual activities in which they engaged." Id. at 116.
In a search in 2003 pursuant to a warrant, agents found, inter alia, 76 video files on Irving's home computer, which had been downloaded on two days in July 2000. The government introduced the hard drive of that computer at trial. The video files "revealed `prepubescent boys engaging in various sexual acts with each other and in other cases of sexual acts by themselves.'" Id.

B. The Verdicts and Sentence

The jury found Irving guilty on all five of the counts against him: (1) traveling to Mexico with the intent to engage in a sexual act with a minor, in violation of 18 U.S.C. § 2423(b); (2) traveling to Honduras with the intent to engage in a sexual act with a minor, in violation of the same section; (3) traveling to Honduras with the intent to engage in a sexual act with a minor under the age of 12, in violation of 18 U.S.C. § 2241(c); (4) receiving child pornography, in violation of 18 U.S.C. § 2252A(a)(2)(B); and (5) possessing child pornography, in violation of 18 U.S.C. § 2252A(a)(5)(B).
The district court sentenced Irving using the 1998 version of the Guidelines, as the defense requested. As set forth in greater detail in Part II.B.1. below, with respect to counts 1, 2, and 3 (collectively the "travel counts"), the court used the base offense level provided in § 2A3.1, which applies to crimes of sexual abuse, or attempted sexual abuse, of children; and, as discussed in Part II.B.3., it increased that level pursuant to § 3A1.1(b)(1) on the ground that Irving knew that the children he abused were homeless and without parental supervision, and hence were unusually vulnerable. To determine Irving's base offense level for counts 4 and 5 (collectively the "child pornography counts"), the court looked to Guidelines § 2G2.2, which applies to, inter alia, receiving material involving the sexual exploitation of a minor. See Part II.B.2. below.
Applying the grouping rules for multi-count convictions, the court concluded that Irving's total offense level for all counts combined was 36. Given his criminal history category of II, the recommended *70 Guidelines range was 210-262 months. Denying both Irving's motion for a downward departure and the government's motion for an upward departure, the court sentenced Irving at the top of the recommended range to 262 months' imprisonment, stating that Irving was "a predator" who had "abused . . . a lot of children" (Sentencing Transcript ("S.Tr.") 34); that he was "an extremely dangerous individual with respect to . . . sexual abuse of children" (id. at 39); and that Irving had shown himself to be quite proficient at abusing children, including "providing financial support, at least for a while, to keep the house in Acapulco, Ca[s]tillo Vi[st]a del Mar, open so that the service of providing young kids hustled off the streets of Acapulco to American pedophiles could go on" (id.).
The court also referred to Irving's conviction some 20 years earlier for attempted sexual abuse of a seven-year-old boy, pointing out that Irving, "as a school physician, [had taken] of that position to abuse the kids [he was] supposed to be caring for." (Id. at 40.) Thus, Irving "ha[d] spent a lifetime doing a great deal of harm to a great many extremely vulnerable children." (Id. at 39-40.)
Further, the court noted that the record contained no indication that Irving conceded that his conduct toward children was in any way wrong. The court reminded Irving of
a letter you wrote at the end of August or thereabouts, 1996, to somebody about some of your activities, all of which focused on young boys, and there is a handwritten postscript at the end and in relevant part it reads as follows:
"You asked if I would be writing more explicitly about Mexico. Sadly, the newest focus of the witch hunt is on travel with intent to have underaged sex, so that kind of journal won't be possible until the government finds something more important to pay attention to."
You may think it's a witch hunt. Your fellow citizens think it is protecting the children of this country. The fact that you think it's a witch hunt proves to me that you have to be locked up for a very long time.
(S.Tr.40.)

C. Irving's Initial Appeal

Irving appealed, principally challenging the sufficiency of the evidence to support his conviction on any count. He also challenged the district court's calculation of his sentence. This Court affirmed Irving's conviction on counts 1, 4, and 5, the counts relating to Irving's travel to Mexico and to his receipt and possession of child pornography; but as to counts 2 and 3, we initially ruled that his convictions could not stand because there was insufficient evidence as to Irving's intent in traveling to Honduras. See Irving I, 432 F.3d at 404. Subsequently, however, on the government's petition for rehearing, we were persuaded that Irving's conduct in Mexico provided competent evidence, admissible under Fed.R.Evid. 404(b), as to his intentions in traveling to Honduras. Accordingly, we withdrew the decision issued in Irving I, and concluded that the evidence was sufficient to support Irving's convictions on all five counts. See Irving II, 452 F.3d at 114, 119.
Because Booker, which ruled that the Guidelines are not mandatory but advisory, had been decided during the pendency of Irving's appeal, and the district court had treated the Guidelines as mandatory, we concluded that a Crosby remand was required in order to allow the district court to determine whether it would have imposed a nontrivially different sentence had it known that the Guidelines were not mandatory. Given the need for the Crosby *71 remand, we refrained from addressing Irving's challenges to the details of the court's calculation of his original sentence. See Irving II, 452 F.3d at 114.

D. The District Court's Order on the Crosby Remand

On remand, the district court declined to impose a different sentence. See United States v. Irving, S3 03 Crim. 0633, 2007 WL 831814 (S.D.N.Y. Mar.19, 2007) ("Irving III"). Adhering to the original sentence, the court stated:
As the original sentencing minutes make clear, the Court sentenced the defendant at the high end of the Sentencing Guideline range because the defendant, in the Court's view, "is an extremely dangerous individual with respect to the sexual abuse of 28 children," that "there isn't the slightest hint that [the defendant] . . . recognize[s] that there is anything wrong" with his conduct, and that a sentence "at the top end of the [Guideline[s]] range is necessary for specific deterrence, that is to say, to prevent [defendant] from abusing others in the future."
The Court now has considered all of the factors enumerated in [18] U.S.C. § 3553. It is persuaded that the sentence imposed is sufficient, but no greater than necessary, to serve the other factors there enumerated and that all of the factors, taken together, justify the sentence previously imposed.
Irving III, 2007 WL 831814, at *1.

II. DISCUSSION
Irving has appealed from Irving III, largely renewing the challenges he made in his initial appeal with respect to the district court's calculation of his sentence. He does not otherwise challenge the district court's Irving III refusal to resentence him in light of Booker.
Irving contends that the district court erred by calculating his base offense level for counts 1, 2, and 3 under Guidelines § 2A3.1, rather than § 2A3.2; by calculating his base offense level for counts 4 and 5 under Guidelines § 2G2.2, rather than § 2G2.4; by increasing his offense level on the ground that his victims were vulnerable; and by failing to consider the need to avoid unwarranted sentencing disparities. And in response this Court's sua sponte inquiry, Irving contends that his conviction on count 4 or count 5 should be vacated on the ground that possession of child pornography is a lesser-included offense of his count-4 offense of receipt of child pornography, and that his conviction on both counts thus violates his rights under the Double Jeopardy Clause. For the reasons that follow, we find no merit in his contentions.

A. Sentencing and the Standard of Review After Booker

In the wake of Booker and the Supreme Court's elaborations on its import, see, e.g., Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), our review of sentencing decisions "is limited to determining whether they are `reasonable.'" Id. at 594. In conducting reasonableness review, we apply "the familiar abuse-of-discretion standard of review." Id.; see, e.g., Rita v. United States, 551 U.S. 338, 127 S.Ct. 2456, 2465, 168 L.Ed.2d 203 (2007).
Reasonableness review has both a procedural and a substantive component. See, e.g., United States v. Canova, 485 F.3d 674, 679 (2d Cir.2007). Review for procedural reasonableness requires us to
ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the *72 Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence.
Gall, 128 S.Ct. at 597. We review a district court's interpretations of the Guidelines de novo and its factual findings for clear error. See, e.g., United States v. Selioutsky, 409 F.3d 114, 119 (2d Cir.2005). The burden of proving a fact relevant to sentencing is on the government, which must prove the fact "by a preponderance of the evidence." United States v. Proshin, 438 F.3d 235, 238 (2d Cir.2006); see also United States v. Garcia, 413 F.3d 201, 220 n. 15 (2d Cir.2005) ("Judicial authority to find facts relevant to sentencing by a preponderance of the evidence survives Booker.").
As to substantive reasonableness, Booker instructed that "[s]ection 3553(a). . . sets forth numerous factors that guide sentencing. Those factors [are to] guide appellate courts . . . in determining whether a sentence is unreasonable." 543 U.S. at 261, 125 S.Ct. 738. In the absence of record evidence suggesting otherwise, we presume that the district court has faithfully discharged its duty to consider the § 3553(a) factors. See, e.g., United States v. Fernandez, 443 F.3d 19, 30 (2d Cir.), cert. denied, 549 U.S. 882, 127 S.Ct. 192, 166 L.Ed.2d 143 (2006).
The same standards of review also apply to our review of a sentence after the district court has declined to resentence following a Crosby remand. See United States v. Williams, 475 F.3d 468, 474 (2d Cir.2007), cert. denied, ___ U.S. ___, 128 S.Ct. 881, 169 L.Ed.2d 739 (2008).

B. Determination of the Applicable Guidelines


1. The Travel Counts

In calculating Irving's offense level for the travel counts, i.e., his travels to Mexico (count 1) and Honduras (counts 2 and 3), with intent to engage in sexual acts with minors, the district court began with Guidelines § 2A3.1, entitled "Criminal Sexual Abuse; Attempt to Commit Criminal Sexual Abuse." The 1998 version of that guideline provided a base offense level of 27, see Guidelines § 2A3.1(a), and required a four-step enhancement "[i]f the victim had not attained the age of twelve years," id. § 2A3.1(b)(2)(A). Irving contends that the court should instead have applied Guidelines § 2A3.2 (entitled "Criminal Sexual Abuse of a Minor (Statutory Rape) or Attempt to Commit Such Acts"), which provided a base offense level of 15, with no calibrations based on the minor's age. He argues that "the facts do not indicate anything beyond sexual contact with a minor (as opposed to a sexual act or sexual abuse)." (Irving brief on appeal at 23.) We see no error in the court's application of § 2A3.1 to these three counts.
To begin with, the Statutory Index in Appendix A to the Guidelines Manual ("Statutory Index") specifies which sections in Guidelines "Chapter Two-Offense Conduct" are ordinarily applicable to which statutes of conviction. In the 1998 version of the Guidelines, for a conviction under 18 U.S.C. § 2241(c)the section under which Irving was convicted on count 3the only guideline listed in the Statutory Index was § 2A3.1, governing commission of, and attempts to commit, criminal sexual abuse of minors. The evidence supporting Irving's conviction on count 3 included his own personal journal "detail[ing] his activities while [in Honduras], particularly his luring of a 12-year-old boy back to his hotel with him and the sexual activities in which they engaged," Irving II, 452 F.3d at 116, and the evidence that *73 "Irving told Decker he preferred prepubescent boys, under the age of 11," id. at 115. Irving has not shown that his conduct was atypical in any way that would warrant the calculation of his offense level for count 3 under any guideline other than § 2A3.1.
For a conviction under 18 U.S.C. § 2423(b), the section under which Irving was convicted on counts 1 and 2, the Statutory Index listed Guidelines §§ 2A3.1, 2A3.2, and 2A3.3. When more than one guideline is listed for a count of conviction under a given statutory section, the court is to apply the guideline that is most appropriate for the defendant's offense conduct in that count. See Statutory Index, Introduction. Several factors indicated that § 2A3.1 was the most appropriate guideline for Irving's convictions on counts 1 and 2. First, even if § 2A3.2 would have been applicable to count 2 if it had been the only count of conviction, counts 2 and 3 concerning Irving's trip to Honduras involved the same transaction and the same or overlapping victims and thus were required to be grouped for calculation of a single combined offense level, see Guidelines § 3D1.2(a). When counts of conviction governed by different guidelines are grouped, the court is instructed to apply the "highest offense level of the counts in the Group." Guidelines § 3D1.3(a). Hence the offense level for count 2 was properly calculated, in combination with that for count 3, under § 2A3.1.
Second, the Guidelines provided that "[a]ny criminal sexual abuse with a child less than twelve years of age, regardless of `consent,' is governed by § 2A3.1 (Criminal Sexual Abuse)." Guidelines § 2A3.1 Background. Thus, if, within the meaning of that section, Irving sexually abused a child under the age of 12 on his trip to Mexico, the court was required to apply § 2A3.1 to count 1. Third, the Guidelines provided that "[b]ecause of their dangerousness, attempts are treated the same as completed acts of criminal sexual abuse." Id. Thus, if Irving attempted sexual abuse of a child under 12 on his trips to Mexico and Honduras, there was sexual abuse within the meaning of the Guidelines, and again § 2A3.1 was applicable to both counts 1 and 2.
In concluding that § 2A3.1 was applicable to count 1, the district court found, inter alia, that Irving
clearly went to Mexico to engage in sex with young boys. There was ample evidence that his preferred age group was in the range of roughly six years of age to twelve years of age.
I refer to, among other things, . . . a March 23, 1995 document written by the defendant in which he indicates a preference for boys roughly in the range of age nine to puberty with a little leeway on either side, and Government Exhibit 103, where he speaks in terms of ages six to twelve.
I find that there was attempted, at least attempted sexual abuse of a child under twelve in Mexico.
(S.Tr.5.) In concluding that § 2A3.1 was applicable to Irving's trip to Honduras, the court stated that
[t]he same analysis applies to [counts 2 and 3]. I find that there was at least attempted sexual abuse of one or more children under twelve during the 1999 trip to Honduras.
(Id.)
These findings that Irving at least attempted sexual abuse children under the age of 12 on his trips to both Mexico and Honduras were amply supported by the evidence referred to by the district court and by other evidence at trialsummarized in Part I.A. abovewhich Irving II found was sufficient to support Irving's *74 convictions on the travel counts. We see no error in the district court's conclusion that § 2A3.1 was the appropriate guideline to apply to Irving's convictions on counts 1, 2, and 3.

2. The Child Pornography Counts

In calculating Irving's offense level for count 4, receiving child pornography in violation of 18 U.S.C. § 2252A(a)(2)(B), and count 5, possessing child pornography in violation of id. § 2252A(a)(5)(B), the district court applied Guidelines § 2G2.2, entitled "Trafficking in Material Involving the Sexual Exploitation of a Minor; Receiving, Transporting, Shipping, or Advertising Material Involving the Sexual Exploitation of a Minor; Possessing Material Involving the Sexual Exploitation of a Minor with Intent to Traffic" (italics omitted; emphases added). Irving argues that the district court should instead have applied Guidelines § 2G2.4, entitled "Possession of Materials Depicting a Minor Engaged in Sexually Explicit Conduct" (italics omitted; emphasis added), because he was not shown to have received or possessed child pornography with the intent to traffic in it. For several reasons, we see no error.
First, on count 4, the jury found Irving guilty of receiving child pornography, in violation of § 2252A(a)(2)(B). At the times relevant to Irving's conduct, that section applied to any person who knowingly "receives or distributes . . . any material that contains child pornography that has been mailed, or shipped or transported in interstate or foreign commerce by any means, including by computer," 18 U.S.C. § 2252A(a)(2)(B). Nothing in that section or in Guidelines § 2G2.2 imposed any intent-to-traffic requirement with respect to an offense of receiving such material.
Second, the 1998 version of § 2G2.4, the guideline that Irving argues should have been applied to counts 4 and 5, could not have been applied to count 4 because that guideline provided offense levels only for possession, not for receipt, of child pornography. Further, the history of that guideline reveals that its inapplicability to receipt at the time of Irving's receipt offense was deliberate. When § 2G2.4 was first added to the Guidelines in 1991, it was in fact entitled "Receipt or Possession of Materials Depicting a Minor Engaged in Sexually Explicit Conduct," Guidelines Appendix C, amend. 372 (effective Nov. 1, 1991) (emphasis added). Less than a month later, however, the words "Receipt or" were deleted from the title of § 2G2.4, see Guidelines Appendix C, amend. 436 (effective Nov. 27, 1991). The deletion was made to "implement[ ] . . . instructions to the [Sentencing] Commission" from Congress, id., to "[change g]uideline 2G2.4 to provide that such guideline shall apply only to offense conduct that involves the simple possession of [child pornography] and [change] guideline 2G2.2 to provide that such guideline shall apply to offense conduct that involves receipt or trafficking," Treasury, Postal Service and General Government Appropriations Act of 1992, Pub.L. No. 102-141, § 632(1)(B), 105 Stat. 834, 876 (Oct. 28, 1991) (emphases added). Accordingly, § 2G2.4 could not properly have been applied to Irving's receipt-of-child-pornography conviction on count 4.
Third, although Irving's offense level for his count-5 possession offense would have been calculated under § 2G2.4 if it had been unaccompanied by any other child pornography conviction, his convictions on counts 4 and 5 were for closely related offenses of the same general type, and it was not unreasonable for the court to group those counts for calculation of a single combined offense level. In such circumstances, the court is directed to "apply the offense guideline that produces the *75 highest offense level." Guidelines § 3D1.3(b). Hence, Irving's base offense level for counts 4 and 5 was properly calculated under § 2G2.2.

3. The Vulnerable Victim Adjustment

After calculating Irving's base offense level for counts 1, 2, and 3, i.e., traveling to Mexico and Honduras with intent to engage in sexual acts with minors, the district court adjusted Irving's offense level upward by two steps pursuant to Guidelines 3A1.1(b)(1). That guideline provides that "[i]f the defendant knew or should have known that a victim of the offense [of conviction] was a vulnerable victim," his offense level should be increased by two steps. Guidelines § 3A1.1(b)(1). The commentary with respect to subsection (b) states, inter alia, as follows:
"vulnerable victim" means a person . . . who is unusually vulnerable due to age, physical or mental condition, or who is otherwise particularly susceptible to the criminal conduct.

Subsection (b) applies to offenses involving an unusually vulnerable victim in which the defendant knows or should have known of the victim's unusual vulnerability.. . .
Do not apply subsection (b) if the factor that makes the person a vulnerable victim is incorporated in the offense guideline. For example, if the offense guideline provides an enhancement for the age of the victim, this subsection would not be applied unless the victim was unusually vulnerable for reasons unrelated to age.

Guidelines § 3A1.1 Application Note 2 (emphases added).
Irving contends that the vulnerable victim adjustment, as explicated by the Guidelines commentary, was inappropriate because his victims' vulnerability was already accounted for by the enhancement provided in § 2A3.1 for offenses against children under the age of 12 years, and that his victims had no "unusual" vulnerability. We disagree.
In imposing the vulnerable victim adjustment, the district court stated that Irving
is getting bumped up not because they were kids, but because they were street urchins who were especially vulnerable because anybody who comes along and offers the promise of a free meal has a special attraction to people in that economic and social circumstance.
. . . [S]ome 11 year old who is living on the street in Acapulco is a little bit more likely to fall for a predator of a sexual nature than an 11 year old coming out of the Dalton School into a limousine to go home.
(S.Tr. at 18.)
We see no error in this decision. The facts that Irving's victims in Mexico and Honduras were children who were homeless and were without parental or other appropriate guidance made them unusually vulnerable, independently of their ages. The adjustment was entirely appropriate.

C. Consideration of Possible Sentencing Disparity

In arguing that the district court erred in failing to consider "the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct," 18 U.S.C. § 3553(a)(6), Irving contends that the district court was required to consider "statistics kept by the Sentencing Commission regarding sentences imposed locally and nationally on similarly situated offenders." (Irving brief on appeal, at 29.) We find no merit in this contention.
*76 Preliminarily, we note that Irving relies on the statistics found in the United States Sentencing Commission Statistical Information Packet, Fiscal Year 2004, Second Circuit, Table 7. That Table, however, refers to "Sexual Abuse" crimes generally and provides no assurance of comparability because it does not distinguish between defendants who committed crimes of sexual abuse against children and those who committed such crimes against adults. And nothing reveals how many other defendants went to the lengths that Irving did to secure his victims. The district court was not required to consult these statistics. "[A]verages of sentences that provide no details underlying the sentences are unreliable to determine unwarranted disparity because they do not reflect the enhancements or adjustments for the aggravating or mitigating factors that distinguish individual cases." United States v. Willingham, 497 F.3d 541, 544 (5th Cir.2007).
More importantly, "a reviewing court's concern about unwarranted disparities is at a minimum when a sentence is within the Guidelines range," id. at 545. The "avoidance of unwarranted disparities was clearly considered by the Sentencing Commission when setting the Guidelines ranges." Gall, 128 S.Ct. at 599. Thus, where, as here, "the District Judge correctly calculated and carefully reviewed the Guidelines range, he necessarily gave significant weight and consideration to the need to avoid unwarranted disparities." Id.; see also United States v. Boscarino, 437 F.3d 634, 638 (7th Cir.2006) ("A sentence within a properly ascertained range. . . cannot be treated as unreasonable by reference to § 3553(a)(6)."), cert. denied, ___ U.S. ___, 127 S.Ct. 3041, 168 L.Ed.2d 755 (2007).
The district court here stated that it had "considered all of the factors enumerated in 28 [18] U.S.C. § 3553," Irving III, 2007 WL 831814, at *1, a statement that is well supported by the detailed explanations given by the court in imposing sentence.

D. Double Jeopardy

The Double Jeopardy Clause provides that no person shall "be subject for the same offence to be twice put in jeopardy of life or limb." U.S. Const, amend. V. As to whether two convictions are for the same offense where "`the same act or transaction constitutes a violation of two distinct statutory provisions, the test to be applied . . . is whether each provision requires proof of a fact which the other does not.'" Rutledge v. United States, 517 U.S. 292, 297, 116 S.Ct. 1241, 134 L.Ed.2d 419 (1996) (quoting Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 76 L.Ed. 306 (1932)). Typically, when one offense is lesser than and wholly included within another offense, the two offenses are considered to be the same for double jeopardy purposes. See, e.g., Rutledge, 517 U.S. at 297 & n. 6, 116 S.Ct. 1241. In Ball v. United States, 470 U.S. 856, 105 S.Ct. 1668, 84 L.Ed.2d 740 (1985), for example, the Court held that statutes directed at "receipt" and "possession" of a firearm amounted to the "same offense" for double jeopardy purposes, in that proof of receipt "necessarily" included proof of possession. Id. at 861-64, 105 S.Ct. 1668 (emphasis in original).
While it is permissible to prosecute a defendant simultaneously on two or more counts charging offenses that are the same for double jeopardy purposes, the Double Jeopardy Clause protects him against multiple punishments for the same offense. When the jury returns verdicts of guilty on more than one such count, the district court should enter judgment on only one. See, e.g., id. at 865, 105 S.Ct. *77 1668; Illinois v. Vitale, 447 U.S. 410, 415, 100 S.Ct. 2260, 65 L.Ed.2d 228 (1980).
Two of our Sister Circuits have ruled that a defendant's convictions of both "receiving and possessing the same images of child pornography" violated his right to be free from double jeopardy, United States v. Miller, 527 F.3d 54, 58 (3d Cir. 2008) ("Miller"); see United States v. Davenport, 519 F.3d 940, 947 (9th Cir. 2008) ("Davenport"), reasoning that to receive an item means to take possession of it, see Miller, 527 F.3d at 71 & n. 15; Davenport, 519 F.3d at 943; see also United States v. Morgan, 435 F.3d 660, 662-63 (6th Cir.2006) (referring briefly in dicta to possession of child pornography as a lesser-included offense of receipt). But see Missouri v. Hunter, 459 U.S. 359, 366-68, 103 S.Ct. 673, 74 L.Ed.2d 535 (1983) (the presumption against allowing multiple punishments for the same crime may be overcome if there is a clear indication of legislative intent to allow courts to impose them); id. at 368, 103 S.Ct. 673 ("`Where Congress intended . . . to impose multiple punishments, imposition of such sentences does not violate the Constitution.'" (quoting Albernaz v. United States, 450 U.S. 333, 344, 101 S.Ct. 1137, 67 L.Ed.2d 275 (1981) (emphasis in Hunter))); Davenport, 519 F.3d at 948-49 (Graber, J., dissenting) (expressing the "view[that] Congress clearly intended to authorize cumulative punishment for receipt of child pornography and possession of child pornography," as the two prohibitions are directed at "distinct harms").
This Court in United States v. Anson, No. 07-0377, 2008 WL 4585338, ___ Fed. Appx. ___ (2d Cir. Oct.15, 2008) ("Anson"), considered the arguments of a defendant who had been convicted of receiving and possessing child pornography, but we did not reach the merits of the double jeopardy issue because it was possible that the jury had found the defendant guilty of receiving one group of images and guilty of possessing a different group. Compare Anson with Miller, 527 F.3d at 58 (defendant convicted of "receiving and possessing the same images"). The defendant in Anson had not requested a jury charge that would have instructed the jury that the same images could not support guilty verdicts on both counts. We concluded, citing United States v. Washington, 861 F.2d 350, 352-53 (2d Cir.1988) ("Washington"), that any objection on the ground that both verdicts might have been based on the same set of images was waived. See Anson, 2008 WL 4585338, at *4, ___. In Washington, we had stated that if a defendant believes that the evidence on which the jury might rely in its consideration of multiple counts would expose him to multiple punishments for the same offense, he must request an instruction that ensures that the jury not consider evidence on which a conviction on a given count cannot properly be based; we ruled that in the absence of such a request the objection is deemed waived. See Washington, 861 F.2d at 352-53; see also id. at 353 ("it is not plain error to fail to give such a[n unrequested] charge").
On the present appeal, although Irving had not made a double jeopardy argument, this Court sua sponte requested that the parties address the issue of whether Irving's right to be free from double jeopardy was violated by the entry of judgment convicting him on both count 4 and count 5. In response, Irving contends that the entry of judgment on both convictions violated the Double Jeopardy Clause because receipt of child pornography and possession of child pornography are, for double jeopardy purposes, "the same crime," as a person "cannot receive child pornography without possessing it." (Irving Nov. 13, 2008 letter brief on appeal at 4, 5.) The government, in addition to contending that *78 Irving's argument is procedurally barred, contends that there was no double jeopardy violation. It argues, inter alia, that Congress evidently intended to create separate and distinct crimes, as the prohibition against possession of child pornography was added to an existing criminal scheme that prohibited receipt of such pornography and the prohibitions against receipt and possession are directed toward different evils. The government points out that "the receiver [of child pornography] creates a market for exploitation and production, whether or not he retains them," whereas "the possessor (i.e., retainer) often uses the pornography to seduce children and whet his sexual appetite, and also helps create a permanent record of the exploitation." (Government Nov. 13, 2008 letter brief on appeal at 19.)
This case is similar to Anson, and although we decided Anson by nonprecedential summary order, "[d]enying summary orders precedential effect does not mean that the court considers itself free to rule differently in similar cases," Order dated June 26, 2007, adopting 2d Cir. Local R. 32.1. In the district court, Irving raised no double jeopardy issue with respect to the counts charging him with receiving and possessing child pornography, either by requesting a jury instruction or a special verdict that would have required the jury to specify which of the 76 images it relied on in returning verdicts of guilty on the respective child pornography counts, or by requesting that the court enter judgment on only count 4 or 5, but not both, on the ground that they resulted in two convictions for the same offense. And in this Court, Irving made no double jeopardy challenge to the district court's entry of judgment on both counts, either in his initial appeal or in his original briefs in the present appeal. Nonetheless, "[a] plain error that affects substantial rights may be considered even though it was not brought to the court's attention." Fed. R.Crim.P. 52(b).
In order to reverse on the ground of plain error, "there must be (1) `error,' (2) that is `plain,' and (3) that `affect[s] substantial rights.'" Johnson v. United States, 520 U.S. 461, 467-68, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) (quoting United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)). An error is "plain" if the ruling was contrary to law that was clearly established by the time of the appeal. See Johnson, 520 U.S. at 468, 117 S.Ct. 1544. "If all three conditions are met, an appellate court may then exercise its discretion to notice a forfeited error, but only if (4) the error `"seriously affect[s] the fairness, integrity, or public reputation of judicial proceedings."'" Id. (quoting Olano, 507 U.S. at 732, 113 S.Ct. 1770 (quoting United States v. Young, 470 U.S. 1, 15, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985)) (other internal quotation marks omitted)).
We conclude that Irving has not met this standard. First, assuming that possessing child pornography is a lesser-included offense of receiving such pornography, a question we need not resolve here, it remains unclear that the entry of judgment on both count 4 and count 5 in this case was error. The court had instructed the jury that the statute under which Irving was charged in count 4 provided that "`Any person who knowingly receives or distributes any material that contains child pornography that has been mailed, or shipped or transported in interstate or foreign commerce by any means, including by computer' commits a crime." (Trial Transcript ("T.Tr."), at 537 (quoting former 18 U.S.C. § 2252(a)(2)(B)) (emphases ours).) As to count 5, the court instructed the jury that the government was required to prove that Irving "possessed *79 three or more images of child pornography." (T.Tr. 544, 545 (emphasis added)). We note that, in giving this instruction, the court apparently invoked the version of § 2252A(a)(5)(B) that was in effect from September 30, 1996, through October 29, 1998, which prohibited possession of "material that contains 3 or more images of child pornography," rather than the stricter version of that section that was in effect from October 30, 1998, through November 1, 2002. The latter version of § 2252A(a)(5)(B) covered most of the period from in or about July 2000 through May 6, 2003during which time Irving possessed the imagesand prohibited possession of "material that contains an image of child pornography," setting no threshold number of images. In any event, given that the government introduced Irving's computer hard drive containing 76 images of child pornography, the effect of these instructions was to allow the jury to find Irving guilty of possessing child pornography based on any three of those 76 images and guilty of receiving child pornography based on any one of the 76 images, including 73 that were not needed for the return of a verdict of guilty on the possession count. If the jury's verdicts on counts 4 and 5 were based on different images, there was no double jeopardy violation in the entry of judgment on both counts.
Second, even if the jury based its verdicts on counts 4 and 5 on the same images, it is questionable whether we could call that result a "plain" error given the lack of a clearly established principle that possessing child pornography is a lesser-included offense of receiving such pornography. At the time of trial, no court of appeals had so held; as of the writing of this opinion, this Court still has not so held; so far as we are aware at the present time, only the Third and Ninth Circuits have so held, with a member of the Ninth Circuit panel in Davenport dissenting; and the Seventh Circuit, in the context of a Guidelines challenge, has held it reasonable to impose different base offense levels for receiving and possessing child pornography on the ground that "possession and receipt are not the same conduct and threaten distinct harms," United States v. Myers, 355 F.3d 1040, 1043 (7th Cir.2004).
Finally, even if the first three Olano factors were met, we could not conclude that Irving's convictions on both counts 4 and 5 seriously affect the fairness, integrity, or public reputation of judicial proceedings. It was within Irving's power to request clarifying instructions or a special verdict to have the jury particularize the bases of its verdicts on those counts. It hardly serves the interests of fairness to overturn verdicts that his inaction allowed to be ambiguous and that may be substantively unflawed.

CONCLUSION
We have considered all of Irving's arguments on this appeal and have found them to be without merit. The order of the district court is affirmed.
