Kamadeen Idowu Oladimeji appeals from judgments of conviction covering two indictments entered in the United States District Court for the Eastern District of New York (Glasser, J.) based on his plea of guilty. Oladimeji argues (i) that the convictions should be overturned because he received ineffective assistance of counsel at several stages, including his making of plea agreements; (ii) that he is entitled to a sentencing remand pursuant to United States v. Crosby, 397 F.3d 103 (2d Cir.2005); and (iii) that the district court’s restitution order under 18 U.S.C. §§ 3663A-3664 was in error and unconstitutional. We find that Oladimeji’s ineffective-assistance-of-counsel claims cannot properly be considered on appeal but may be asserted in a petition for habeas corpus under 28 U.S.C. § 2255; we deny provisionally Oladimeji’s claim to a remand under Crosby; and we find no error in the restitution order. Accordingly, we affirm the judgments of conviction.

BACKGROUND

On March 1, 2001, pursuant to a plea agreement, Oladimeji pleaded guilty on Indictment 00-709 (the “00” indictment) to one count of possessing fraudulent alien registration and Social Security cards in violation of 18 U.S.C. § 1546(a). The plea agreement contained an appeal-waiver provision, which stated that “defendant will not file an appeal or otherwise challenge the conviction or sentence” if the court imposes a “range of imprisonment” of ten to sixteen months.

Prior to sentencing in that case, additional charges were brought against Ola-dimeji in Indictment 01-957 (the “01” indictment). On June 10, 2002, Oladimeji executed an agreement in the 01 case to plead guilty to two counts of bank fraud in violation of 18 U.S.C. § 1344 and one count of fraudulent possession of unauthorized access devices in violation of 18 U.S.C. § 1029(a)(3). The two bank-fraud counts alleged that Olademeji participated in schemes to obtain a $30,000 home-equity loan by making false representations to a financial institution, and to steal funds from a deceased woman’s bank account. The unauthorized-access-device count alleged that Oladimeji possessed, with intent to defraud, fifteen or more unauthorized access devices, consisting of more than 200 Social Security numbers and credit cards.

The plea agreement noted that restitution was “mandated” by 18 U.S.C. § 3663A. It included an appeal-waiver provision covering both cases, which stated:

The defendant will not file an appeal or otherwise challenge the conviction or sentence in 00-709 or 01-957 in the event that the Court imposes a total term of imprisonment of 114 months ... or below.

Oladimeji entered a guilty plea on the new counts at a hearing held June 10, 2002. With regard to the charge of unauthorized access cards, the government advised the court that agents had seized from Oladimeji’s residence approximately 40 credit cards in various people’s names.[*154] Initially, Oladimeji appeared to dispute his possession of these cards, indicating that they belonged to another individual living in his house. However, Oladimeji then acknowledged under oath his own possession of two to three credit cards in others’ names, for the purpose of obtaining money that did not belong to him, and with respect to the other credit cards, that he was aware they were in his home, that they were “funny,” that they were intended to be used by a person to obtain money that did not belong to him, and that he was “aiding and abetting” and “assisting” in that venture.

On March 3, 2003, Oladimeji moved to withdraw both guilty pleas. On June 17, 2003, the district court denied his motion, and proceeded to impose a sentence covering both cases of 71 months of imprisonment, five years of supervised release, a special assessment of $400, and restitution payments of $152,545.72. The latter sum included $42,545.72 to credit card companies based on the fraudulent use of thirteen credit cards seized from Oladimeji’s residence.

Oladimeji brought this appeal.

DISCUSSION

I. Ineffective Assistance of Counsel

Oladimeji contends that his guilty pleas and his convictions should be set aside because he received ineffective assistance of counsel in making his plea agreements, in attempting to withdraw his pleas, and at his sentencing.

Where the record on appeal does not include the facts necessary to adjudicate a claim of ineffective assistance of counsel, our usual practice is not to consider the claim on the direct appeal, but to leave it to the defendant to raise the claims on a petition for habeas corpus under 28 U.S.C. § 2255. See, e.g., United States v. Morgan, 386 F.3d 376, 383 (2d Cir.2004); United States v. Khedr, 343 F.3d 96, 99-100 (2d Cir.2003); United States v. Williams, 205 F.3d 23, 35-36 (2d Cir.2000). As the Supreme Court has noted, collateral review typically provides a far better opportunity for an evaluation of an ineffective-assistance claim than direct review, because a factual record focused on the defendant’s claim can be developed in the district court, including by “takfing] testimony from witnesses for the defendant and the prosecution and from the counsel alleged to have rendered the deficient performance.” Massaro v. United States, 538 U.S. 500, 504-05, 123 S.Ct. 1690, 155 L.Ed.2d 714 (2003) (noting the benefits of deciding ineffective-assistance claims through § 2255 proceedings instead of on direct appeal).

The record currently before us does not contain the information necessary to the resolution of Oladimeji’s ineffective-assistance-of-counsel claims. We decline to consider them as a part of this direct appeal. Oladimeji may raise those claims in the district court by petition under § 2255, upon which the court could determine whether ineffective assistance of counsel nullified the defendant’s waiver of his right to challenge his conviction.

II. The Effect of Oladimeji’s Ineffective-Assistance-of-Counsel Claim on His Other Challenges to His Conviction

In addition to his claim of ineffective assistance, Oladimeji contends that he is entitled to a remand under Crosby for reconsideration of his sentence and to a reduction of the restitution payments ordered. The government asserts that those challenges are barred by Oladimeji’s second appeal waiver because his sentence of 71 months imprisonment was within the range (of 114 months or below) as to which[*155] Oladimeji committed himself not to challenge the convictions. Oladimeji contends that the ineffective assistance of counsel he received tainted his acceptance of the plea agreements, including the appeal-waiver provision. Ineffective assistance with respect to an appeal waiver, if proven, would cast doubt on enforceability of the appeal-waiver provision.

In United States v. Monzon, 359 F.3d 110 (2d Cir.2004), discussing similar circumstances, we said:

[I]f the merits of the ineffeetive-assis-tance-of-counsel claim cannot be determined on the basis of the record on appeal, it is appropriate to enforce the appeal waiver and dismiss the appeal. If the rule were otherwise, a defendant who secured the benefits of a plea agreement by, inter alia, knowingly and voluntarily waiving the right to appeal could escape the fairly bargained-for appeal waiver by the simple expedient of asserting an ineffective-assistance-of-counsel claim that had no merit.

Id. at 119. That statement was dictum in Monzon, because we did review the merits of that defendant’s ineffective-assistance-of-counsel claim. Id. at 111-12, 119-20. Nonetheless, we find the reasoning of Monzon to be persuasive, and we adopt it here.

As the record does not permit assessment of the claim of ineffective assistance and its potential effect on the appeal waiver, the defendant’s undertaking not to appeal will be provisionally enforced as to any appellate claim that falls under the appeal waiver, unless and until he prevails (by a habeas petition) in proving that his appeal waiver should be voided because he received ineffective assistance of counsel. When and if he proves that contention, any such claim would be considered as a part of the habeas petition. For purposes of this appeal, the appeal waiver will be enforced.

III. Crosby Remand

In United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), the Supreme Court found that the United States Sentencing Guidelines, when applied in accordance with the compulsory terms of the governing statutes, violated defendants’ jury trial rights under the Sixth Amendment. In response to that ruling, this court determined that defendants sentenced under the Guidelines on direct appeal who did not object below to the constitutionality of the Sentencing Guidelines generally should be entitled to a remand to the district court for a determination whether their sentences would have been significantly more lenient had the sentencing court followed the standards of Booker, and accordingly should be resentenced. See Crosby, 397 F.3d at 119; cf. United States v. Lake, 419 F.3d 111, 113 (2d Cir.2005) (finding that remand for resentencing, instead of a remand to determine whether to resentence, is appropriate in a case of preserved error); United States v. Fagans, 406 F.3d 138, 140-42 (2d Cir.2005) (same). Such a remand to determine whether to resentence is now commonly referred to as a “Crosby remand.”

Oladimeji contends he should receive a Crosby remand for reconsideration of his sentence. We ruled in United States v. Morgan, 406 F.3d 135 (2d Cir.2005), however, that a defendant who pleads guilty under an agreement containing an appeal-waiver provision waives the right to a Crosby remand. Id. at 137. As for defendants who entered a plea agreement with an appeal waiver before the Supreme Court decided Booker, we stated that “the possibility of a favorable change in the law after a plea is simply one of the risks that accompanies pleas and plea agreements.”[*156] Id,.; see also United States v. Rodriguez, 416 F.3d 123, 128-29 (2d Cir.2005); United States v. Haynes, 412 F.3d 37 (2d Cir.2005) (per curiam) (finding that the reasoning of Morgan applies also when the defendant preserved an objection to the constitutionality of the Guidelines).

As explained above, despite the possibility that Oladimeji’s claim of ineffective assistance of counsel may ultimately invalidate his appeal waiver, we will not consider that claim on this appeal. Unless and until Oladimeji succeeds in invalidating the appeal waiver, we will treat it as valid. Accordingly, we dismiss this claim without prejudice to its reassertion among the claims for relief on Oladimeji’s petition for habeas corpus if he proves this appeal waiver should be nullified because he received ineffective assistance.

Furthermore, we reject Oladimeji’s contention that his attempt in the district court to withdraw his plea should change the result. It is true that in Morgan we addressed circumstances where the defendant “did not in a timely fashion seek relief from the underlying plea.” Morgan, 406 F.3d at 137. Nonetheless, Oladimeji’s unsuccessful motion to withdraw his plea creates a distinction without a difference. It does not change the fact that he made a plea bargain which included as a term his waiver of appeal. Unless he shows that provision should be invalidated, he is bound by it, regardless of whether he later tried to withdraw from the bargain.

IV. Mandatory Restitution

Oladimeji raises several challenges to the district court’s restitution order. Most broadly, he argues that the district court’s imposition of restitution violated his jury trial rights under the Sixth Amendment. As a preliminary matter, we must determine whether Oladimeji’s challenges to the restitution order fall within the scope of his appeal waiver.

A. Scope of Appeal-Waiver Provision

As noted, as part of his agreement relating to his second plea, Oladimeji agreed he would “not file an appeal or otherwise challenge the conviction or sentence in 00-709 or 01-957 in the event that the Court imposes a total term of imprisonment of 114 months ... or below.” The question we face is whether this commitment bars Oladimeji’s appeal from the portion of his sentence commanding payment of restitution.

We find the answer not immediately clear. Without doubt, a restitution order is part of the sentence, and the defendant made a commitment not to challenge his sentence. The apparent logic of the agreement, however, was that the defendant would give up any challenges to the lawfulness of his conviction and the determination of his prison sentence if his period of imprisonment was below a specified maximum. It is not self-evident that this agreement was intended to waive appellate review of any restitution — without limit— that the court might order.

To illustrate the issue, we consider the hypothetical case of a defendant who stole $100, pled guilty to theft, and agreed not to appeal his conviction or sentence if he received less than 3 months in jail. The court sentenced him to one month imprisonment but also imposed a restitution order, altogether without basis, in the amount of $5 million. Should the defendant’s agreement be construed as barring-appeal from the restitution order? Can the waiver of appeal be reasonably understood to cover only the conviction and the aspects of the sentence that determined the scope of the waiver — the maximum jail term of 3 months?

[*157] We have previously stated that we apply appeal-waiver provisions “narrowly” and construe them “strictly against the Government,” in recognition of the fact that prosecutors’ bargaining power generally exceeds that of defendants and that the government typically drafts such agreements. United States v. Cunningham, 292 F.3d 115, 117 (2d Cir.2002) (internal quotation marks omitted). Here, although a broad and literal reading of the agreement would bar appeal from any aspect of the sentence, the agreement could also be reasonably construed to bar challenges to the conviction and to the duration of confinement, but not to cover determinations of restitution. See United States v. Ready, 82 F.3d 551, 559 (2d Cir.1996) (finding that the defendant’s waiver did not encompass his right to challenge the legality of a provision of his sentence, in that case a restitution order, where “the record d[id] not instill confidence” that the defendant understood the waiver as encompassing challenges to legality).

In further support for the latter reading, twice the agreement refers to the fact that Oladimeji’s “sentence” in his second case will run consecutively with the “sentence” imposed in his first case. That wording, which makes sense only if “sentence” refers to the period of imprisonment, reinforces the likelihood that the word “sentence” in the pertinent clause of the agreement refers to the period of imprisonment. Also, the agreement’s adoption of the 114-month non-appeal ceiling derived from the estimated adjusted offense levels and criminal-history categories, which affect terms of imprisonment under the Sentencing Guidelines, but not restitution.

We find that the agreement’s use of the term “sentence” was at least ambiguous, and we resolve that ambiguity against the government. Having found that Oladime-ji’s appeal of his restitution order is not covered by the applicable appeal-waiver provision, we proceed to the merits of his arguments.

B. Sixth Amendment Violation

Challenging the constitutionality of the restitution order imposed against him, Oladimeji argues that the precedent set by Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), and United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), requires that restitution be based on facts either proven to a jury beyond a reasonable doubt or admitted by a defendant. In the present case, both sides concede that the restitution order was based on findings made by the judge, using the standard of preponderance of the evidence.

We delayed deciding this aspect of Ola-dimeji’s case pending our court’s resolution of United States v. Reifler, 446 F.3d 65 (2d Cir.2006). We have now ruled in Reifler that, under the precedents set by Appren-di, Blakely, and Booker, the Sixth Amendment does not bar a district court from imposing a restitution order that is based on findings it has made by a preponderance of the evidence. See Reifler, 446 F.3d at 114. Reifler’s holding, squarely on point in this case, requires that we reject Oladimeji’s Aoo/cer-based challenges to the restitution order.

C. Other Restitution Arguments

1. Loss caused by conduct underlying offense of conviction.

Oladimeji argues that the district court committed various other errors in formulating its restitution order, including that in ordering him to pay $42,545.72 in restitution for Count Five of his second indictment (i.e., possession of unauthorized[*158] access devices with intent to defraud), the court exceeded its authority under the Supreme Court’s ruling in Hughey v. United States, 495 U.S. 411, 110 S.Ct. 1979, 109 L.Ed.2d 408 (1990), in light of the fact that the $42,545.72 in damages arose not from his possession of those unauthorized access devices, which was the crime of conviction, but from their use. There is some arguable ambiguity in 18 U.S.C. § 3663A on the question whether restitution of losses deriving from use are mandated when a defendant is convicted of possession with intent to defraud. We find that the language of 18 U.S.C. § 3663A confirms that Congress did intend that restitution orders encompass such damages.

Pursuant to 18 U.S.C. § 3663A, a court sentencing a defendant convicted of offenses against property under Title 18, including offenses committed “by fraud or deceit,” 18 U.S.C. § 3663A(c)(l)(A)(ii), “shall order, in addition to ... any other penalty authorized by law, that the defendant make restitution to the victim of the offense,” 18 U.S.C. § 3663A(a)(l). A “victim” is defined as “a person directly and proximately harmed as a result of the commission of an offense for which restitution may be ordered including, in the case of an offense that involves as an element a scheme, conspiracy, or pattern of criminal activity, any person directly harmed by the defendant’s criminal conduct in the course of the scheme, conspiracy, or pattern.” 18 U.S.C. § 3663A(a)(2).

In Hughey, the Supreme Court considered the legality of a restitution order that encompassed damages caused by the defendant’s fraudulent use of many credit cards, where his conviction was for the fraudulent use only of a single card. See Hughey, 495 U.S. at 414-15, 110 S.Ct. 1979. The Court ruled that the courts lacked authority, under the relevant statute, ^[1] to order a defendant, who was charged with multiple offenses but pleaded guilty to only one, to make restitution for losses arising from related offenses to which he had not pleaded guilty. The Court based its ruling on its conclusion that the language of the statute indicated Congress’s intent that “the loss caused by the conduct underlying the offense of conviction establishes the outer limits of a restitution order.” Id. at 420, 110 S.Ct. 1979; see also id. at 413, 110 S.Ct. 1979 (a court may order “an award of restitution only for the loss caused by the specific conduct that is the basis of the offense of conviction”); United States v. Silkowski, 32 F.3d 682, 689-90 (2d Cir.1994).

Oladimeji argues that, under Hughey, the district court was not authorized by statute to order restitution to credit card companies based on the use of thirteen credit cards seized from Oladimeji’s residence, given that the offense to which he pleaded guilty was possession of unauthorized access devices with intent to defraud, not fraudulent use of the devices. As a result, he contends, the ordered restitution was for losses that were not “caused by the specific conduct that is the basis of the offense of conviction.” Hughey, 495 U.S. at 413,110 S.Ct. 1979.

We conclude that the principle of Hu-ghey does not bar the restitution order in this case. In Hughey the defendant pleaded guilty to illegal use of a single credit card; the sentencing court imposed resti[*159] tution for losses resulting from the defendant’s illegal use of other credit cards. The Supreme Court ruled that incorporating losses caused by use of the other cards into the restitution calculation was not permitted under the terms of the restitution statute, which authorized restitution to the victims only of the offense of conviction. Oladimeji, in contrast, pleaded guilty to a charge involving numerous credit cards. Section 1029(a)(3), which defines the offense of his conviction, applies only to possession with intent to defraud of “fifteen or more” unauthorized access devices. The restitution order was formulated to compensate the victims of the fraudulent use of the very cards covered by the charge.

The question nonetheless remains whether Oladimeji’s offense, consisting of possession of unauthorized access devices with intent to defraud, “result[edj” in loss of property to anyone “directly and proximately harmed as a result of the commission of [the] offense,” as those terms are defined in 18 U.S.C. § 3663A(b)(l) and 18 U.S.C. § 3663A(a)(2). In terms of the Supreme Court’s explanation in Hughey, the question is whether losses resulting from fraudulent use of the cards is “loss caused by the specific conduct that is the basis of the offense of conviction.” Hughey, 495 U.S. at 413, 110 S.Ct. 1979. Oladimeji’s offense — the possession of the unauthorized access devices with intent to defraud — was undoubtedly a but-for cause of the $42,545.72 in damages to the owners of the cards. On the other hand, mere possession of the cards, even with intent to defraud, was not sufficient to cause a loss. Fraudulent use was required.

The arguable ambiguity is resolved by the statutory definition of a “victim.” 18 U.S.C. § 3663A(a)(2). “Victim” is defined as “a person directly and proximately harmed as a result of the commission of an offense for which restitution may be ordered including, in the case of an offense that involves as an element a scheme, conspiracy, or pattern of criminal activity, any person directly harmed by the defendant’s criminal conduct in the course of the scheme, conspiracy, or pattern.” Id. (emphasis added). This language makes clear Congress’s intent to include losses resulting from harmful acts committed in the course of inchoate crimes.

It is clear under the statute that a defendant convicted of devising a scheme to defraud must be sentenced to restitution of the proceeds of the fraudulent action, even though the loss was caused not by the devising of the scheme alone but by its implementation. Section 1029(a)(3) includes as an element that the possession be “with intent to defraud.” Intent to defraud is a “scheme,” as used in § 3663A(a)(2). It follows that losses suffered as the result of the fraudulent use of a credit card whose illegal possession ivith intent to defraud is charged under § 1029(a)(3) are compensable by restitution orders under § 3663A(a)(l). Although the possession with intent to defraud without more did not cause the loss, the implementation of that intent to defraud did. We conclude that the statute reveals the intent of Congress that it be deemed to command restitution for frauds which implement the intent to defraud where the crime of conviction is possession with intent to defraud. ^[2]

[*160] 2. Accounting for home-equity loan.

Oladimeji also contends that the district court erred when it determined that Household Finance — the financial institution that Oladimeji had defrauded by using bogus documentation to secure a $30,000 home-equity loan — had suffered $30,000 in actual losses. He argues that Household Finance might have recovered some part of that $30,000 either through the sale of the property securing the loan or by loan repayments Oladimeji had already made to the institution. The court never addressed these possibilities in the sentencing proceedings. Oladimeji argues that the government therefore failed to meet its “burden of demonstrating the amount of the loss sustained by a victim as a result of the offense.” 18 U.S.C. § 3664(e).

We agree with the defendant that, had Household Finance recouped some part of the $30,000 — whether by receipt of loan payments or by foreclosure — it would have been error to require restitution in the full amount of the loan. See 18 U.S.C. § 3663A(b)(l)(B) (indicating that a court’s calculation of restitution must take into account any portion of property that has already been returned to the victim); see also United States v. Catoggio, 326 F.3d 323, 328-29 (2d Cir.2003) (confirming that restitution orders must reflect “actual losses”).

His challenge to the $30,000 restitution order nonetheless fails. The district court based its restitution order on the findings of the presentence report (“PSR”) that Oladimeji’s fraudulently obtained $30,000 loan “ha[d] been in default since July 2001”; that Oladimeji himself was heavily in debt but had no source of legitimate income; and that the underlying property was burdened with mortgages and liens exceeding its value. The district court, therefore, had a reasonable basis for finding that the bank had suffered a loss in the full amount of the loan. In the sentencing proceedings, Oladimeji made no contention that the bank had recouped, or could recoup, any part of its loss, although Judge Glasser asked Oladimeji’s counsel if he wished to be heard on any PSR-related issues. On the present appeal, moreover, Oladimeji offers nothing but conjecture as to the possibility that Household Finance might have recovered a part of the loan. Oladimeji has failed to establish any basis for vacating the restitution order.

CONCLUSION

For the foregoing reasons, the judgments of conviction and sentence are affirmed.