
501 F.3d 116 (2007)
Spencer DULAL-WHITEWAY, Petitioner,
v.
U.S. DEPARTMENT OF HOMELAND SECURITY, Respondent.
Docket No. 05-3098-ag.
United States Court of Appeals, Second Circuit.
Argued: March 27, 2007.
Decided: September 19, 2007.
*117 *118 Sandra Greene, York, PA, for petitioner.
Manuel A. Palau, Trial Attorney, Office of Immigration Litigation (Terri J. Scadron, Assistant Director, on the brief), for Peter D. Keisler, Assistant Attorney General, Civil Division, United States Department of Justice, Washington, DC, for respondent.
Before: FEINBERG, SOTOMAYOR and KATZMANN, Circuit Judges.
SOTOMAYOR, Circuit Judge:
Spencer Dulal-Whiteway ("Dulal") petitions for review of an order of the Board of Immigration Appeals ("BIA") affirming the decision of Immigration Judge ("IJ") Alan Vomacka ordering Dulal removed on the grounds that his conviction for making false statements in connection with the acquisition of a firearm, in violation of 18 U.S.C. § 922(a)(6), was a removable firearm offense within the meaning of 8 U.S.C. § 1227(a)(2)(C), and that his conviction for fraud in connection with unauthorized access devices, in violation of 18 U.S.C. § 1029(a)(2), was an aggravated felony within the meaning of 8 U.S.C. § 1101(a)(43)(M)(i). In re Spencer Hamilton Dulal-Whiteway, No. A45 164 992 (B.I.A. May 10, 2004), aff'g No. A45 164 992 (Immig. Ct. New York City May 27, 2003). We hold that the IJ did not err in finding Dulal removable for the firearm offense, but erred in finding him removable for the fraud offense. It was improper for the IJ and BIA to have relied upon a restitution order to determine that Dulal was convicted of an offense "involv[ing] fraud or deceit in which the loss to the victim or victims exceeds $10,000," 8 U.S.C. § 1101(a)(43)(M)(i), because no part of the record of conviction established that Dulal had been convicted of fraud causing loss over that amount. We GRANT in part and DISMISS in part Dulal's petition for review, VACATE the BIA's removal order insofar as it is based on a finding that Dulal was convicted of an aggravated felony, and REMAND for further proceedings consistent with this decision.

BACKGROUND
Dulal, a citizen of Trinidad and Tobago, was lawfully admitted to the United States on May 6, 1996. On March 22, 2001, a federal grand jury returned an indictment against him, alleging that he had stolen the identity of Wayne Nashaud Barakat and used that identity to obtain credit and calling cards, submit a car loan application, make withdrawals from Barakat's personal bank account and purchase firearms. Count One of the indictment charged Dulal with using a number of unauthorized access devices (specifically, credit and calling cards) to obtain things of value aggregating $1000 or more, in violation of 18 U.S.C. § 1029(a)(2). Counts Two, Three and Four, which the government ultimately moved to dismiss, charged Dulal with one *119 count of making false statements in connection with loan applications, in violation of 18 U.S.C. § 1014, and two counts of bank fraud, in violation of 18 U.S.C. § 1344. Count Five alleged that Dulal gave Barakat's name and Social Security number to Alexander's Pawn Shop in order to purchase a .380 caliber pistol, and charged Dulal with making false statements in connection with the acquisition of a firearm in violation of 18 U.S.C. § 922(a)(6). Count Six, which the government also eventually moved to dismiss, charged a similar crime in connection with the purchase of a different firearm.
On October 5, 2001, Dulal appeared before the United States District Court for the Southern District of Florida (Hurley, J.) and entered a guilty plea as to Counts One and Five. The court accepted his plea, and dismissed the other counts on the motion of the government. The Probation Office prepared a Presentence Investigation Report ("PSR"), which, in relevant part, identified the seven unlawfully obtained credit cards forming the basis of the conduct charged in Count One, and set forth the amount of loss associated with each card. The PSR noted that the Mandatory Victims Restitution Act ("MVRA"), 18 U.S.C. § 3663A(a)(1), required the court to order restitution, and recommended that Dulal be ordered to pay $20,824.09, the sum of the losses from the seven cards, "to the victims in the attached list," presumably referring to the list of unlawfully obtained cards.
The district court sentenced Dulal principally to thirteen months' imprisonment for each of the two counts of conviction, to be served concurrently, imposed a three-year term of supervised release, and ordered him to pay restitution. The restitution order set the total amount of loss and the restitution amount at $20,824.09, and identified the payees as those "indicated in the Presentence Investigation Report."
On April 3, 2002, the Immigration and Naturalization Service ("INS")[1] issued Dulal a notice to appear ("NTA"), alleging that his conviction for fraud in connection with access devices was an offense that "involves fraud or deceit in which the loss to the victim or victims exceeds $10,000," 8 U.S.C. § 1101(a)(43)(M)(i), and that he was therefore removable as an aggravated felon under 8 U.S.C. § 1227(a)(2)(A)(iii). Seven months later, the INS lodged an additional charge against Dulal, alleging that his conviction for making false statements to acquire a firearm was a firearm offense rendering him removable under 8 U.S.C. § 1227(a)(2)(C), which authorizes the removal of aliens convicted of "purchasing, selling, offering for sale, exchanging, using, owning, possessing, or carrying" a firearm or attempting or conspiring to do so.
Dulal appeared with counsel before the Immigration Court in New York (Vomacka, I.J.) on May 27, 2003. Dulal admitted the facts alleged in the NTA, but denied that his convictions rendered him removable. He did not seek any relief from removal. The IJ rejected Dulal's arguments and ordered him removed. The IJ found first that 8 U.S.C. § 1227(a)(2)(C) "is broad enough to cover a crime committed in reference to purchasing or attempting to purchase a firearm, even if the crime is not related to violence or firearms, as in this case, making false statements." Thus, the IJ found, Dulal's conviction under 18 U.S.C. § 922(a)(6) made him removable. *120 With regard to Dulal's fraud offense, the IJ rejected Dulal's argument that the record failed to establish a loss to his victims greater than $10,000, as required to establish that the crime was an aggravated felony. The IJ held that it was proper to consult both the PSR and the restitution order to determine the amount of loss resulting from the offense, and that these documents reflected a loss of slightly over $20,000. He thus found that Dulal also was removable on the second ground of having been convicted of an aggravated felony.
Dulal appealed the IJ's determination to the BIA, which affirmed without opinion. He timely petitioned this Court for review.

DISCUSSION
I. Jurisdiction and Standard of Review
Under the REAL ID Act of 2005, Pub.L. No. 109-13, 119 Stat. 231, this Court lacks jurisdiction to review orders of removal based on an alien's conviction for certain criminal offenses, including aggravated felonies and firearm offenses. Our jurisdiction to consider "questions of law," 8 U.S.C. § 1252(a)(2)(D), however, allows us to review whether an alien's conviction qualifies as a removable offense under the immigration laws. See Blake v. Gonzales, 481 F.3d 152, 155-56 (2d Cir.2007). If we find that it does, we must dismiss the petition for lack of jurisdiction. See id. at 156.
"Where, as here, the BIA summarily affirms the IJ pursuant to 8 C.F.R. § 1003.1(e)(4)(I), we review the IJ's decision directly." Dos Santos v. Gonzales, 440 F.3d 81, 83 (2d Cir.2006). Though we ordinarily grant deference under Chevron U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), to the BIA's construction of the immigration laws, we do not "extend Chevron deference to any statutory construction of the INA set forth in a summarily affirmed IJ opinion," like the one in this case. Shi Liang Lin v. U.S. Dep't of Justice, 416 F.3d 184, 191 (2d Cir.2005). We also do not extend Chevron deference to the BIA's or an IJ's construction of federal criminal laws. Michel v. INS, 206 F.3d 253, 262 (2d Cir.2000).
As noted, the IJ found Dulal removable on two grounds. We address both grounds, despite finding Dulal removable on the first ground, because the parties have agreed that removal for a firearms offense and removal for an aggravated felony carry different collateral consequences. For example, removal for an aggravated felony imposes a permanent bar on an alien's reentry to the United States, while removal based on a firearm offense imposes only a ten-year bar. 8 U.S.C. § 1182(a)(9)(A)(ii) ("Any alien . . . who . . . has been removed under [8 U.S.C. § 1229a] . . . and who seeks admission within 10 years of the date of such alien's departure or removal (. . . or at any time in the case of an alien convicted of an aggravated felony) is inadmissible."). The parties have also conceded that were we to decline to reach the BIA's aggravated felony determination, that finding likely would continue to bind future agency adjudicators. Cf. Johnson v. Ashcroft, 378 F.3d 164, 172 (2d Cir.2004) ("[R]es judicata may, in appropriate circumstances, apply to removal proceedings."). Because a refusal on our part to reach the aggravated felony ground could result in harsher immigration consequences to Dulal, he has a stake in our correcting any erroneous finding by the BIA concerning an aggravated felony conviction. See United States v. Hamdi, 432 F.3d 115, 121 (2d Cir.2005) ("`[H]av[ing] a chance at reentering the United States' in the discretion of the immigration authorities `is sufficient to give *121 petitioner a personal stake in the litigation that presents a live case or controversy.'") (quoting Swaby v. Ashcroft, 357 F.3d 156, 161 (2d Cir.2004) (second alteration in original)); cf. Kamagate v. Ashcroft, 385 F.3d 144, 151 (2d Cir.2004) (holding that an alien's challenge to his removal order was not rendered moot by his actual removal because he could be subject to "significant adverse collateral consequences from the fact that his removal order identifies that crime as an aggravated felony" which "a judicial ruling in [his] favor could remedy").
II. Removability for Firearms Conviction
Dulal's first count of conviction was under 18 U.S.C. § 922(a)(6), which provides, in pertinent part:
It shall be unlawful . . . for any person in connection with the acquisition or attempted acquisition of any firearm or ammunition from a licensed importer, licensed manufacturer, licensed dealer, or licensed collector, knowingly to make any false or fictitious oral or written statement or to furnish or exhibit any false, fictitious, or misrepresented identification, intended or likely to deceive such importer, manufacturer, dealer, or collector with respect to any fact material to the lawfulness of the sale or other disposition of such firearm or ammunition under the provisions of this chapter.
The IJ concluded that Dulal's conviction under 18 U.S.C. § 922(a)(6) rendered him removable under 8 U.S.C. § 1227(a)(2)(C), which authorizes the removal of
[a]ny alien who at any time after admission is convicted under any law of purchasing, selling, offering for sale, exchanging, using, owning, possessing, or carrying, or of attempting or conspiring to purchase, sell, offer for sale, exchange, use, own, possess, or carry, any weapon, part, or accessory which is a firearm or destructive device (as defined in section 921(a) of Title 18) in violation of any law. . . .
The IJ reasoned that this provision was "broad enough" to encompass Dulal's fraudulent statements conviction. We agree.
In determining whether an alien's conviction was for an offense that renders him or her removable under the federal immigration laws, the BIA and this Court have employed a "categorical approach." Blake, 481 F.3d at 156. Under this approach, we "look to the elements and the nature of the offense of conviction, rather than to the particular facts relating to petitioner's crime," Canada v. Gonzales, 448 F.3d 560, 565 (2d Cir.2006) (internal quotation marks omitted), in order to determine whether "the minimum criminal conduct necessary to sustain a conviction under a given statute" amounts to a removable offense, Vargas-Sarmiento v. U.S. Dep't of Justice, 448 F.3d 159, 167 (2d Cir.2006) (quotation marks and alterations omitted). See also Dickson v. Ashcroft, 346 F.3d 44, 48 (2d Cir.2003) ("In describing the categorical approach, we have held that every set of facts violating a statute must satisfy the criteria for removability in order for a crime to amount to a removable offense; the BIA may not justify removal based on the particular set of facts underlying an alien's criminal conviction."). Where "a criminal statute encompasses diverse classes of criminal actssome of which would categorically be grounds for removal and others of which would not we have held that such statutes can be considered `divisible' statutes," at least under some circumstances. Id. (quoting Kuhali v. Reno, 266 F.3d 93, 106 (2d Cir. 2001)); see also Vargas-Sarmiento, 448 F.3d at 167 ("A criminal statute is `divisible' if it encompasses multiple categories *122 of offense conduct, some, but not all, of which would categorically constitute" a removable offense.). Faced with a divisible statute, we examine the "record of conviction" to ascertain whether it indicates that the alien's own conviction fell into a category of the divisible statute that proscribes removable offenses. See Dickson, 346 F.3d at 48-49. We, and other courts, have described this process of dividing the statute and consulting the record of conviction as the "modified categorical approach." Canada, 448 F.3d at 566.
Here, Dulal argues that he cannot be found removable under the categorical approach because the conduct necessary to sustain a conviction under § 922(a)(6) is different in nature than the conduct set forth in the removability statute. In essence, he claims that the gravamen of a § 922(a)(6) offense is the making of false statements or the misrepresentation of one's identity, not the "affirmative act" of acquiring or possessing a firearm. Section 922(a)(6) is fundamentally a fraud offense, he contends, not a firearm offense.
The plain language of § 922(a)(6), however, requires as an element of the offense that the fraudulent statements be made "in connection with the acquisition or attempted acquisition" of a firearm.[2]See Huddleston v. United States, 415 U.S. 814, 819, 94 S.Ct. 1262, 39 L.Ed.2d 782 (1974) ("Reduced to a minimum, § 922(a)(6) relates to any false statement made `in connection with the acquisition . . . of a firearm' from a licensed dealer. . . ."); see also United States v. Dillon, 150 F.3d 754, 759 (7th Cir.1998) ("To sustain a conviction that a defendant violated § 922(a)(6), the government must introduce evidence to establish (1) that the defendant knowingly made a false statement to a licensed firearms dealer, (2) that the false statement was made in acquisition of a firearm, and (3) that the false statement was intended to or likely to deceive the firearms dealer as to the lawfulness of the sale of a firearm.").
The BIA has read § 1227(a)(2)(C) to encompass the types of conduct listed purchasing, possessing, and carrying firearms, among others"not simply as crimes in their own right, but also as elements of other crimes." Kuhali, 266 F.3d at 102-03 (describing BIA's position in, among other cases, In re Kuhali, No. A35 283 015 (B.I.A. July 29, 1999)). Thus, so long as at least one element necessary for conviction itself constitutes an action enumerated in § 1227(a)(2)(C), the BIA would find all offenses under the statute removable. We have endorsed this construction of the statute as a reasonable one. Kuhali, 266 F.3d at 103; cf. Mizrahi v. Gonzales, 492 F.3d 156 (2d Cir. 2007) (employing similar reasoning to hold that a controlled substance offense renders an alien inadmissible so long as "an essential element" of that crime satisfies the criteria for removability). In Kuhali, the crime of conviction was conspiracy to export firearms and ammunition without a license, in violation of 18 U.S.C. §§ 2778 and 371. 266 F.3d at 103-04. We concluded that possession of a firearm, as required by the removal statute, was an element of the statutory offense because the act of export necessarily involved constructive possession of the item being exported. Id. at 104-05.
Here, anyone convicted of violating § 922(a)(6) must either have acquired or attempted to acquire a firearm. Thus, all such individuals have "purchas[ed] . . . or . . . attempt[ed] . . . to purchase" a firearm within the meaning of 8 U.S.C. § 1227(a)(2)(C), or, to the extent that the verb "to acquire" has some meaning beyond *123 merely "to purchase," have "exchang[ed], . . . [or] possess[ed], or . . . attempt[ed] . . . [to] exchange, . . . [or] possess" a firearm. See Huddleston, 415 U.S. at 820, 94 S.Ct. 1262 (holding that "acqui[re]" in § 922(a)(6) means "to come into possession, control, or power of disposal of," and encompasses the act of redeeming a firearm by a pawnor (internal quotation marks omitted)); Kuhali, 266 F.3d at 104-05 (interpreting the term "possess[ion]" in 8 U.S.C. § 1227(a)(2)(C) broadly to include either "tangible, physical dominion or control over an object" or "the power and intention to exercise dominion and control over an object without actually possessing it"). We thus reject Dulal's argument that his offense was simply fraud, as his fraudulent activity necessarily involved firearm-related conduct that is removable under § 1227(a)(2)(C).
Section 922(a)(6), however, also criminalizes the making of false statements in connection with the acquisition of ammunition, which, unlike the acquisition of a firearm, is not removable conduct. Thus, it is possible to be convicted of violating § 922(a)(6) without having committed a removable offense. Because not "every set of facts violating [the] statute" satisfies the criteria for removability, we cannot find Dulal removable under the categorical approach. Dickson, 346 F.3d at 48.[3] As we did when confronted with this firearm/ammunition distinction in Kuhali, we apply the modified categorical approach, dividing the statute of conviction and consulting the record of conviction to determine whether Dulal's conviction was related to firearms or to ammunition. See Kuhali, 266 F.3d at 106-07. Dulal's judgment of conviction describes the "nature of [his] offense" under § 922(a)(6) as "[f]alse statements for acquisition of a firearm," and Count Five of the indictment, to which Dulal pleaded guilty, explicitly describes misrepresentations made in connection with the acquisition of a firearm. Thus, the IJ correctly concluded that Dulal's conviction under § 922(a)(6) constituted a removable firearm offense under 8 U.S.C. § 1227(a)(2)(C), and we dismiss the portion of his petition challenging that determination for lack of jurisdiction.
III. Removability for Aggravated Felony Conviction
Title 8, Section 1227(a)(2)(A)(iii) of the United States Code renders removable "[a]ny alien who is convicted of an aggravated felony at any time after admission." Title 8, Section 1101(a)(43)(M)(i) of the United States Code defines "aggravated felony" as, inter alia, an offense that "involves fraud or deceit in which the loss to the victim or victims exceeds $10,000."
Dulal was convicted of fraud in connection with access devices in violation of 18 U.S.C. § 1029(a)(2), which provides:
Whoever . . . knowingly and with intent to defraud traffics in or uses one or more unauthorized access devices during any one-year period, and by such conduct obtains anything of value aggregating $1,000 or more during that period . . . shall, if the offense affects interstate or foreign commerce, be punished as provided. . . .
Dulal concedes that his conviction under this statute "involves fraud or deceit" within the meaning of the removability provision. He contends, however, that his record of conviction fails to establish that the loss to the victims of his crime exceeded $10,000. In particular, he argues that it *124 was error for the IJ to consult the PSR and the restitution order, which indicated that the loss to his victims was roughly $20,000, because neither should have been considered part of his record of conviction. We agree that relying upon these materials to prove that Dulal was convicted of a fraud involving loss greater than $10,000 violated the modified categorical approach to determining aliens' removability based on criminal convictions.
Our holding has its roots in Taylor v. United States, 495 U.S. 575, 110 S.Ct. 2143, 109 L.Ed.2d 607 (1990), and its progeny, Shepard v. United States, 544 U.S. 13, 17, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005), two sentencing cases in which the Supreme Court described the basic structure and underlying rationales of the modified categorical approach.
In Taylor, the Supreme Court considered the circumstances under which a court could apply a statutory enhancement to the sentence of a defendant with a prior conviction for burglary. See 495 U.S. at 578, 110 S.Ct. 2143 (considering application of 18 U.S.C. § 924(e), which provides for a sentence enhancement for a defendant with three previous convictions for, inter alia, a "violent felony," defined in part as "any crime . . . [that] is burglary"). After concluding that the word "burglary" in the statute referred to the "generic sense in which the term is now used in the criminal codes of most states," i.e., a crime having "the basic elements of unlawful or unprivileged entry into, or remaining in, a building or structure, with intent to commit a crime," the Court addressed "the problem of applying this conclusion to cases in which the state statute under which a defendant is convicted varies from the generic definition of `burglary.'" Id. at 599, 110 S.Ct. 2143. To determine whether a defendant's prior conviction was for the generic crime, the Court held, a sentencing court should use "a formal categorical approach, looking only to the statutory definitions of the prior offenses, and not to the particular facts underlying those convictions." Id. at 600, 110 S.Ct. 2143. The Court justified its adoption of this approach on three grounds relevant to our present discussion. First, the language of the sentence-enhancement statute stated that it applied to persons who had been "convicted" of violent felonies, not persons "who ha[d] committed" such crimes. Id. (emphasis added). Second, the legislative history of the statute indicated that Congress did not contemplate "an elaborate factfinding process" by the sentencing court. Id. at 601, 110 S.Ct. 2143. And third, a factual approach would entail "daunting" "practical difficulties and potential unfairness." Id. The "practical difficulties" would include those associated with taking and weighing a vast array of extraneous evidence offered to prove the basis of the defendant's former conviction; the "potential unfairness" concerned, among other things, possible infringement of the right to a jury trial. Id. Finally, the Court recognized an exception to the categorical approach. Where a defendant's prior burglary conviction was under a statute broader than the generic offense (for example, because it also encompassed entry into an automobile), the enhancement would nonetheless be applicable in "a narrow range of cases where a jury was actually required to find all the elements of generic burglary." Id. at 602, 110 S.Ct. 2143. In such cases, the sentencing court could go beyond the mere fact of conviction to examine the "indictment or information and jury instructions," in order to determine whether the jury found all the required elements, such as entry into a building rather than an automobile. Id.
In Shepard, the Court extended the holding of Taylor, including the "exception" *125 to the categorical approach,[4] to cases where the prior conviction resulted from a guilty plea rather than a jury verdict. 544 U.S. 13, 17, 125 S.Ct. 1254, 161 L.Ed.2d 205. The Court concluded that in cases resting on pleas, the sentencing court could consider only those facts (a) that the defendant had actually admitted or confirmed, and (b) upon which the defendant's plea "necessarily rested" (i.e., because they constituted an element of the offense). Id. at 20-21, 125 S.Ct. 1254 (internal quotation marks omitted). Such facts would have to be reflected in the defendant's charging document and "the statement of factual basis for the charge, shown by a transcript of the plea colloquy or by written plea agreement presented to the court, or by a record of comparable findings of fact adopted by the defendant upon entering the plea." Id. at 20, 125 S.Ct. 1254; see also id. at 26, 125 S.Ct. 1254 ("We hold that enquiry under the [sentence-enhancement provision] to determine whether a plea of guilty to burglary defined by a nongeneric statute necessarily admitted elements of the generic offense is limited to the terms of the charging document, the terms of a plea agreement or transcript of colloquy between judge and defendant in which the factual basis for the plea was confirmed by the defendant, or to some comparable judicial record of this information."). Consequently, the Court rejected the government's argument that the enhancement could be based on a police report alleging facts (namely, that the defendant had broken into a building, rather than a boat or car) that would satisfy the elements of the generic crime. Id. at 21, 125 S.Ct. 1254. The Court reasoned that the limitations it imposed on the universe of materials a sentencing court could consult was necessary to effectuate the purposes discussed in Taylor: the implementation of congressional intent (as evidenced by the language of the statute requiring "convictions") and the avoidance of collateral trials to address evidentiary disputes. Id. at 21, 23 n. 4, 125 S.Ct. 1254. In addition, the Court found, "[d]evelopments in the law since Taylor" in the area of Sixth Amendment jury rights "provide[d] a further reason to adhere to the demanding requirement" that a prior plea necessarily have admitted the requisite elements. Id. at 24, 125 S.Ct. 1254. To permit judicial factfinding beyond what was apparent in the prior plea, the Court suggested, might run afoul of Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000).
In Ming Lam Sui v. INS, 250 F.3d 105 (2d Cir.2001), we reviewed the BIA's application of a categorical approach to determine when an alien's conviction renders him or her removable under the immigration laws. Id. at 116 & n. 10. Specifically, we sought to determine whether Sui was removable under 8 U.S.C. § 1227(a)(2)(A)(iii), which defines an aggravated felony as fraud in which the loss to the victims exceeds $10,000, where his criminal conviction was for attempt to make, utter, or possess counterfeit securities (in any amount) with the intent to deceive. Id. at 108. Finding the sentencing and removal contexts analogous, we held that Taylor's reasoning similarly justified the use of the categorical approach to establish removability. Id. at 116-17. We noted that, like the burglary sentencing enhancement, the Immigration and Nationality Act ("INA"), 8 U.S.C § 1227(a)(2)(A)(iii), rendered removable "an alien who has been `convicted' of an aggravated felony, not one who has `committed' an aggravated felony." Id. at 117. Moreover, we reasoned, nothing in the legislative history suggested a factfinding role *126 for the BIA in ascertaining whether an alien had committed an aggravated felony, just as, in Taylor, nothing suggested such a role for the sentencing court in evaluating the factual basis of a prior burglary conviction. Id. We also found that the practical evidentiary difficulties and potential unfairness associated with looking behind the offense of conviction were "no less daunting" in the immigration than in the sentencing context. Id. Finally, acknowledging the exception in Taylor, we concluded that when a statute of conviction criminalizes both conduct that would constitute a removable offense and conduct that would not, IJs might appropriately consult an indictment or jury instructions to determine the basis of an alien's conviction. Id. at 117-18. Because Sui's conviction followed a guilty plea, we examined his indictment, which alleged only that Sui possessed $22,700 in securities with intent to deceive. Id. at 118. We determined that these facts were not sufficient to establish a substantial step toward causing a loss over $10,000, and therefore concluded that Sui was not removable. Id. at 118-19.[5]
As described above, this Court, following Sui, has applied the modified categorical approach as a two-step inquiry: first, we determine if the statute is "divisible," such that some categories of proscribed conduct render an alien removable and some do not; second, we consult the record of conviction to ascertain the category of conduct of which the alien was convicted. See Dickson, 346 F.3d at 48.
In the present case, the government argues that 18 U.S.C. § 1029(a)(2), the statute criminalizing fraud in connection with access devices, is a divisible statute. The provision encompasses fraud by which the perpetrator obtains a thing or things valuing more than $1000; however, under 8 U.S.C. § 1101(a)(43)(M)(i), such fraud is only a removable offense when the loss to the victims exceeds $10,000. Thus, the government argues, the statute proscribes some conduct that is not removablefraud causing a loss between $1000 and $10,000and some conduct that is removablefraud causing a loss greater than $10,000and we should consult the record of conviction to determine which of the two types of conduct actually underlay Dulal's conviction.
In Sui, we implicitly assumed that a statute criminalizing the possession of counterfeit securities with intent to deceive was divisible because it comprised non-removable conduct causing loss up to $10,000 and removable conduct causing loss greater than $10,000. See Sui, 250 F.3d at 118. Our analysis, however, preceded our earliest exposition of divisibility as its own concept,[6] and did not consider the appropriateness of our finding under the categorical approach. Up to this point, we have explicitly found statutes divisible only where the removable and non-removable offenses they describe are listed in different subsections or comprise discrete elements of a disjunctive list of proscribed conduct. In Kuhali, for example, the alien's statute of conviction, 22 U.S.C. § 2778, prohibited the export of defense articles on the United States Munitions List. 266 F.3d at 104. That list enumerated, in separate numbered categories, both firearmsthe possession of which is a removable offenseand ammunitionthe possession of which is not a removable offense. Id. at 106. We divided the statute *127 and consulted the alien's "judgment of conviction" to determine that his conviction was for export of firearms, rendering him removable. Id. at 107. In Dickson, the alien was convicted under a statute proscribing unlawful imprisonment, the definitional section of which describes, in separate subsections, two forms of unlawful restraint: restraint of a competent adult and restraint of a child or incompetent adult. 346 F.3d at 47. Because the former would necessarily involve the risk of force, making it a removable offense, while the latter would not, we found the statute divisible. Id.
In Canada, we explicitly confronted an alien's argument that the statute under which he was convicted, which proscribed assault on public safety officers, was not divisible because the categories of officers covered by the statute were listed one after another in a single sentence, rather than in separate subsections. 448 F.3d at 567. Emphasizing that "the various categories of public safety officers protected by the statute are listed sequentially, each separated by a comma, and are phrased in the disjunctive," we concluded that the categories were easily distinguished, and thus the statute was not meaningfully different from one featuring discrete subsections. Id. at 568. Since Canada, however, we have not explicitly queried whether this logic extends to a statutesuch as the one at issue herewhere only one type of generic conduct (fraud to obtain things valuing over $1000) is proscribed, but an alien can commit the conduct both in ways that would render him removable (fraud over $10,000) and in ways that would not (fraud between $1000 and $10,000). Neither Supreme Court nor Second Circuit precedent compels a conclusion one way or the other.
There are strong arguments for finding divisible only those statutes where the alternative means of committing a violation, some of which constitute removable conduct and some of which do not, are enumerated as discrete alternatives. Were we not to impose this limit on the divisibility inquiry, we would deem a far greater number of criminal statutes divisible, and would thus more frequently consult the alien's record of conviction. At its extreme, this practice would call into question the categorical approach's commitment to a limited review of the "fact of conviction," rather than the "particular factual circumstances" underlying a conviction. Dickson, 346 F.3d at 52. Moreover, resting immigration determinations on anything beyond the actual language of the criminal statute could, at least in principle, jeopardize the ex ante fairness generally ensured by the categorical approach. See Michel, 206 F.3d at 264 (deeming the categorical approach "sound" because "[i]t is the essence of evenhanded administration of the law to define rules ex ante and apply them regardless of the particular circumstances of a given case"). And because resorting to the record of conviction involves some additional level of administrative burden, doing so less frequently would serve, to a limited extent, the practical goals set forth in Taylor and Shepard.
The Third Circuit, apparently responding to these concerns, has determined that a criminal statute may be considered divisible only if one of two conditions is met. See Singh v. Ashcroft, 383 F.3d 144, 161-62 (3d Cir.2004). The first of these is that the statute of conviction is phrased in the disjunctive or divided into subsections, because such a statutory structure "call[s] for an exploration of which of the alternative elements was the actual basis for conviction." Id. at 162. The second is that the relevant federal immigration statute enumerating removable crimes "invite[s] inquiry into the facts underlying the conviction at issue." Id. at 161. The Court *128 opined that "[t]he qualifier `in which the loss to the victim or victims exceeds $10,000' in 8 U.S.C. § 1101(a)(43)(M)(i) is the prototypical exampleit expresses such a specificity of fact that it almost begs an adjudicator to examine the facts at issue." Id.
Of course, we could also take the position that all statutes of conviction may be considered "divisible" regardless of their structure, so long as they contain an element or elements that could be satisfied either by removable or non-removable conduct. This approach also has much to recommend it. Although neither Taylor and Shepard nor Sui addressed the concept of "divisibility" per se, both, by proceeding to examine the individual's record of conviction, implicitly assumed what we now refer to as the statute's divisibility.[7] These cases suggest that while the issue of statute divisibility and reliance upon the record of conviction are theoretically separable, in practice they demand a single inquiry: has an alien been actually and necessarily convicted of a removable offense? More importantly, a broader concept of divisible statutes could more fully effectuate the purpose of the immigration laws. Statutes of conviction rarely correlate precisely with statutes of removabilityfor example, few statutes criminalizing fraud enumerate distinct violations corresponding to the $10,000 loss amount required by the removability statute at issue in this case. Far more frequently, an alien's conviction will have been under a criminal statute structured like 18 U.S.C. § 1029(a)(2), delineating a single crime that can be committed both by removable and non-removable conduct. In order to countenance the removal of such aliens (and thus implement Congress's desire that aliens committing fraud causing loss in excess of $10,000 be removed), we would have to find the statute divisible and consult the record of conviction.
In any event, we need not decide this question because Dulal has not challenged the divisibility of 18 U.S.C. § 1029(a)(2). Accordingly, we too presume that the statute is divisible and proceed, as did the IJ, to examine Dulal's record of conviction. The government maintains that it was proper for the IJ to rely upon both the PSR and the restitution order as part of that record in order to establish the loss amount associated with Dulal's fraud and thus his removability. We disagree.
In applying the modified categorical approach, we have looked to a variety of sources as part of the "record of conviction." Drawing from the list of materials that may supply "proof of a criminal conviction," 8 U.S.C. § 1229a(c)(3)(B),[8] we *129 have stated that permissible materials include a charging document (such as an indictment), a signed plea agreement, a verdict or judgment of conviction, a record of the sentence; a plea colloquy transcript, and jury instructions. See Dickson, 346 F.3d at 53; see also Canada, 448 F.3d at 566.
The government's argument that a PSR is properly considered among these materials, such that the IJ could rely upon the loss amount it described, is foreclosed by Dickson, where we rejected a virtually identical claim. 346 F.3d at 46, 48. There, as described above, the IJ relied upon the narrative statement of facts in Dickson's PSR to show that his conviction under a divisible statute was for removable, as opposed to non-removable, conduct. Id. at 53. We vacated the BIA's affirmance of the IJ's decision, holding that "the BIA may not rely on the factual narratives in a PSR to determine the crime for which an alien has been convicted." Id. at 55.[9] We reasoned that because a PSR is designed to be a sentencing aid, and therefore can contain various types of background information and details about a crime drawn from probation officers' own interviews, "it typically describes conduct that demonstrates the commission of an offense even if the alien was never convicted of it." Id. at 54. We held that these unproven (and sometimes inadmissible) facts were an inappropriate basis on which to rest a removal decision. Id. Indeed, Sui already had recognized this when it held that the IJ erred in relying on the PSR to indicate the underlying facts of the alien's conviction. 346 F.3d at 116-18. In the instant case, the fact that the district court in Dulal's criminal prosecution referred to the PSR in its restitution order to identify the payees is irrelevant to the rationales we articulated in Dickson, as is the fact that Dulal's criminal attorney did not object to the PSR's loss calculations. We therefore reject the government's argument that the IJ properly consulted the loss amount set forth in Dulal's PSR.
The restitution order itself provides the same information about the amount of loss caused by Dulal's fraud, however, and neither Dickson nor Sui, nor *130 any other Second Circuit case, has addressed whether the information in a restitution order may establish that an alien's conviction was for a removable offense. As the government notes, such an order is a "record of sentence," which Dickson stated (albeit in dicta) forms part of the record of conviction. 346 F.3d at 53; see also 8 U.S.C. § 1229a(c)(3)(B)(ii). Sui and Dickson, however, relied on Taylor,[10] upon whose reasoning the Supreme Court has since elaborated in Shepard. And under the Taylor-Shepard modified categorical approach, Dulal's restitution order does not fall within the permissible "evidentiary cast." Shepard, 544 U.S. at 21, 125 S.Ct. 1254. As Shepard carefully explained, when determining whether a prior conviction in a pleaded case was based on a particular offense (there, generic burglary), the court's inquiry should be limited to facts on which "the plea had `necessarily' rested." Id. (citing Taylor, 495 U.S. at 602, 110 S.Ct. 2143 (emphasis added)). These, Shepard held, could be gleaned from the terms of the charging document, a written plea agreement, or a statement of facts confirmed by the defendant as indicated in the transcript of the plea colloquy. Id. at 20, 125 S.Ct. 1254. Though the Shepard Court did not address the issue of a restitution order, its logic clearly excludes such a document. The restitution set by a judge is based on a loss amount established by a preponderance of the evidence and need not be tied to the facts admitted by a defendant's plea. See 18 U.S.C. § 3664(e) ("Any dispute as to the proper amount or type of restitution shall be resolved by the court by the preponderance of the evidence."); United States v. Reifler, 446 F.3d 65, 118 (2d Cir.2006) (rejecting defendants' contentions "that the orders requiring them to make restitution for loss amounts not admitted in their plea allocutions violated their rights under the Sixth Amendment as enunciated in [United States v.] Booker, [543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005)]," because the "principle that jury findings, or admissions by the defendant, establish the `maximum' authorized punishment has no application to MVRA orders of restitution"). In other words, the amount of restitution is not constrained by facts on which the plea "necessarily" rested.
Of course, Taylor and Shepard were sentencing decisions, and differences between criminal punishment and the civil removal power might justify a circumscribed application of those decisions in the latter context. The First Circuit so concluded in Conteh v. Gonzales, 461 F.3d 45 (1st Cir.2006), when it "[d]ecline[d] the invitation to transplant the categorical approach root and branchwithout any modification whateverinto the civil removal context":
Instead, we hold that, in removal proceedings . . . the government is not required to show[,] . . . where a guilty plea has taken place, that the defendant necessarily admitted[] every element of an offense enumerated in 8 U.S.C. § 1101(a)(43). Rather, the government bears the burden of proving, by clear and convincing evidence derived solely from the record of the prior proceeding, that (i) the alien was convicted of a crime and (ii) that crime involved every element of one of the enumerated offenses.
Id. at 55. Taylor and Shepard, the court explained, were "informed by constitutional concerns," which are "crucial in the criminal context but entirely irrelevant in *131 the removal context." Id. Moreover, the court reasoned that the pure categorical approach "impermissibly elevates the government's burden in civil removal proceedings," id., effectively requiring a showing of removability beyond a reasonable doubt rather than by clear, unequivocal and convincing evidence, as provided in the INA, see 8 U.S.C. § 1229a(c)(3)(A). Applying its adapted, less stringent approach, the court concluded that the alien's restitution order, imposing $34,200 in restitution, permitted it to conclude that the alien's conviction was for removable conduct. Conteh, 461 F.3d at 61.
For the reasons that follow, we disagree with the First Circuit, and hold that the BIA, in determining whether an alien is removable based on a conviction for an offense set forth in the INA, may rely only upon information appearing in the record of conviction that would be permissible under the Taylor-Shepard approach in the sentencing context. For convictions following a trial, the BIA may rely only upon facts actually and necessarily found beyond a reasonable doubt by a jury or judge in order to establish the elements of the offense, as indicated by a charging document or jury instructions. For convictions following a plea, the BIA may rely only upon facts to which a defendant actually and necessarily pleaded in order to establish the elements of the offense, as indicated by a charging document, written plea agreement, or plea colloquy transcript.[11] The "necessarily pleaded" requirement links the record of conviction inquiry to the divisibility inquiry: once we determine that a criminal statute is divisible, because one or more of its elements can be satisfied both by conduct that is removable and by conduct that is not, we may consult the record of conviction to determine which type of conduct represents the basis of the conviction.
Three principles compel our holding. First, as we noted in Sui, it is sound statutory construction to accord the words of the INA their plain meaning. See Sui, 250 F.3d at 117. The aggravated felony removal provision, 8 U.S.C. *132 § 1227(a)(2)(A)(iii), "renders deportable an alien who has been `convicted' of an aggravated felony, not one who has `committed' an aggravated felony." Sui, 250 F.3d at 117. Restitution orders, like other sentencing determinations, need not be based on facts of which a defendant was actually "convicted," i.e., those established beyond a reasonable doubt or to which the defendant admitted. Here, for example, Dulal was only "convicted" of committing fraud causing loss of greater than $1000, not of the $20,824.09 indicated in the restitution order. Our holding also implements the statutory requirement that IJs determine removability by "clear, unequivocal and convincing evidence." 8 U.S.C. § 1229a(c)(3)(A). For an IJ to rely upon sentencing facts established by the lower preponderance of the evidence standard would permit the government to order an alien removed in the absence of the clear, unequivocal and convincing evidence required by law. Nor is the language of 8 U.S.C. § 1229a(c)(3)(B), describing documentation that establishes "proof of convictions," in tension with our holding, because a restitution orderlike the other documents listedmay still offer proof that a conviction exists. It simply may not be read to establish that the underlying facts of that conviction constitute a removable offense.[12]See Dickson, 346 F.3d at 53 (explaining the distinction between reliance on a PSR "for its indication of the `existence of a conviction,'" and reliance on it "for its narrative statement of the facts underlying Dickson's offense").
Second, the Taylor and Shepard Courts' concern about the "daunting" practical difficulties associated with scrutinizing the facts underlying a conviction is equally applicable in the removal context. We have emphasized that the BIA and reviewing courts are ill-suited to readjudicate the basis of prior criminal convictions. See Sui, 250 F.3d at 119 ("The INS asks us to assume the position of fact-finder. . . . [T]his is an inappropriate role for a reviewing court or for the BIA to undertake, and we decline the invitation to piece together an underlying attempt conviction by weighing evidence and drawing conclusions in a manner appropriate only for a criminal jury."). It was this very concern about collateral trials, and the oppressive administrative burden they impose, that led the BIA to adopt (and us to endorse) the categorical approach to removability in the first instance. See id. at 117-18; Michel, 206 F.3d at 264; In re Pichardo-Sufren, 21 I. & N. Dec. 330, 335 (B.I.A. 1996).
Third and finally, our holdinglike Taylor's  is fair. It is true that Sixth Amendment concerns do not figure into removability calculations in the same way they do in sentencing; it goes without saying that there is no Sixth Amendment right to a jury determination of removability. But, even were we to read the INA's requirement of a "conviction" as having no relation whatsoever to the constitutional right to a jury trial,[13]Taylor was motivated not only by the Sixth Amendment but by general conceptions of fairness.[14]See Taylor, *133 495 U.S. at 601, 110 S.Ct. 2143 (noting the "potential unfairness of a factual approach"). "[I]f a guilty plea to a lesser, [non-removable] offense was the result of a plea bargain, it would seem unfair to [order removal] as if the defendant had pleaded guilty to [a removable offense]." Id. at 601-02, 110 S.Ct. 2143. By permitting the BIA to remove only those aliens who have actually or necessarily pleaded to the elements of a removable offense, our holding promotes the fair exercise of the removal power.
At least two courts of appeals have agreed with our conclusion. In Chung Ping Li v. Ashcroft, 389 F.3d 892, the Ninth Circuit held that removability could be established only by facts of which the alien was convicted: in a jury trial, those elements that the government was actually required to prove and the jury to find; in a pleaded case, those elements to which the alien actually pleaded guilty. Id. at 896 n. 7, 898. In determining whether the alien's fraud conviction involved loss greater than $10,000, the court in Chung Ping Li refused to countenance the IJ's reliance on the loss finding reflected in the judge's Guidelines sentencing decision: "That finding does not satisfy the categorical approach . . . because it does not satisfy the requirement that the defendant have been convicted of each element of the generic crime." Id. at 898;[15]accord Ferreira v. Ashcroft, 390 F.3d 1091, 1098, 1100 (9th Cir.2004) (relying on the restitution amount to establish fraud causing loss over $10,000 where the plea agreement set forth the amount of restitution, and, under California law, restitution may only be ordered for actual loss claimed by the victim); Chang v. INS, 307 F.3d 1185, 1187-88, 1190 (9th Cir.2002) (rejecting restitution order as basis for finding loss exceeding $10,000 because the alien's plea agreement specifically stated an amount of loss of $605.30, and restitution was eventually imposed not just for the conduct pleaded to but for other conduct).
Similarly, in Obasohan v. U.S. Att'y Gen., 479 F.3d 785, the Eleventh Circuit refused to rely on the restitution amount to establish that an alien's prior conviction for conspiracy to use counterfeit access devices involved loss greater than $10,000. Neither Obasohan's indictment nor his plea agreement specified a loss amount, the court found, and the restitution amountbased on findings made by a preponderance of the evidencecould not, standing alone, establish removability by clear, unequivocal and convincing evidence. Id. at 789; see also id. at 790 ("[W]hile a sentencing court in the criminal context may order restitution not only for convicted conduct but also for a broad range of relevant conduct, the plain language of the INA requires that an alien have been convicted of an aggravated felony to be removable.") (footnote omitted).
Applying these principles to the facts of the present case, we find that it was error for the IJ to conclude that Dulal was convicted of fraud involving loss greater than $10,000. Dulal's indictment alleged only that he had caused a loss greater than $1000, which was an element of the offense, but did not specify that he had satisfied that element by causing loss of a particular amount in excess of that sum. Nothing in the record before the IJ or the BIA provides any evidence of a plea allocution or any written plea agreement. Dulal's *134 judgment of conviction indicates that Dulal pleaded guilty to Counts One and Five, but does not indicate that he admitted to causing any specific loss amount associated with either count. It was improper, under Dickson, for the IJ to have consulted the PSR. And as discussed above, the amount of loss indicated in the restitution order was found by the judge by a preponderance of the evidence and was not necessarily limited to the admissions in his plea or to the elements alleged. Thus, that amount is an inappropriate basis for a determination, by clear, unequivocal and convincing evidence, that Dulal was convicted of fraud involving a loss to the victims of greater than $10,000.[16]
Because Dulal's record of conviction did not establish that his conviction for fraud in connection with access devices involved loss over $10,000, the IJ erred in finding him removable as an aggravated felon under 8 U.S.C. § 1227(a)(2)(A)(iii) and 8 U.S.C. § 1101(a)(43)(M)(i).

CONCLUSION
For the foregoing reasons, we hold that (1) the IJ erred in finding Dulal removable as an aggravated felon under 8 U.S.C. § 1101(a)(43)(M)(i) based on his conviction for fraud in connection with access devices, in violation of 18 U.S.C. § 1029(a)(2), because it was improper to rely on Dulal's restitution orderwhich reflected an amount of loss to which Dulal did not actually or necessarily pleadto establish loss to his victims of greater than $10,000; and (2) the IJ correctly determined that Dulal was removable under 8 U.S.C. § 1227(a)(2)(C) because his conviction for making false statements in connection with the acquisition of a firearm, in violation of 18 U.S.C. § 922(a)(6), had removable conduct as an essential element.
We GRANT in part and DISMISS in part Dulal's petition for review, VACATE the BIA's removal order insofar as it is based on a finding that Dulal was convicted of an aggravated felony, and REMAND for further proceedings consistent with this decision.
NOTES
[1]  On March 1, 2003, the INS was reconstituted as the Bureau of U.S. Immigration and Customs Enforcement ("BICE") and the Bureau of U.S. Citizenship and Immigration Services ("BCIS"). See Monter v. Gonzales, 430 F.3d 546, 548 n. 1 (2d Cir.2005). In this opinion, we refer to the agency by the name it bore at the time of the relevant agency action.
[2]  The statute states "firearm or ammunition." We return to this below.
[3]  Dulal has not raised any argument in this petition related to the firearms/ammunition distinction in § 922(a)(6). We must nonetheless apply the categorical approach faithfully to assure ourselves that his conviction was for removable conduct.
[4]  It is this "exception" that we now describe as the "modified categorical approach."
[5]  Although Shepard had not yet been decided, we looked to Taylor for guidance notwithstanding the fact that Sui was convicted following a guilty plea.
[6]  We first set forth the divisibility concept as its own inquiry in Kuhali, 266 F.3d at 106, and Sutherland v. Reno, 228 F.3d 171, 177 (2d Cir.2000).
[7]  Taylor described the exception to the categorical approach as a single inquiry that presumed what we now call statute divisibility and focused on what the record of conviction could establish: "This categorical approach . . . may permit the sentencing court to go beyond the mere fact of conviction in a narrow range of cases where a jury was actually required to find all the elements of generic burglary." 495 U.S. at 602, 110 S.Ct. 2143; see also Shepard, 544 U.S. at 17, 125 S.Ct. 1254 (citing Taylor for this proposition).

Similarly, both the Ninth and the Eleventh Circuits have implicitly found that statutes similar to the one under which Dulal was convicted are divisible. See Obasohan v. U.S. Att'y Gen., 479 F.3d 785, 788 (11th Cir.2007) (dividing the criminal statute we consider in this case, proscribing fraud in connection with access devices, by the amount of loss and proceeding to examine the alien's record of conviction); Chung Ping Li v. Ashcroft, 389 F.3d 892, 896-97 (9th Cir.2004) (finding that, because the statutes under which the alien was convicted do not require proof of a particular monetary loss, it was appropriate to consult the record of conviction).
[8]  Section 1229a(c)(3)(B) states in full:

(B) Proof of convictions. In any proceeding under this Act, any of the following documents or records (or a certified copy of such an official document or record) shall constitute proof of a criminal conviction:
(i) An official record of judgment and conviction.
(ii) An official record of plea, verdict, and sentence.
(iii) A docket entry from court records that indicates the existence of the conviction.
(iv) Official minutes of a court proceeding or a transcript of a court hearing in which the court takes notice of the existence of the conviction.
(v) An abstract of a record of conviction prepared by the court in which the conviction was entered, or by a State official associated with the State's repository of criminal justice records, that indicates the charge or section of law violated, the disposition of the case, the existence and date of conviction, and the sentence.
(vi) Any document or record prepared by, or under the direction of, the court in which the conviction was entered that indicates the existence of a conviction.
(vii) Any document or record attesting to the conviction that is maintained by an official of a State or Federal penal institution, which is the basis for that institution's authority to assume custody of the individual named in the record.
See also Dickson, 346 F.3d at 53 (construing 8 U.S.C. § 1229a(c)(3)(B) and 8 C.F.R. § 1003.41(a)); 8 C.F.R. § 1003.41(a) (elaborating on evidence admissible to prove a conviction).
[9]  The question was not settled by 8 U.S.C. § 1229a(c)(3)(B)(vi), we noted, because even if a PSR were considered a "document prepared at the direction of the court" within the meaning of that provision, the BIA could use it only to prove the existence of the conviction, not the factual basis underlying the conviction. Dickson, 346 F.3d at 53.
[10]  While Dickson did not cite Taylor directly, it relied repeatedly on Sui (and other cases relying on Sui), which, as discussed above, drew its logic from Taylor. See Dickson, 346 F.3d at 52, 54; Sui, 250 F.3d at 116-18.
[11]  Of course, we could not examine the facts established in this way by the record of conviction when the removability provision, unlike the one in the instant case, directs our attention to the elements actually required by the statute. In Chrzanoski v. Ashcroft, 327 F.3d 188 (2d Cir.2003), the BIA found that Chrzanoski's third-degree assault conviction rendered him removable under 18 U.S.C. § 16(a), which defined a crime of violence as "an offense that has as an element the use, attempted use, or threatened use of physical force." Id. at 189 (emphasis added). We stated that "the District Court erred to the extent it consulted the transcript of petitioner's plea colloquy to determine that petitioner's conviction was for a crime of violence as defined in § 16(a) through reference to the particular facts supporting petitioner's guilt as opposed to the elements of § 16(a)." Id. at 192 n. 8. In other words, it was the fact that § 16(a) directed us to look at the elements actually required by the statuteon which a plea colloquy would shed no lightthat foreclosed consultation of the facts to which the defendant admitted. See id. at 196 (emphasizing difference between 18 U.S.C. § 16(a), which addresses misdemeanors and requires that the use of force be an element of the crime, and § 16(b), which addresses felonies and has a "less restrictive definition" that does not look to a statute's elements).

We also note that to the extent dictum in Kuhali appears to foreclose our current holding, see Kuhali, 266 F.3d at 103 (commenting that among the virtues of the categorical approach is that "examining the transcript of the plea colloquy (or the trial) to determine the actual facts of the crime could prove burdensome and produce arbitrary results"), that remark reflected an understanding of Taylor, which we cited for the proposition, that Shepard later explicitly foreclosed. See Shepard, 544 U.S. at 20, 125 S.Ct. 1254 (citing a plea colloquy transcript as among the "closest analogs" in pleaded cases to the jury instructions approved of by Taylor).
[12]  Moreover, if a statute of conviction were to proscribe crimes with different statutory maximums, and a sentencing order revealed that only the crime with the greater maximum could have been the basis of the conviction, our holding would not preclude use of the sentencing order to determine the specific crime of conviction.
[13]  Of course, the concept of a "conviction" does carry with it the assurance that the convicted individual was accorded constitutional protections before a judgment was imposed against him.
[14]  Indeed, when we first applied Taylor's reasoning in the immigration context, see Sui, 250 F.3d at 117, Shepard had yet to fully articulate its Sixth Amendment rationale.
[15]  The court also rejected the government's argument that it could look to the guilty verdict combined with the indictment, which specified a loss amount greater than $10,000, because "amount of loss is not an element of the underlying crimes of conviction," and there was no indication that the jury actually was required to find the loss amount in the indictment. Chung Ping Li, 389 F.3d at 897-98.
[16]  It is highly possible that Dulal pleaded guilty to the counts in question, but would have acceded only to some loss amount between the $1000 minimum in the statute and the $10,000 threshold. In any event, we have no way of knowing what he believed at the time of the plea, because we have no evidence that he indicated any loss amount at that time, nor would he have had to do so in order for his plea to be valid and to result in a valid conviction.
