Lavon Savage (“Savage”) appeals from a judgment of the United States District Court for the District of Connecticut (Burns, /.), entered on August 24, 2006, convicting him, pursuant to a guilty plea, of possession of ammunition by a convicted felon, in violation of 18 U.S.C. § 922(g)(1), and sentencing him principally to seventy-seven months’ imprisonment and three years’ supervised release. Savage appeals only the sentence. The district court’s calculation of the applicable Guidelines’ sentencing range was based, in relevant part, on the court’s determination that one of Savage’s previous felony convictions, entered following an Alford plea, was a conviction for a “controlled substance offense,” as that term is defined in U.S. Sentencing Guidelines Manual (“Guidelines”) § 4B1.2(b). Because nothing in the statute of conviction, the charging document, the plea colloquy or other comparable judicial record established with certainty that Savage necessarily pleaded guilty to the elements of a controlled substance offense, the district court committed procedural error in its calculation of the Guidelines sentencing range. Accordingly, we vacate the sentence and remand for resentencing.

BACKGROUND

On December 12, 2005, Savage, pursuant to a plea agreement, pleaded guilty to possessing ammunition subsequent to a felony conviction, in violation of 18 U.S.C. § 922(g)(1). Guidelines § 2K2.1(a)(2) calls for a base offense level of twenty-four “if the defendant committed any part of the instant offense subsequent to sustaining at least two felony convictions of either a crime of violence or a controlled substance offense.” U.S.S.G. § 2K2.1(a)(2). Guidelines § 2K2.1(a)(4)(A) calls for a base offense level of twenty if the defendant had only one such predicate conviction. Id. § 2K2.1(a)(4)(A). Prior to sentencing, the Probation Office calculated a base offense level of twenty-four, based on its conclusion that Savage had sustained two predicate convictions under Guidelines § 2K2.1(a)(2): (i) a 1999 felony conviction for assault in the second degree, which, beyond dispute, qualified as a felony conviction of a crime of violence; (ii) a 2002 conviction for a violation of Connecticut General Statute § 21a-277(b) (“Connecticut Statute”), which, here disputed, allegedly qualified as a felony conviction of a controlled substance offense. After applying a three-point reduction for acceptance[*961] of responsibility, the PSR calculated an adjusted offense level of twenty-one, which, combined with Savage’s criminal history category of VI, resulted in a Guidelines’ recommended range of seventy-seven to ninety-six months’ imprisonment. The district court, over objections from defense counsel, adopted the sentencing range calculated by the PSR. On August 24, 2006, the court sentenced Savage, at the lowest end of the Guidelines’ range, to seventy-seven months’ imprisonment, three years’ supervised release, and $100 special assessment.

The only dispute in the calculation of the sentence is whether Savage’s 2002 Connecticut conviction was a conviction for a controlled substance offense, as defined in Guidelines § 4Bl.l(b). ^[2] If it was not, then the district court should have applied a base offense level of twenty, rather than twenty-four, under Guidelines § 2K2.1(a)(4)(A). Applying the same three-point reduction for acceptance of responsibility, this would have resulted in a Guidelines’ range of fifty-one to sixty-three months’ imprisonment. U.S.S.G. Table, Ch.5, Pt.A.

The Connecticut Statute provides, in pertinent part:

Any person who manufactures, distributes, sells, prescribes, dispenses, compounds, transports with intent to sell or dispense, possesses with intent to sell or dispense, offers, gives or administers to another person any controlled substance ... may, for the first offense, ... be imprisoned not more than seven years....

Conn. GemStat. § 21a-277(b) (emphases added). And the Connecticut statute defines a “sale” of a controlled substance, in pertinent part, as “any form of delivery[,] which includes barter, exchange or gift, or offer therefor .... ” Conn. Gen.Stat. § 21a-240(50) (emphasis added).

The Guidelines definition of a “controlled substance offense” provides, in pertinent part:

The term “controlled substance offense” means an offense under ... state law ... that prohibits the manufacture, import, export, distribution, or dispensing of a controlled substance ... or the possession of a controlled substance ... with intent to manufacture, import, export, distribute or dispense.

U.S.S.G. § 4B1.2(b). Application Note 1 to this section further provides that a controlled substance offense “include[s] the offenses of aiding and abetting, conspiring, and attempting to commit such offenses.” Id. cmt. n. 1.

In an objection letter to the Pre-Sen-tence Report, defense counsel argued that the Connecticut conviction was not a conviction for a controlled substance offense because the Connecticut Statute criminalized some conduct that falls outside the federal definition of a “controlled substance offense.” Specifically, defense counsel argued that a mere offer of a controlled substance is criminalized by the Connecticut Statute but does not qualify as a controlled substance offense under the Guidelines.

In response, the government introduced evidence from the Connecticut court of conviction in an attempt to show that Savage pleaded guilty to the narrowed charge of exchanging a controlled substance for money, which, the government argued, qualifies as a controlled substance offense. The government submitted the following[*962] two pieces of evidence: (i) a transcript of the plea colloquy from the state court; (ii) a certificate of disposition from the state court, indicating that the defendant was convicted of “Count One in the Information,” which charged: “Sale of Controlled Substance ... in violation of [Connecticut General Statute § ] 21a-277(b).”

Plea Colloquy

The transcript of the state plea proceedings revealed the following. Savage pleaded guilty under the Alford doctrine, whereby he “voluntarily, knowingly, and understanding^ consented] to the imposition of a prison sentence even [though] he [was] unwilling or unable to admit his participation in the acts constituting the crime.” North Carolina v. Alford, 400 U.S. 25, 37, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970). The distinguishing feature of an Alford plea is that the defendant does not confirm the factual basis for the plea. See State v. Faraday, 268 Conn. 174, 842 A.2d 567, 588 (2004) (“A guilty plea under the Alford doctrine is a judicial oxymoron in that the defendant does not admit guilt but acknowledges that the state’s evidence against him is so strong that he is prepared to accept the entry of a guilty plea nevertheless.”).

At the beginning of the proceedings, the following exchange occurred:

[Prosecutor]: L[a]von Savage ... you are charged in count one of the Information, sale of marijuana, in violation of Connecticut General Statute 21a-277(b), what is your plea, guilty or not guilty?

[Savage]: Guilty.

The prosecutor then recited the State’s view of the factual basis for the plea:

[Prosecutor]: Your honor, the factual basis ... [is that] police acting in an undercover capacity purchased drugs ... from Mr. Savage....

After the judge asked some preliminary questions, Savage attempted to contest the prosecutor’s rendition of the facts, but the state judge interrupted:

The Court: Is that under the — do you want the sale to be taken under the Alford doctrine?

[Defense Counsel]: I think it would be well advised.

[Savage]: Yeah, cuz somebody else—

The Court: All right. We’ll cover that. What I’m asking you now is, is anybody forcing you — I know that you may have a disagreement with the facts that [the prosecutor] just said, but are you deciding to plead guilty today voluntarily and of your own free will?

[Savage]: Yes, sir.

The following exchange then occurred:

The Court: All right. Now, you’ve heard the State recite the facts. Now, in one of the cases ^[3] the State claims that you sold a quantity of marijuana. That charge you pled guilty to under what’s called the Alford doctrine. I take that to mean that you don’t agree with all or some of the facts that [the prosecutor] just reported to the Court but after discussing the case with your lawyer, you feel that if you went to trial, even though you don’t agree with the facts, you feel there’s a significant chance that you could get convicted of that charge.

[Savage]: Yeah.

The state court then completed the colloquy, without asking the defendant to allo-cute to the factual basis for the charge. Prior to accepting the plea, the court[*963] asked the defendant if he had any questions.

[Savage]: I just want to tell you the reason for the Alford Doctrine charge.

The Court: You don’t have to if you don’t want to.

[Savage]: Because somebody else gave it to him and it wasn’t me. I didn’t give him the weed, I didn’t take the money, nothing. I was just there, but the police think I’m the ringleader, they just picked me and they overlooked the guy that gave them this stuff and took the money.

The Court: Well, that’s why I — ...— assume that you’re pleading guilty under the Alford Doctrine. Even though you don’t agree with the facts you want to take advantage, by pleading guilty, of the indicated sentence because you feel that if you went to trial there’s a risk that the jury ... could find you guilty even though you have a different story. Am I right about that?

[Savage]: Yup.

The court then accepted the plea.

Charging Document

The Certificate of Disposition reprinted the Information, which revealed that Savage was charged with, and pleaded guilty to, “Sale of Controlled Substance ... in violation of [Connecticut General Statute § ] 21a-277(b).” At sentencing, the government argued that this charging document established that the charge was narrowed to the sale of a controlled substance.

In response, Savage argued that the charging document did not narrow the charge and that, even if it did, it did not narrow the charge to predicate limits. Specifically, Savage argued that if the charge was narrowed, it was narrowed only to a “sale” and that, under Connecticut law, a “sale” encompasses more conduct than falls within the Guidelines’ definition of a controlled substance offense.

Prior to oral argument, in a submission pursuant to Federal Rule of Appellate Procedure 28(j), the government, at first, partly abandoned its reliance on the charging document. Citing our recent decision in United States v. Green, 480 F.3d 627 (2d Cir.2007), the government requested that, in the event we were to conclude that neither the statute of conviction nor the plea colloquy established that Savage was convicted of a controlled substance offense, we should remand for further fact-finding on the issue of whether the “Sale of a Controlled Substance” notation in the Information was (a) a case-specific descriptor of the charges brought against this particular defendant or (b) computer-generated shorthand used by default for generic charges brought under the Connecticut Statute.

At oral argument, the government abandoned its reliance on the charging document entirely. The government conceded that the charging document did not narrow the charge because the government had not shown, nor would attempt to show on remand, that the notation was a case-specific descriptor of the offense rather than something generated by a computer upon entry of the statutory section alone.

Thus, the only remaining issues on appeal are (a) whether the Connecticut Statute criminalizes conduct that falls outside the federal definition of a controlled substance offense; and, if so, (b) whether the plea colloquy established that Savage was convicted of a narrowed charge that falls exclusively within the Guidelines’ definition of a controlled substance offense.

DISCUSSION

“[A] district court should begin all sentencing proceedings by correctly calcu[*964] lating the applicable Guidelines range.” Gall v. United States, — U.S. —, 128 S.Ct. 586, 596, 169 L.Ed.2d 445 (2007). In reviewing a sentence on appeal, we must “first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range.” Id. at 597.

We review de novo the district court’s determination of whether a prior offense was a “controlled substance offense,” as defined by U.S.S.G. § 4B1.2, and we review de novo “the scope of a district court’s authority to make factual findings.” United States v. Rosa, 507 F.3d 142, 151 & n. 8 (2d Cir.2007); see also United States v. Lynch, 518 F.3d 164, 168 (2d Cir.2008). The government bears the burden of showing that a prior conviction counts as a predicate offense for the purpose of a sentencing enhancement. Green, 480 F.3d at 635.

In determining whether a prior conviction qualifies as a predicate offense under U.S.S.G. § 4B1.2, “we take a [modified] categorical approach; that is, we generally look only to the statutory definition of the prior offense of conviction rather than to the underlying facts of that offense.” United States v. Brown, 514 F.3d 256, 265 (2d Cir.2008); see also Green, 480 F.3d at 631-32 (applying modified categorical approach to determination of whether prior conviction qualified as a controlled substance offense under U.S.S.G. § 2K2.1).

Under the modified categorical approach, we conduct a two-part inquiry. First, in the categorical inquiry, we ask whether the statute of the prior conviction criminalizes conduct that falls exclusively within the federal definition of a predicate offense. If so, “there is no problem, because the conviction necessarily implies that the defendant has been found guilty of’ a predicate offense. Taylor v. United States, 495 U.S. 575, 599, 110 S.Ct. 2143, 109 L.Ed.2d 607 (1990). If, however, the statute of the prior conviction criminalizes both predicate and non-predicate conduct, then the second part of the modified categorical inquiry requires that we ask whether the government has shown that the plea “necessarily” rested on a fact identifying the conviction as a predicate offense. Shepard v. United States, 544 U.S. 13, 24, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005).

As a preliminary matter, the parties do not dispute that a conviction entered pursuant to an Alford plea may serve as a predicate offense under Guidelines § 2K2.1(2). See Burrell v. United States, 384 F.3d 22, 31 (2d Cir.2004) (holding that under Connecticut law, a conviction based on an Alford plea is a prior conviction that may serve as a predicate felony under 18 U.S.C. § 922(g)(1)). Thus, if the state statute of conviction criminalized conduct that falls exclusively within the federal definition of a predicate offense, or if the charge was narrowed to include only predicate conduct, then an Alford plea entered pursuant to such a charge would constitute a predicate offense.

7. Categorical Inquiry: Connecticut Statute

Assuming the government has not waived the issue, ^[4] cf. Rosa, 507 F.3d at 154 & n. 11, we conclude that a conviction under the Connecticut Statute cannot categorically qualify as a “controlled substance offense” within the meaning of Guidelines[*965] § 4B1.2(b) because the Connecticut Statute criminalizes some conduct that falls outside the Guidelines’ definition.

Under Connecticut law, “the statutory definition of ‘sale’ as applied to illegal drug transactions is much broader than [the] common definition” of a sale as an “exchange of an object for value.” State v. Myers, 101 Conn.App. 167, 921 A.2d 640, 648-49 (2007), certification granted on other grounds by 927 A.2d 919 (Conn.2007). Under this broad statutory definition of sale, a “ ‘Sale’ is any form of delivery[,] which includes barter, exchange or gift, or offer therefor .... ” Conn. Gen.Stat. § 21a-240(50) (emphasis added); see State v. Wassil, 233 Conn. 174, 658 A.2d 548, 557 (1995). Thus, as the government appears to recognize, the statute plainly criminalizes, inter alia, a mere offer to sell a controlled substance. ^[5] Other state courts have interpreted similar statutory definitions of “sale” to include a mere offer to sell a controlled substance. See, e.g., State v. Allen, 292 A.2d 167, 170, 171 (Me.1972) (statutory definition of sale to include “barter, exchange, or gift, or offer therefor” covers “mere offer to transfer” a controlled substance); Porter v. Sheriff, Clark County, 87 Nev. 274, 485 P.2d 676, 676 (1971) (same); People v. Robinson, 14 Ill.2d 325, 153 N.E.2d 65, 69 (1958) (under same definition, “a simple offer or agreement to sell ... constitutes a sale of narcotics”); see also State v. Hairiston, 33 Conn.Supp. 183, 369 A.2d 255, 256 (1976) (“Connecticut’s controlled drug statute contains a definition of sale which includes gifts or offers.”). Further, under Connecticut law, “there is no requirement that one be in possession of goods or have control over them in order to sell them.” State v. Brown, 163 Conn. 52, 301 A.2d 547, 553 (1972); cf. United States v. Palacios-Quinonez, 431 F.3d 471, 476 (5th Cir.2005) (“Someone who offers to sell need not have possession as required by the guidelines. Rather, one can misrepresent ownership or control of the offered goods, such as where one is offering to sell the proverbial Brooklyn Bridge.”).

We agree with the Fifth Circuit that “a mere offer to sell, absent possession, does not fit within the Guidelines’ definition” of a controlled substance offense. United States v. Price, 516 F.3d 285, 288-89 (5th Cir.2008). An offer to sell can be fraudulent, such as when one offers to sell the Brooklyn Bridge. See Palacios-Quinonez, 431 F.3d at 476. In such a circumstance, the offer to sell is fraudulent in the sense that the person offering the bridge or the drug does not have the intent to distribute or sell the item. As we have held, “a crime not involving the men[*966] tal culpability to commit a substantive narcotics offense [does not] serve as a predicate ‘controlled substance offense’ ” under the Guidelines. United States v. Liranzo, 944 F.2d 73, 78-79 (2d Cir.1991). ^[6] Thus, the Connecticut statute, by criminalizing a mere offer to sell, criminalizes more conduct than falls within the federal definition of a controlled substance offense.

II. Modified Categorical Inquiry

Where, as here, the statute of conviction is overly inclusive, we address whether the government has shown that the plea “necessarily” rested on the fact identifying the conviction as a predicate offense. Shepard, 544 U.S. at 21, 125 5.Ct. 1254. In conducting this modified categorical inquiry, we are constrained by “Taylor’s demand for certainty.” Id. Accordingly, in the context of a conviction based on a plea, the inquiry 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.” Id. at 26, 125 S.Ct. 1254. The determinative issue is whether the judicial record of the state conviction established with “certainty” that the guilty plea “necessarily admitted elements of the [predicate] offense.” Id. at 25, 26, 125 S.Ct. 1254; see Rosa, 507 F.3d at 161 (applying “Shepard’s requirement that district courts limit their consideration to particular documents that can identify the underlying facts of a prior conviction with certainty ” (emphasis added)). We apply Shepard in determining whether a conviction qualified as a “controlled substance offense” for the purpose of a Guidelines sentencing enhancement. See Green, 480 F.3d at 632.

The Shepard Court identified two types of proof, relevant here, that might suffice to establish that a plea “necessarily” rested on the elements of a predicate offense: (i) proof that the defendant admitted to predicate conduct when confirming the factual basis for a valid plea; (ii) proof that the charge was narrowed to include only predicate conduct. 544 U.S. at 21-22, 125 S.Ct. 1254.

Because Savage entered an Alford plea in which he refused “to admit his participation in the acts constituting the crime,” Alford, 400 U.S. at 37, 91 S.Ct. 160, Savage did not, by design, confirm the factual basis for his plea. The state judge carefully explained this, by reassuring Savage that the plea would be accepted even though Savage did not “agree with the facts.” Thus, the government cannot rely on any factual admissions during the plea colloquy to establish the predicate nature of Savage’s conviction. See Shepard, 544 U.S. at 20, 26, 125 S.Ct. 1254 (holding that factual admissions made by the defendant are made part of the conviction only when “the factual basis for the plea was confirmed by the defendant” and the admissions were made “by the defendant upon entering the plea”); see also Rosa, 507 F.3d at 158 (holding that factual findings by judge are made part of the conviction only when they are confirmed by the defendant upon entering the plea).

Thus, the sole issue is whether the government has shown that the charge was narrowed to include only predicate conduct. Although the government has conceded that the charging document did not narrow the charge within the meaning of Shepard, the Shepard Court allowed proof[*967] of a narrowed charge to be made by a charging instrument or by “some comparable judicial record of this information.” 544 U.S. at 26, 125 S.Ct. 1254; see Green, 480 F.3d at 632.

The government argues that the plea transcript is a “comparable judicial record” that establishes that Savage pleaded guilty to a narrowed charge. In deciding whether the plea colloquy can be used for this purpose, the dispositive question is whether the plea colloquy establishes, with certainty, that the “plea ... ‘necessarily’ rested on the fact,” Shepard, 544 U.S. at 21, 125 S.Ct. 1254, identifying the conviction as a controlled substance offense. See Rosa, 507 F.3d at 155. We do not think that it did.

The government first seeks to rely on the initial exchange between the state prosecutor and Savage, in which Savage pleaded guilty to the charge, as described by the prosecutor, “in count one of the Information, sale of marijuana, in violation of Connecticut General Statute 21a-277(b).” We need not decide whether this established, with certainty, that the charge was narrowed to a sale, as opposed to a generic violation of the statute, because even if the charge was so narrowed, this statement cannot establish that the charge was narrowed to predicate limits: as we have explained, the Connecticut Statute criminalizes non-predicate conduct by virtue of the broad definition given to “sale” under Connecticut law. Thus, by simply stating that Savage was charged with a sale, the prosecutor did not say anything that could establish that the charge was narrowed to its predicate limits. For similar reasons, even if one could find that Savage’s exchanges with the state judge, wherein the judge described the charge as one for “sale,” were competent evidence under Shepard, these comments would not establish that Savage was convicted of a “controlled substance offense.”

Finally, the government points to Savage’s statement that “someone else gave [the drugs] to the [the undercover] officer” and contends that this established that Savage understood he was charged specifically with exchanging drugs for money. No such conclusion follows: in this exchange, Savage simply contested the state’s recitation of the facts; just as such offhand remarks do not constitute factual admissions that define the nature of the conviction, see Rosa, 507 F.3d at 158, they equally do not define the nature of the conviction by establishing that Savage pleaded guilty to a narrowed charge.

In sum, although everybody understood that the State alleged that Savage exchanged drugs for money, nothing in the plea colloquy established with certainty that Savage necessarily pleaded guilty to this fact. At the narrowest, Savage pleaded guilty to a “sale” of a controlled substance. Because a “sale” under Connecticut law includes a mere offer to sell drugs, and an offer to sell drugs is not a controlled substance offense, the conviction does not qualify as a controlled substance offense.

CONCLUSION

For the foregoing reasons, we vacate Savage’s sentence and remand for resen-tencing.