CALABRESI, Circuit Judge:

Upon conviction for illegally re-entering the United States, see 8 U.S.C. § 1326, defendant Jose Alfredo Garcia-Hernandez was sentenced by the United States District Court for the Southern District of New York (Jones, Judge) to 40 months in prison. The sentence imposed reflected a substantial enhancement for illegal re-entry following a prior conviction for an aggravated felony. See U.S.S.G. § 2L1.2(b)(1)(A). At issue in this appeal is whether the district court was required, pursuant to § 5G1.3(b) of the United States Sentencing Guidelines, to run this sentence concurrently with a New York State term of imprisonment. The state term in question was imposed because defendant's illegal re-entry, in addition to constituting a federal crime, also violated the terms of defendant's parole for a prior drug conviction. We affirm and hold that the district court properly evaluated defendant's sentence under § 5G1.3(c), not § 5G1.3(b).

I

In October 1992 appellant was convicted in New York State court of drug possession and was sentenced to five years to life in prison. He was released on parole in January 1997 and was deported. Garcia-Hernandez then illegally re-entered the country, in violation of his parole conditions, and was taken into state custody in April 1999. New York revoked his parole and incarcerated him.

Next, a federal grand jury indicted appellant on a charge of illegal re-entry. After being transferred to federal custody to face that charge, Garcia-Hernandez pled guilty and remained in federal custody until his sentencing in May 2000.

The Pre-Sentence Report ("PSR") recommended a total offense level of 21, including a 16-level enhancement for illegal re-entry after a prior conviction for an aggravated felony, see U.S.S.G. § 2L1.2(b)(1)(A), and a criminal history category of III, yielding a Guidelines range of 46-57 months' imprisonment. Without the § 2L1.2(b)(1)(A) enhancement, that range would have been reduced to 1-7 months. See U.S.S.G. ch. 5, pt. A (sentencing table). There is no dispute over these calculations.

Relying on Guidelines § 5G1.3(b), the PSR also recommended that the sentence run concurrently, nunc pro tunc, with the period of confinement resulting from Garcia-Hernandez's parole violation; Garcia-Hernandez adopted this position. The Government objected to the recommendation of concurrent sentencing, arguing that this case is governed by § 5G1.3(c) (granting the district court discretion to impose the sentence concurrently, consecutively, or in some combination of the two) and that the sentence should be imposed to run consecutively to the period of imprisonment arising from the parole violation. The district court agreed with the Government that defendant should receive no credit for the time already spent in state custody, and it imposed a sentence consecutive to that prior custody.

II

On appeal, Garcia-Hernandez argues only that the district court should have applied § 5G1.3(b), which mandates concurrent sentencing, see United States v. Maria, 186 F.3d 65, 69 (2d Cir. 1999). He disclaims any argument that if, as the district court concluded, § 5G1.3(c) applies, the court should have exercised its discretion under that sub-section and imposed a sentence to run concurrently with all or part of the time already served on account of his parole violation. Cf. Maria, 186 F.3d at 69-72 (holding that, when sentencing parole violators under § 5G1.3(c), district courts have discretion to impose a federal sentence that runs concurrently with the period of imprisonment arising from the parole violation, though they are discouraged from doing so).

Section 5G1.3(b) provides that "[i]f . . . the undischarged term of imprisonment resulted from offense(s) that have been fully taken into account in the determination of the offense level for the instant offense, the sentence for the instant offense shall be imposed to run concurrently to the undischarged term of imprisonment"; see also id. comment., n. 2 (directing that sentences imposed under § 5G1.3(b) should be shortened to account for periods of imprisonment already served in satisfaction of the sentence with which the federal sentence is to run concurrently). To assess this Guideline's applicability in light of appellant's parole revocation and § 2L1.2(b)(1)(A) enhancement, we must determine (1) which "offense" resulted in the term of imprisonment imposed by the state as a result of Garcia Hernandez's parole violation, and (2) whether that offense was "fully taken into account in the determination of the offense level" for appellant's illegal re-entry.

A. The "Offense" Is The Underlying State Conviction

Although it was appellant's illegal re-entry into the United States that triggered revocation of his parole, New York's authority to prescribe conditions of parole, and to imprison appellant if he violated those conditions, was drawn from the sentence that New York originally imposed for drug possession. See United States v. Meeks, 25 F.3d 1117, 1121 (2d Cir. 1994) ("[S]upervised release, like parole, is an integral part of the punishment for the underlying offense.") Both Garcia-Hernandez's illegal re-entry and his drug possession were causes of the imprisonment triggered by the parole violation, but the underlying state crime was the only criminal "offense" that, by operation of law, "resulted" in the additional period of imprisonment imposed for Garcia-Hernandez's violation of parole.

We have applied this principle in the closely related context of granting "time served" credit for pre-sentencing detention, see 18 U.S.C. § 3585(b) (requiring credit for detention "as a result of the offense for which the sentence was imposed"). And, we have there held that, when a defendant is imprisoned on account of a parole or supervised release violation, it is the underlying crime, not the conduct that violates parole or supervised release, that constitutes the "offense" that "results" in further custody. See United States v. Whaley, 148 F.3d 205, 207 (2d Cir. 1998) (per curiam) (holding that the district court erred in "interpreting § 3585(b)(1) as applying to the offense of violating supervised release rather than as applying to the underlying offense"); United States v. Galicia-Delgado, 130 F.3d 518, 522 (2d Cir. 1997) ("[T]he time [defendant] spent in state custody after violating his parole was part of his sentence for the [underlying state crime].").

Appellant has cited no authority for treating custody resulting from a parole violation differently under Guidelines § 5G1.3(b) than under 18 U.S.C. § 3585(b)(1), nor has he offered any reasoned basis for such a distinction. Finding no such basis ourselves, we hold that the time appellant spent in state custody after violating his parole was, for § 5G1.3(b) purposes, the "result" of the "offense" for which he was originally convicted in state court, and is not properly attributable to the conduct that violated the terms of his release on parole. Accordingly, § 5G1.3(b) applies in this case only if appellant's state drug possession conviction (the "offense" for purposes of § 5G1.3(b)) was "fully taken into account in the determination of the offense level" in the Guidelines calculation of his sentence for illegal re-entry.

B. A § 2L1.2(b)(1)(A) Enhancement Does Not Fully Take Into Account The Conviction Triggering That Enhancement

In order to trigger the application of § 5G1.3(b), an offense other than the one for which a defendant is being sentenced (a "separate offense") must not only (1) be taken into account "in the determination of the offense level for the instant offense [of conviction]," but it must also (2) be " fully taken into account" (emphasis added) in that determination. Unlike situations in which prior convictions play a role solely in a defendant's criminal history calculation, and hence do not affect the defendant's offense level, there can be no doubt that here appellant's drug possession conviction was taken into account, at least to some degree, in the determination of his offense level. For, on account of that conviction, his offense level was increased by sixteen points pursuant to § 2L1.2(b)(1)(A). Cf. United States v. Lange, 146 F.3d 555, 556 (8th Cir. 1998) (holding that consideration of past offenses in the determination of a defendant's criminal history category does not trigger application of § 5G1.3(b)); United States v. Hornsby, 88 F.3d 336, 339 (5th Cir. 1996) (same); United States v. Puckett, 61 F.3d 1092, 1097 n. 5 (4th Cir. 1995) (same).

In fact, the Guidelines calculation of a defendant's offense level may take into account separate offenses through a number of different mechanisms — for instance, offense-specific enhancements such as § 2L1.2(b)(1)(A), consideration of the prior offense as "relevant conduct" under § 1B1.3, and application of career offender provisions, see §§ 4B1.1-2. But all such mechanisms trigger application of § 5G1.3(b) if and only if they take into account the separate offense(s) fully. See United States v. Caraballo, 200 F.3d 20, 24-25 (1st Cir. 1999). We therefore read the modifier "fully" to restrict § 5G1.3(b) to a particular sub-set of all those circumstances in which a separate offense is, in some way, considered in determining the Guidelines offense level.

Appellant argues that his drug possession conviction was taken into account fully by virtue of the fact that it had a substantial effect on his offense level and his sentence. The Government counters that the conviction could not have been fully accounted for because it was not treated as relevant conduct. We reject appellant's argument but need not, and do not, adopt the Government's categorical approach in order to reach that result.

We believe that § 5G1.3(b)'s prohibition of consecutive sentences is aimed at situations in which separate, non-offense conduct could, absent operation of this sub-section, otherwise be the basis both (1) for sentencing defendant as if that conduct had been part of the offense(s) of conviction, and (2) for additional punishment of that same conduct in another, and separate, criminal proceeding. The guideline's purpose, in other words, is to prevent such double-counting, thereby ensuring that "punishments approximate the total penalty that would have been imposed had the sentences for the different offenses been imposed at the same time ( i.e., had all of the offenses been prosecuted in a single proceeding)." Witte v. United States, 515 U.S. 389, 404-05, 115 S.Ct. 2199, 132 L.Ed.2d 351 (1995). In order to effectuate this purpose, we treat a prior offense as "fully taken into account" if and only if the Guidelines provide for sentencing as if both the offense of conviction and the separate offense "had . . . been prosecuted in a single proceeding." Id. at 405, 115 S.Ct. 2199. Accordingly, we hold that when (for whatever reason) such a separate offense has, in fact, been criminally punished in another proceeding, § 5G1.3(b) applies.

This approach is consistent with what little guidance the Guidelines and the cases provide in understanding the concept of a "full" taking into account. Thus, we have recognized that, generally speaking, consideration of separate offenses as relevant conduct does meet the "fully taken into account" requirement of § 5G1.3(b). See United States v. Brown, 232 F.3d 44, 48-49 (2d Cir. 2000) (per curiam); United States v. Livorsi, 180 F.3d 76, 82-83 (2d Cir. 1999); see also U.S.S.G. § 5G1.3 comment., n. 2 (giving, as an example of when sub-section (b) should apply, a scenario in which conduct for which a defendant has been convicted in a prior state proceeding is subsequently included as relevant conduct in the instant federal sentencing); United States v. Blanc, 146 F.3d 847, 851 (11th Cir. 1998). Conversely, in circumstances where a separate offense has affected a defendant's offense level, but not by virtue of its being treated as if it had been an offense of conviction in the instant proceeding, various circuits have refused to apply § 5G1.3(b). See United States v. Contreras, 210 F.3d 1151, 1153 (10th Cir. 2000) (career offender provisions, see U.S.S.G. § 4B1.1); United States v. Gondek, 65 F.3d 1, 4 (1st Cir. 1995) (possession of firearms after prior convictions, see U.S.S.G. § 2K2.1).

These principles make clear that, in this case, application of § 5G1.3(b) is inappropriate. The Guidelines do not treat appellant's prior drug conviction as if it had been prosecuted in the present proceeding. To the contrary, § 2L1.2(b)(1)(A) is premised on defendant having been convicted of an aggravated felony prior to his deportation and his subsequent illegal re-entry. As a result, this is not a case in which application of § 5G1.3(b) would "mitigate the possibility that the fortuity of two separate prosecutions will grossly increase a defendant's sentence," Witte, 515 U.S. at 405, 115 S.Ct. 2199. Far from a fortuity, an incremental increase in defendant's punishment is, in the instant case, the plain purpose of § 2L1.2(b)(1)(A). Moreover, § 2L1.2(b)(1)(A) takes the prior conviction into account by increasing defendant's offense level by a fixed amount, irrespective of the sentence that would have been appropriate if, counterfactually, defendant were being sentenced in the instant prosecution for drug possession in addition to illegal re-entry. Accordingly, we conclude that the enhancement in question did not "fully take into account" appellant's prior drug conviction and, therefore, that the district court was correct in applying § 5G1.3(c), not § 5G1.3(b), in this case.

III

To summarize, we hold (1) that when a criminal defendant is imprisoned as a result of his violation of the terms of his parole, the "offense" that "results" in his imprisonment is, for the purposes of § 5G1.3(b), the underlying prior offense of conviction, not the conduct violative of his parole conditions, and (2) that § 2L1.2(b)(1)(A) does not "fully take into account" prior aggravated felonies because the defendant is not sentenced as if those felonies were being prosecuted in the same proceeding as the instant offense.

Having fully considered all of appellant's arguments, we find them to lack merit. Accordingly, we AFFIRM the sentence imposed by the district court.