HARTZ, Circuit Judge.

Marvin B. Davis, a state prisoner appearing pro se and in forma pauperis, seeks a certificate of appealability (COA) to appeal the denial of his application for a writ of habeas corpus under 28 U.S.C. §§ 2241 and 2254. He also seeks to appeal the denial of his motion for reconsideration and appeals the denial of a writ of coram nobis under 28 U.S.C. § 1651. All claims derive from a challenge to a prior sentence that he had fully served by the time he sought relief in federal court. Exercising jurisdiction under 28 U.S.C. §§ 2253 and 1291, we deny a COA with respect to his claims under §§ 2241 and 2254, and we affirm the denial of a writ of coram nobis. Each of the three forms of relief sought by Mr. Davis is clearly barred.

I. BACKGROUND

Mr. Davis's claims concern two state sentences. In 1991 he pleaded guilty to felony theft. He was sentenced to one to five years in prison but placed on probation. In 1992 his probation was revoked, and he was imprisoned. In 1993 Kansas enacted a statute providing for sentencing guidelines. Kan. Stat. Ann. § 21-4724. According to Mr. Davis, the statute required that the Kansas Department of Corrections (KDC) produce a report setting forth what his sentence would be under the guidelines and that he then be resentenced under the guidelines. See id. Mr. Davis challenges the execution of the 1991 sentence because of the KDC's failure to issue such a report, which, he contends, would have resulted in a shorter sentence. Mr. Davis completed his 1991 sentence on December 22, 1996.

Mr. Davis was later convicted of aggravated burglary, aggravated kidnapping, aggravated indecent liberties with a child, and domestic violence. His sentence of 230 months' imprisonment, imposed on April 17, 1997, was based on a criminal history score of "G." Mr. Davis contends that proper execution of the 1991 sentence would have reduced that criminal history and thus shortened the duration of the 1997 sentence, which he is currently serving.

Mr. Davis sought post-sentencing relief in Kansas state court under Kan. Stat. Ann. § 60-1507. The state district court denied the petition. On appeal the Kansas Court of Appeals dismissed the claim for lack of jurisdiction because Mr. Davis had already completed his 1991 sentence. Davis v. Kansas, 77 P.3d 1288, 2003 WL 22283015, at *2 (Kan.Ct.App. 2003). The state supreme court denied review.

On January 8, 2004, Mr. Davis filed in the United States District Court for the District of Kansas a pleading on a form with the printed title "Petition for Writ of Habeas Corpus Pursuant to 28 U.S.C. § 2254 by a Person in State Custody." He wrote in "28 U.S.C. § 2241; 28 U.S.C. § 1651" after the printed title. His pleading contended that (1) his first sentence was constitutionally infirm because the state had not converted it under Kan. Stat. Ann. § 21-4724, and (2) this alleged error rendered unconstitutional the related enhancement to his second sentence. The court dismissed his claims as barred by the one-year limitations period under the Antiterrorism and Effective Death Penalty Act (AEDPA), see 28 U.S.C. 2244(d)(1) (2). It also found no circumstances warranting the equitable tolling of the limitations period. See Burger v. Scott, 317 F.3d 1133, 1141-44 (10th Cir. 2003). The district court did not explicitly address the applicability of either § 2241 or § 1651.

On January 21, 2004, Mr. Davis filed a motion for reconsideration, arguing that the federal limitations period had not begun to run until he was hired as a law-library research clerk in 2001 and discovered the alleged error in his first sentence. Construing the pleading as a motion under Fed.R.Civ.P. 59(e), the district court denied relief, noting that 28 U.S.C. § 2244(d)(1)(D) requires that a prisoner exercise due diligence to discover the factual predicate of a habeas claim.

Mr. Davis argues in this court that (1) a COA is not required for his § 2241 petition; (2) the district court should not have sua sponte recharacterized his claims as a § 2254 application; (3) § 2241 is not subject to the one-year limitations period under AEDPA when the factual predicate underlying the claim was discovered years later; (4) an expired conviction may be challenged under § 2241 when the conviction was the result of ineffective assistance of counsel or there is no review available through no fault of the petitioner; and (5) the district court has jurisdiction under 28 U.S.C. § 1651(a) to issue a writ of coram nobis to correct an expired conviction even though the convict is no longer in custody on that conviction.

II. DISCUSSION

A. Characterization of Mr. Davis's Claims

At the outset we need to determine what avenues of relief Mr. Davis is pursuing. First, a challenge to the execution of a sentence should be brought under 28 U.S.C. § 2241. Bradshaw v. Story, 86 F.3d 164, 166 (10th Cir. 1996) ("A petition under 28 U.S.C. § 2241 attacks the execution of a sentence rather than its validity. . . ."). Thus, this is the provision that would ordinarily apply to Mr. Davis's challenge to the failure to convert his 1991 sentence to a lesser term after enactment of Kan. Stat. Ann. § 21-4724. Second, to the extent that Mr. Davis contends that his present sentence is unlawful (because it was influenced by the improper execution of his 1991 sentence), the claim should be brought under 28 U.S.C. § 2254. Montez v. McKinna, 208 F.3d 862, 865 (10th Cir. 2000) (a challenge to the validity of a conviction and sentence is properly brought under § 2254). Third, he seeks relief concerning a sentence he has already served (the 1991 sentence) by bringing a petition for a writ of coram nobis under 28 U.S.C. § 1651(a). Cf. United States v. Torres, 282 F.3d 1241, 1245 n. 6 (10th Cir. 2002) (noting availability of coram nobis relief for federal convictions). As we shall explain, all three forms of relief are barred.

B. § 2241 Relief

Contrary to Mr. Davis's first assertion, "a state prisoner must obtain a COA to appeal the denial of a habeas petition, whether such petition was filed pursuant to § 2254 or § 2241, whenever `the detention complained of [in the petition] arises out of process issued by a State court.'" Montez, 208 F.3d at 867 (quoting 28 U.S.C. § 2253(c)(1)(A)). Mr. Davis's initial confinement is a "matter flowing from a state court detention order." Id. at 869. We therefore consider whether Mr. Davis is entitled to a COA on his § 2241 claim. See id. at 867-69.

Section 2253(c)(2) states: "A certificate of appealability may issue . . . only if the applicant has made a substantial showing of the denial of a constitutional right." Although the statutory language does not address a district court denial of habeas relief on procedural grounds, the Supreme Court has said:

When the district court denies a habeas petition on procedural grounds without reaching the prisoner's underlying constitutional claim, a COA should issue when the prisoner shows, at least, that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and that jurists of reason would find it debatable whether the district court was correct in its procedural ruling.

Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). It follows that "[w]here a plain procedural bar is present and the district court is correct to invoke it to dispose of the case, a reasonable jurist could not conclude either that the district court erred in dismissing the petition or that the petitioner should be allowed to proceed further. In such a circumstance, no appeal would be warranted." Id.

The Supreme Court did not discuss what the proper course would be when there is a "plain procedural bar" that the district court did not invoke. But the answer seems clear. In general, "[w]e have discretion to affirm on any ground adequately supported by the record." Elkins v. Comfort, 392 F.3d 1159, 1162 (10th Cir. 2004). No reason suggests itself why this principle should be rejected in considering an application for a COA. Accordingly, we may deny a COA if there is a plain procedural bar to habeas relief, even though the district court did not rely on that bar.

Here, there is a plain procedural bar to Mr. Davis's § 2241 claim. The issue is a pure matter of law, and there is nothing unfair in resolving the claim on this basis. See id. (factors to be considered in determining whether to affirm on ground not relied on by district court include whether issue has been briefed, whether there was opportunity to develop factual record, and whether issue is solely question of law). "The federal habeas statute gives the United States district courts jurisdiction to entertain petitions for habeas relief only from persons who are ` in custody in violation of the Constitution or laws or treaties of the United States.'" Maleng v. Cook, 490 U.S. 488, 490, 109 S.Ct. 1923, 104 L.Ed.2d 540 (1989) (quoting 28 U.S.C. § 2241(c)(3) and citing 28 U.S.C. § 2254(a)). A habeas petitioner does not remain "`in custody' under a conviction after the sentence imposed for it has fully expired, merely because of the possibility that the prior conviction will be used to enhance the sentences imposed for any subsequent crimes of which he is convicted." 490 U.S. at 492, 109 S.Ct. 1923. To the extent that Mr. Davis raises a claim challenging the execution of his 1991 sentence, the district court lacked jurisdiction to hear the claim because he was no longer in custody under that sentence when he filed for relief in that court. Therefore, dismissal of Mr. Davis's § 2241 claim was clearly correct and we deny a COA on that claim.

C. § 2254 Claim

To the extent that Mr. Davis is challenging the validity or legality of the sentence he is currently serving, his claim should be brought under § 2254. Montez, 208 F.3d at 864; Bradshaw, 86 F.3d at 166. He complains, however, that he did not invoke § 2254 and that the district court improperly recharacterized his claim as proceeding under that section. We recognize that even if his claim should have been brought under § 2254, he may prefer to have his claim dismissed rather than be recharacterized as a § 2254 claim because of the potential consequences with respect to any § 2254 claim he may file in the future. AEDPA places strict limitations on second or successive claims. See 28 U.S.C. §§ 2244(b), 2255. As a result, a district court must follow certain procedures before recharacterizing pro se pleadings as claims under §§ 2254 or 2255. In the context of § 2255 the Supreme Court has stated:

[T]he district court must notify the pro se litigant that it intends to recharacterize the pleading, warn the litigant that this recharacterization means that any subsequent § 2255 motion will be subject to the restrictions on "second or successive" motions, and provide the litigant an opportunity to withdraw the motion or to amend it so that it contains all the § 2255 claims he believes he has.

Castro v. United States, 540 U.S. 375, 383, 124 S.Ct. 786, 157 L.Ed.2d 778 (2003); accord United States v. Kelly, 235 F.3d 1238, 1242 (10th Cir. 2000) (recharacterization as § 2255 motion); see Martin v. Overton, 391 F.3d 710, 713 (6th Cir. 2004) (recharacterization as § 2254 application).

But here there was no recharacterization by the district court. Mr. Davis's initial pleading in federal district court was on a form describing the pleading as a "Petition for Writ of Habeas Corpus Pursuant to 28 U.S.C. § 2254 by a Person in State Custody." He inserted "28 U.S.C. § 2241; 28 U.S.C. § 1651" after this printed language but he did not cross out the printed language. Even more telling, in his January 21, 2004, motion Mr. Davis claimed relief under "28 U.S.C. §§ 2241, 2254, [and] 1651" and referenced § 2254 throughout his pleading. Thus, Mr. Davis plainly intended to bring a § 2254 claim.

Turning to the substance of the § 2254 claim, it was not cognizable in district court. In Lackawanna County District Attorney v. Coss, 532 U.S. 394, 121 S.Ct. 1567, 149 L.Ed.2d 608 (2001), the Supreme Court addressed whether a current sentence enhanced by a prior allegedly unconstitutional expired sentence may be challenged under § 2254. Although it held that a prisoner serving such an enhanced sentence was "in custody," the Court said:

[O]nce a state conviction is no longer open to direct or collateral attack in its own right because the defendant failed to pursue those remedies while they were available (or because the defendant did so unsuccessfully), the conviction may be regarded as conclusively valid. If that conviction is later used to enhance a criminal sentence, the defendant generally may not challenge the enhanced sentence through a petition under § 2254 on the ground that the prior conviction was unconstitutionally obtained.

532 U.S. at 403-04, 121 S.Ct. 1567 (internal citation omitted). "The only exceptions [to this general rule] exist when: 1) counsel is not appointed in violation of the Sixth Amendment; or 2) no channel of review is available through no fault of the petitioner." Broomes v. Ashcroft, 358 F.3d 1251, 1254 (10th Cir. 2004). In particular, prisoners are not entitled to an exception on the ground that their counsel provided inadequate representation. Lackawanna, 532 U.S. 394, 121 S.Ct. 1567, 149 L.Ed.2d 608 (no § 2254 remedy for ineffective assistance of counsel with respect to prior conviction).

Neither exception applies here. Mr. Davis does not claim that counsel was not appointed in the prior proceeding, only that his counsel was ineffective. Nor was he faultless in failing to obtain timely review of his constitutional claims. Although he explains that he did not discover the error with respect to his first sentence until he became a law-library research clerk in 2001, he failed to exercise due diligence in challenging the alleged error in his 1991 sentence. "[I]gnorance of the law, even for an incarcerated pro se petitioner, generally does not excuse prompt filing." Marsh v. Soares, 223 F.3d 1217, 1220 (10th Cir. 2000) (internal quotation marks omitted). Accordingly, the § 2254 claim was properly dismissed, and we deny a COA.

D. Coram Nobis Claim

Finally, we reject Mr. Davis's petition for a writ of coram nobis under 28 U.S.C. § 1651. It has long been settled in this circuit that federal courts have no jurisdiction to issue writs of coram nobis with respect to state criminal judgments. See Rivenburgh v. Utah, 299 F.2d 842, 843 (10th Cir. 1962); see also Obado v. New Jersey, 328 F.3d 716, 718 (3d Cir. 2003) (joining the Fourth, Fifth, Seventh, and Tenth Circuits in holding "that coram nobis is not available in a federal court as a means of attack on a state criminal judgment"); Larry W. Yackle, Postconviction Remedies § 35, at 162 (1981) ("[T]he writ [of coram nobis] is available only in the sentencing court to petitioners challenging federal convictions and sentences.").

E. Motion to Reconsider

Mr. Davis's motion to reconsider in district court raised no issues that survive the procedural grounds for rejection discussed above.

III. CONCLUSION

With respect to Mr. Davis's claims under 28 U.S.C. §§ 2241 and 2254, dismissal was undoubtedly correct and we DENY a COA. With respect to his claims under 28 U.S.C. § 1651, we AFFIRM the judgment below.