ORDER
Booker T. Duke, a pro se federal prisoner, appeals a district court judgment dismissing his habeas corpus petition filed under 28 U.S.C. § 2241. This case has been referred to a panel of the court pursuant to Rule 34(j)(l), Rules of the Sixth Circuit. Upon examination, this panel unanimously agrees that oral argument is not needed. Fed. R.App. P. 34(a).
In May 1993, Duke was convicted in the United States District Court for the Southern District of Indiana following a bench trial of possessing heroin with the intent to distribute and carrying or using a firearm in connection with a crime of violence, violations of 21 U.S.C. § 841(a)(1) and 18 U.S.C. § 924(c). Duke was sentenced to a total of 180 months of imprisonment, including sixty months for the § 924(c) conviction. The Seventh Circuit affirmed his convictions and sentence in February 1994. United States v. Duke, No. 93-2174, 1994 WL 36797 (7th Cir. Feb.8, 1994). Thereafter, Duke filed a (pre-AEDPA) motion to vacate his sentence under 28 U.S.C. § 2255, and the district court denied the motion. The Seventh Circuit affirmed the district court’s judgment in November 1995. Duke v. United States, No. 94-3776, 1995 WL 703727 (7th Cir. Nov.27, 1995). In January 1996, Duke filed a second § 2255 motion to vacate his sentence, arguing inter alia that his § 924(c) conviction was invalid in light of the Supreme Court’s decision in Bailey v. United States, 516 U.S. 137, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995). In May 1996, the district court denied this motion as without merit, concluding that Duke’s § 924(c) conviction was valid. Both the district court and the Seventh Circuit denied Duke a certificate of appealability.
In his current § 2241 habeas corpus petition filed in December 1999, Duke argued that: 1) his Fifth Amendment right to due process and his Eighth Amendment right against cruel and unusual punishment have been violated because his § 924(c) conviction is invalid in light of the Supreme Court’s decision in Bailey; and 2) the Bureau of Prisons has violated his Fifth Amendment right to equal protection by depriving him of programs offered to other inmates.
The district court dismissed Duke’s first claim because Duke was improperly seeking to challenge the imposition of his sentence under § 2241, yet he had failed to show that his remedy under § 2255 was inadequate or ineffective. It dismissed Duke’s second claim because Duke had not exhausted his available administrative remedies. Duke has filed a timely appeal, essentially reasserting his claims.
*500Upon review, we conclude that the district court properly dismissed Duke’s petition. This court renders de novo review of a district court judgment dismissing a habeas corpus petition filed under 28 U.S.C. § 2241. See Charles v. Chandler, 180 F.3d 753, 755 (6th Cir.1999).
With respect to Duke’s first claim, under highly exceptional circumstances, a federal prisoner may challenge his conviction and imposition of sentence under § 2241, instead of § 2255, if he is able to establish that his remedy under § 2255 is inadequate or ineffective to test the legality of his detention. See 28 U.S.C. § 2255 (last clause in fifth paragraph); Charles, 180 F.3d at 755-56. It is the prisoner’s burden to prove that his remedy under § 2255 is inadequate or ineffective. See id. at 756.
Reviewing recent decisions that have invoked this savings clause, the Sixth Circuit in Charles concluded that the courts have done so essentially to permit prisoners to submit claims of actual innocence that would otherwise have been barred under AEDPA. See id. at 756-57. Because the petitioner had failed to submit a facially valid claim of actual innocence in Charles, the court withheld judgment as to whether a claim of actual innocence would permit a petitioner to have a second bite of the apple. Id. at 757; see also Pack v. Yusuff, 218 F.3d 448, 453 (5th Cir.2000) (court declines to articulate circumstances when burden would be met because prisoner had a prior opportunity to present claims and he had not presented a claim of actual innocence); United States v. Barrett, 178 F.3d 34, 52-53 (1st Cir.1999) (same), cert. denied, 528 U.S. 1176, 120 S.Ct. 1208, 145 L.Ed.2d 1110 (2000).
Duke has not met his burden to prove that his § 2255 remedy is inadequate or ineffective for several reasons. First, Duke does not cite to an intervening change in the law or to any extraordinary circumstances which reflect that he may be actually innocent of his crimes. Unlike other prisoners who have obtained review of their claims because they did not have a prior opportunity to present their claims on appeal or in a prior § 2255 motion to vacate, see In re Davenport, 147 F.3d 605, 609, 611 (7th Cir.1998); Triestman v. United States, 124 F.3d 361, 363, 378-80 (2d Cir.1997); In re Dorsainvil, 119 F.3d 245, 251 (3d Cir.1997), Duke has had multiple opportunities to challenge his § 924(c) conviction and sentence on appeal and in his two prior § 2255 motions to vacate. Indeed, Duke did raise a Bailey claim in his second § 2255 motion to vacate his sentence, and the district court denied the motion as without merit. Having had a prior opportunity to raise his arguments, Duke is not entitled to do so in a § 2241 habeas petition.
Second, it is unclear whether and to what extent someone like Duke can show actual innocence in relation to his claim challenging the imposition of his sentence. See Wofford v. Scott, 177 F.3d 1236, 1244-45 (11th Cir.1999). We need not resolve this issue in this case, however, because Duke does not rely on any intervening Supreme Court decision for relief.
Third, Duke’s remedy under § 2255 is not rendered deficient for any other reason under the circumstances of this case. As the court explained in Charles, the remedy under § 2255 is not rendered inadequate or ineffective simply because a petitioner has been denied relief under § 2255, because the petitioner may be denied permission to file a second or successive motion to vacate, or because the petitioner has allowed the one-year statute of limitations to expire. Charles, 180 F.3d at 756-58; accord United States v. Lurie, 207 F.3d 1075, 1077-78 (8th Cir.2000). *501The remedy afforded under § 2241 is not an additional, alternative or supplemental remedy to that prescribed under § 2255. See Charles, 180 F.3d at 758.
Finally, we conclude that the district court properly dismissed Duke’s second claim because Duke did not exhaust his administrative remedies with respect to this claim. See Rourke v. Thompson, 11 F.3d 47, 49 (5th Cir.1993); Gonzalez v. United States, 959 F.2d 211, 212 (11th Cir.1992); Tucker v. Carlson, 925 F.2d 330, 332 (9th Cir.1991); Little v. Hopkins, 638 F.2d 953, 953-54 (6th Cir.1981). Duke acknowledged that he did not even attempt to exhaust the administrative remedies available to him with the BOP. Although Duke stated that those remedies were inadequate and ineffective, he did not provide anything to support this allegation.
Accordingly, we affirm the district court’s judgment. Rule 34(j)(2)(C), Rules of the Sixth Circuit.