OPINION OF THE COURT

RENDELL, Circuit Judge.

The question presented by this appeal is whether appellant John Burkey’s release from Bureau of Prisons (“BOP”) custody caused his pending habeas corpus petition — which challenged the BOP’s failure to grant him early release — to be moot because it no longer presented a case or controversy under Article III, § 2, of the Constitution. We agree with the District Court that Burkey’s petition is moot because his assertion of “collateral consequences” is insufficient. We will therefore affirm.

BACKGROUND

In 1996, Burkey was serving a sentence for federal controlled substances convictions at the Federal Correctional Institution at McKean in Bradford, Pennsylvania. The BOP determined that he was eligible for early release pursuant to 18 U.S.C. § 3621(e)(2)(B), 1 because he had completed a residential drug treatment program. Burkey received his early release credit, and was released to serve his term of supervised release.

While on supervised release, Burkey committed new controlled substances crimes and was rearrested. In July of 2003, he was sentenced in United States District Court for the Northern District of Ohio to a term of imprisonment of 57 months, to be followed by 3 years of supervised release. A few weeks later, the sentencing court imposed a three-month supervised release violator term, to be served concurrent with the 57-month term of imprisonment.

Burkey returned to prison and participated once again in the drug treatment program, expecting to again qualify for early release. However, the BOP, relying on a recently adopted rule, namely, Paragraph 5(c) of Program Statement 5331.01, 2 *145 determined that he was ineligible for early release because he had previously received an early release credit under the statute.

Burkey pursued his administrative remedies through the BOP, attempting at first to raise an ex post facto argument. The Warden denied him relief and he lost his appeal at the Regional level. Upon denial of that appeal, he filed a Central Office Administrative Remedy Appeal, arguing for the first time that Paragraph 5(c) of Program Statement 5331.01 was issued in violation of the Administrative Procedures Act and thus was invalid. In March of 2006, Burkey’s Central Office Administrative Remedy Appeal was denied on the basis that his ex post facto claim had no merit. The APA claim was not addressed.

In May of 2006, Burkey filed a pro se petition for writ of habeas corpus, 28 U.S.C. § 2241, in United States District Court for the Western District of Pennsylvania, where he was confined. He challenged the BOP’s determination that he was not eligible for early release under 18 U.S.C. § 3621(e)(2)(B), urging that Paragraph 5(c) of Program Statement 5331.01 was promulgated in violation of the Administrative Procedures Act, 5 U.S.C. § 553, and was, therefore, invalid. Burkey asked to be released from detention. The Federal Public Defender was appointed to represent him.

In August of 2007, the Magistrate Judge issued a thorough Report and Recommendation, concluding that the BOP had violated the APA. The APA provides that an agency may not adopt a rule without providing prior notice through publication in the Federal Register and comment. 5 U.S.C. § 553(b), (c). The Magistrate Judge reasoned that Paragraph 5(c) of Program Statement 5331.01 was neither an exempt “interpretative rule” nor an exempt general statement of policy. See Dia Navigation Co., Ltd. v. Pomeroy, 34 F.3d 1255, 1264 (3d Cir.1994). It was instead a legislative rule, see id., subject to the APA, and the BOP could not avoid the APA’s requirements by placing a legislative rule in a Program Statement, instead of first publishing it in the Federal Register. The Magistrate Judge recommended that Bur-key’s request for habeas corpus relief be granted because he had completed the residential drug treatment program.

On September 7, 2007, the BOP released Burkey from custody, nine days before his statutory release date of September 16, 2007. It then filed in this ease a Notice of Suggestion of Mootness, contending that, because Burkey had, through his release, achieved the object of his habeas corpus petition, his case was moot. Burkey filed a written response, and urged that his petition was not moot because, if the District Court would issue an order approving and adopting the Magistrate Judge’s Report and Recommendation, he then would be able to argue to the sentencing court in Ohio that his supervised release term should be shortened in light of his having *146 been improperly denied early release from prison. 3

The District Court dismissed Burkey’s habeas corpus petition as moot. The court observed that, to avoid a finding of mootness, Burkey would have to demonstrate that the delayed commencement of his supervised release term was likely to be redressed by a favorable judicial decision, Spencer v. Kemna, 523 U.S. 1, 7, 118 S.Ct. 978, 140 L.Ed.2d 43 (1998). The court concluded that it was “pure speculation that a favorable decision from this Court would ‘likely’ result in [Burkey’s] sentencing court reducing or terminating his supervised release term under Section 3583(e).” Burkey v. Lappin, 2007 WL 4480188, at * 2 (W.D.Pa. December 14, 2007). The District Court did not believe it could predict what the sentencing court would do in Burkey’s case, and thus it could not conclude that the relief sought likely would be granted.

The District Court rejected precedent in the Second and Ninth Circuits, Levine v. Apker, 455 F.3d 71 (2d Cir.2006), and Mujahid v. Daniels, 413 F.3d 991 (9th Cir.2005), which permit a case to continue when there is only a “possibility” that a court might modify a term of supervised release, and concluded that more is required to maintain a case or controversy under Article III. The District Court also referred to the view expressed by the Supreme Court in United States v. Johnson, 529 U.S. 53, 120 S.Ct. 1114, 146 L.Ed.2d 39 (2000), that incarceration and supervised release serve distinct objectives and are not to be viewed as interchangeable punitive measures. Burkey, 2007 WL 4480188, at * 2 (citing Johnson, 529 U.S. at 57-58, 120 S.Ct. 1114). This, the District Court reasoned, detracted from the likelihood that the sentencing court would modify Burkey’s term of supervised release based on his having been in prison longer than he perhaps should have been as a result of the BOP’s APA violation.

Burkey appeals. We have jurisdiction pursuant to 28 U.S.C. § 1291. United States v. Cepero, 224 F.3d 256, 264-65 (3d Cir.2000) (certificate of appeal-ability not required to appeal from denial of section 2241 petition). The standard of review over the District Court’s mootness determination is plenary. United States v. Gov’t of Virgin Islands, 363 F.3d 276, 284 (3d Cir.2004). Insofar as Burkey was in BOP custody when he filed his habeas corpus petition under 28 U.S.C. § 2241, he has satisfied the “in custody” jurisdictional requirement, Carafas v. LaVallee, 391 U.S. 234, 238, 88 S.Ct. 1556, 20 L.Ed.2d 554 (1968), and he appropriately filed his habe-as corpus petition in the district of confinement and named the Warden as the respondent, Rumsfeld v. Padilla, 542 U.S. 426, 443, 124 S.Ct. 2711, 159 L.Ed.2d 513 (2004).

DISCUSSION

A challenge to the BOP’s execution of a sentence is properly brought under 28 U.S.C. § 2241. Woodall v. Federal Bureau of Prisons, 432 F.3d at 235, 241-43 (3d Cir.2005); Coady v. Vaughn, 251 F.3d 480, 485 (3d Cir.2001). The BOP waived *147 any exhaustion of administrative remedies argument it might have had concerning the APA claim insofar as 28 C.F.R. § 542.15 prohibits an inmate from raising on appeal an issue that was not raised at the initial and intermediate levels of the administrative remedy process. Burkey’s habeas corpus petition sought release from prison based on the invalidity under the APA of the Program Statement denying him early release. That relief was afforded him when, on the Magistrate Judge’s recommendation, the BOP released him in September of 2007 to begin serving his 3-year term of supervised release. Given this, is a case or controversy still presented? We conclude the answer is no, and, therefore, Burkey’s habeas corpus petition is moot.

Under Article III of the Constitution, a federal court may adjudicate “only actual, ongoing eases or controversies.” Lewis v. Continental Bank Corp., 494 U.S. 472, 477, 110 S.Ct. 1249, 108 L.Ed.2d 400 (1990). “To invoke the jurisdiction of a federal court, a litigant must have suffered, or be threatened with, an actual injury traceable to the defendant and likely to be redressed by a favorable judicial decision.” Id. (citing Allen v. Wright, 468 U.S. 737, 750-751, 104 S.Ct. 3315, 82 L.Ed.2d 556 (1984); Valley Forge Christian College v. Americans United for Separation of Church & State, Inc., 454 U.S. 464, 471-473, 102 S.Ct. 752, 70 L.Ed.2d 700 (1982)). Article III denies the District Court the power to decide questions that cannot affect the rights of litigants before it, and confines it to resolving live controversies “admitting of specific relief through a decree of a conclusive character, as distinguished from an opinion advising what the law would be upon a hypothetical state of facts.” Aetna Life Insurance Co. v. Haworth, 300 U.S. 227, 241, 57 S.Ct. 461, 81 L.Ed. 617 (1937).

The case or controversy requirement continues through all stages of federal judicial proceedings, trial and appellate, and requires that parties have a personal stake in the outcome. Lewis, 494 U.S. at 477-478, 110 S.Ct. 1249. “This means that, throughout the litigation, the plaintiff ‘must have suffered, or be threatened with, an actual injury traceable to the defendant and likely to be redressed by a favorable judicial decision.’ ” Spencer, 523 U.S. at 7, 118 S.Ct. 978 (quoting Lewis, 494 U.S. at 477, 110 S.Ct. 1249). Incarceration satisfies the case or controversy requirement; it is a concrete injury caused by a conviction and is likely to be redressed by invalidation of the conviction. Id. Once a sentence has expired, however, some continuing injury, also referred to as a collateral consequence, must exist for the action to continue. Id.

Following Sibron v. New York, 392 U.S. 40, 88 S.Ct. 1889, 20 L.Ed.2d 917 (1968), the Supreme Court “abandoned all inquiry into the actual existence of collateral consequences,” id. at 55, 88 S.Ct. 1889, and “proceeded to accept the most generalized and hypothetical of consequences as sufficient to avoid mootness” in a challenge to a conviction. Spencer, 523 U.S. at 10, 118 S.Ct. 978. In Lane v. Williams, 455 U.S. 624, 102 S.Ct. 1322, 71 L.Ed.2d 508 (1982), the Court declined to extend the presumption of collateral consequences in the context of a challenge to a mandatory parole violator term when, during the pendency of the litigation, the term had expired. Id. at 632-33, 102 S.Ct. 1322. Most recently in Spencer, the Court “decline[d] to presume that collateral consequences adequate to meet Article Ill’s injury-in-fact requirement resulted from petitioner’s parole revocation,” Spencer, 523 U.S. at 14, 118 S.Ct. 978, once that term had expired. As in Lane, the fact that the parolee was not challenging the validity of his convic *148 tion factored heavily in the decision not to presume collateral consequences.

Thus, collateral consequences will be presumed when the defendant is attacking his conviction while still serving the sentence imposed for that conviction, but we also have held that they will be presumed where the defendant is attacking that portion of his sentence that is still being served. See, e.g., United States v. Jackson, 523 F.3d 234, 242 (3d Cir.2008). In Jackson, we held that collateral consequences are presumed where the appellant was still serving a term of supervised release and her challenge was to the reasonableness of the supervised release term. Id. Where, however, the appellant is attacking a sentence that has already been served, collateral consequences will not be presumed, but must be proven. See United States v. Cottman, 142 F.3d 160, 165 (3d Cir.1998).

Burkey has served his sentence but remains subject to a 3-year term of supervised release. However, he did not challenge the validity or reasonableness of that term in his habeas corpus petition, as did the appellant in Jackson. His challenge was more remote, attacking only what the BOP had done, and urging it as the basis for the sentencing court to now afford him relief against an indisputably valid term of supervised release. In such circumstances, he must demonstrate that collateral consequences exist; they will not be presumed. Cf. Jackson, 523 F.3d at 241 (Cottman held that collateral consequences will not be presumed when “[a] defendant who is serving a term of supervised release ... challenges only his completed sentence of imprisonment”).

Even though collateral consequences are not presumed, a petitioner may still avoid a finding of mootness if he can show a continuing injury, or collateral consequence, that is sufficient. Spencer, 523 U.S. at 14, 118 S.Ct. 978. The delayed commencement of Burkey’s validly imposed term of supervised release is, he alleges, his “continuing injury,” but this is insufficient for mootness purposes in his case, given his release from BOP custody. We reach this conclusion because the Supreme Court, in Lewis and Spencer, addressed the issue of collateral consequences in terms of the “likelihood” that a favorable decision would redress the injury or wrong. In fact, in Spencer, the Court rejected numerous collateral consequences proffered by the petitioner because they were no more than “a possibility rather than a certainty or even a probability,” or pure speculation. 523 U.S. at 14-16, 118 S.Ct. 978. 4

The “likely” outcome here is not that the District Court’s order will cause the sentencing court in Ohio to reduce Burkey’s term of supervised release. Quite apart from the instant petition, Burkey has the *149 right to file in the sentencing court a motion for termination of his term of supervised release pursuant to 18 U.S.C. § 3583(e), because he has served one year of his term. Under 18 U.S.C. § 3583(e)(1), a defendant who has completed one year of his supervised release term may file a motion, and the sentencing court has the authority to terminate a defendant’s supervised release obligations “at any time after the expiration of one year ... if it is satisfied that such action is warranted by the conduct of the defendant released and the interest of justice.” 18 U.S.C. § 3583(e)(1).

However, the District Court reasoned that Burkey’s ability to obtain modification under the supervised release statute turns on a discretionary decision of the sentencing court, which must consider many factors pursuant to 18 U.S.C. § 3553(a), including those which bear directly on the objectives of supervised release. From a practical, and legal, standpoint, we too doubt whether a sentencing judge, having imposed a specific term of imprisonment and supervised release, would alter his view as to the propriety of that sentence because the BOP required the defendant to serve it.

The concept of interchangeability of supervised release for incarceration was specifically rejected by the Supreme Court in Johnson, 529 U.S. at 59-60, 120 S.Ct. 1114, as the District Court noted. The probability that the sentencing court here would reduce Burkey’s term of supervised release — especially given his past recidivism — as an equalizer for his incarceration, has not been established. As the applicable § 3553(a) factors indicate, a decision under § 3583(e) generally is more directly influenced by the particular defendant and the underlying conduct that formed the basis for the term of supervised release. Cf. Lane, 455 U.S. at 632-33, 102 S.Ct. 1322 (observing that discretionary decisions made by sentencing court “are more directly influenced by [] the underlying conduct that formed the basis for the parole violation”).

The possibility that the sentencing court will use its discretion to modify the length of Burkey’s term of supervised release under 18 U.S.C. 3583(e), which it may do as long as the reason for doing so is not to offset excess prison time, Johnson, 529 U.S. at 57-60, 120 S.Ct. 1114, 5 is so speculative that any decision on the merits by the District Court would be merely advisory and not in keeping with Article Ill’s restriction of power. See Flast v. Cohen, 392 U.S. 83, 96 n. 14, 88 S.Ct. 1942, 20 L.Ed.2d 947 (1968) (noting long established rule against advisory opinions). The District Court may not render an advisory opinion in Burkey’s case, because “[t]he duty of [the] court ... is to decide actual controversies by a judgment which can be carried into effect, and not to give opinions upon moot questions or abstract propositions, or to declare principles or rules of law which cannot affect the matter in issue in the case before it,” Mills v. Green, 159 U.S. 651, 653, 16 S.Ct. 132, 40 L.Ed. 293 (1895).

While our sister courts of appeals have found a live case or controversy *150 where a “possibility” exists that a court would reduce a term of supervised release in situations similar to this, see, e.g., Levine, 455 F.3d 71, and Mujahid, 413 F.3d 991, we are unwilling to do so. We do not believe the reasoning of these case is supportable, given the Supreme Court’s directives in Lewis and Spencer. In Cott-man, we concluded that the defendant’s challenge to his sentence, if successful, would “likely” have resulted in a reduced guideline range and a credit — given by the same court which originally sentenced him incorrectly — against his term of supervised release. 142 F.3d at 165. We thus adhere to the requirement that the injury must be “likely” to be redressed by the judicial decision. A “possibility” of redress, which is all that Levine and Mujahid require, is not adequate to survive a mootness challenge. Here, we cannot say that the injury to Burkey will “likely” be redressed by the District Court’s grant of his habeas corpus petition.

A comment is in order as to why other courts may have viewed the “possibility” of redress as sufficient to avoid a finding of mootness. The Ninth Circuit, in Mujahid, 413 F.3d 991, placed a “heavy” burden on the government to show mootness, id. at 994, but a court has a “special obligation to satisfy itself of its own jurisdiction,” McNasby v. Crown Cork & Seal Co., 832 F.2d 47, 49 (3d Cir.1987), and we have held that it is a petitioner’s burden to demonstrate that collateral consequences exist, United States v. Kissinger, 309 F.3d 179, 181 (3d Cir.2002). We think this to be the better view, because it is consistent with the jurisprudence regarding the “presumption” of collateral consequences. For, if not presumed, surely they must be proven; and the petitioner is clearly the one to do so. Cf. Spencer, 523 U.S. at 14, 118 S.Ct. 978 (“The question remains, then, whether petitioner demonstrated such consequences.”). Levine too can be distinguished because there the parties did not raise the mootness issue, leaving the court to address it without the benefit of briefing. 455 F.3d at 77.

We also note that certain permissive language in the Supreme Court’s discussion in Johnson following its statement that incarceration and supervised release are not interchangeable, could be taken as lessening the petitioner’s burden to show a “likelihood” of relief in the context of the mootness inquiry. Following the discussion of its holding, the Court noted that a term of supervised release “may” be modified where an individual serves excess prison time, specifically recognizing the ability of the courts to reduce a term of supervised release when the equities would justify it. The Court stated:

There can be no doubt that equitable considerations of great weight exist when an individual is incarcerated beyond the proper expiration of his prison term. The statutory structure provides a means to address these concerns in large part. The trial court, as it sees fit, may modify an individual’s conditions of supervised release.

Johnson, 529 U.S. at 60, 120 S.Ct. 1114 (citing 18 U.S.C. § 3583(e)(2)).

While this could be said to lower the bar where proving sufficient collateral consequences is required, we view it, instead, as nothing more or less than an appropriate reference to the discretion of a sentencing court to modify a term of supervised release pursuant to § 3583(e). Consistent with this, we have referred to this language in support of our ruling in Cottman that the sentencing court likely would alter the term of supervised release upon a conclusion that the sentence it imposed was improper. 142 F.3d at 165. And, in Jackson, we cited this language from Johnson, and then stated: “Accordingly, a likely *151 credit against a defendant’s term of supervised release for an excess term of imprisonment still remains valid after Johnson.” Jackson, 523 F.3d at 239. However, no court has held that the existence of the discretion available under the supervised release statute, 18 U.S.C. § 3583(e), is probative of the question of whether it is “likely,” as is required by Lewis and Spencer as part of the inquiry into mootness, that a sentencing court in a particular case will provide relief such that a sufficient collateral consequence is shown. Thus, we do not agree with the reasoning of the Second and Ninth Circuits, and conclude that adherence to the appropriate Article III standards set forth in Lewis and Spencer requires affirmance.

For the foregoing reasons, we will AFFIRM the order of the District Court dismissing Burkey’s habeas corpus petition as moot.

. The statute provides:

Period of Custody ... The period a prisoner convicted of a nonviolent offense remains in custody after successfully completing a treatment program may be reduced by the Bureau of Prisons, but such reduction may not be more than one year from the term the prisoner must otherwise serve.

18 U.S.C. § 3621(e)(2)(B).

. Paragraph 5 of Program Statement 5331.01 states in pertinent part:

5. EARLY RELEASE CRITERIA. In this section, we briefly describe the criteria that an inmate must meet to be eligible for early release. For details on the early release criteria, see [28 C.F.R. § 550.58].

a. Eligibility Criteria for Early Release. Inmates must meet the following eligibility criteria to earn early release: * * * *

■ Residential Drug Abuse Program Completion. To earn early release, an inmate must complete all required components of the residential drug abuse program *145 (RDAP) successfully. RDAP completion is defined in the Psychology Services Manual.

c. Inmates Ineligible for Early Release. The Bureau has determined that the following categories of inmates are not eligible for early release:

■ Prior Early Release Granted. Inmates may earn an early release for successful RDAP completion only once. Inmates returning on supervised release violations and/or inmates who are sentenced for new offenses are not eligible for early release if they received it previously....

Bureau of Prisons Program Statement 5331.01, at ¶ 5 (September 29, 2003, as corrected, October 3, 2003).

. Pursuant to 18 U.S.C. § 3583(e), only the sentencing court has the authority to modify Burkey’s term of supervised release. See generally Gozlon-Peretz v. United States, 498 U.S. 395, 400-01, 111 S.Ct. 840, 112 L.Ed.2d 919 (1991) (under Sentencing Reform Act sentencing court oversees “post[-]confinement monitoring” and may "terminate, extend, or alter the conditions of the term of supervised release prior to its expiration” pursuant to § 3583(e)); United States v. Lussier, 104 F.3d 32, 34-35 (2d Cir.1997) (under § 3583(e) sentencing court retains authority to revoke, discharge, or modify terms and conditions of supervised release following its initial imposition of supervised release term).

. The petitioner in Spencer alleged that the revocation of his parole could be used to his detriment in a future parole proceeding, but the Court rejected this as "a possibility rather than a certainty or even a probability" because, under Missouri law, a prior parole revocation is but one factor among many to be considered by the parole authority. Spencer, 523 U.S. at 14, 118 S.Ct. 978. The petitioner also contended that the revocation could be used to increase his sentence in a future sentencing proceeding. The Court rejected this because it was contingent upon the speculative possibility that the petitioner would violate the law, get rearrested, and be convicted. Id. The Court rejected petitioner’s third and fourth contentions — that the finding of a parole violation for forcible rape and armed criminal action could be used to impeach him should he appear as a witness or litigant in a future criminal or civil proceeding, or could be used against him directly pursuant to Federal Rule of Evidence 405— as, again, purely a matter of speculation. Id. at 15-16, 118 S.Ct. 978.

. In Johnson, which did not involve a mootness issue, the defendant served excess prison time as a result of certain vacated sentences. He was released to begin serving his mandatory three-year term of supervised release and filed a motion, seeking a credit against his supervised release term for the excess time he spent in prison, which was denied. The Supreme Court agreed that the motion could not be granted, because, pursuant to the express terms of 18 U.S.C. § 3624(e), a supervised release term does not commence until an individual is released from imprisonment and, therefore, a credit was not automatic. 529 U.S. at 57, 120 S.Ct. 1114.