
594 F.3d 1326 (2010)
Ismael F. ARNAIZ, Petitioner-Appellant,
v.
WARDEN, FEDERAL SATELLITE LOW, Respondent-Appellee.
No. 07-12649.
United States Court of Appeals, Eleventh Circuit.
January 26, 2010.
Courtland L. Reichman (Court-Appointed), King & Spalding, Atlanta, GA, for Arnaiz.
Edmund A. Booth, Jr., U.S. Atty., Augusta, GA, James C. Stuchell, U.S. Atty., Savannah, GA, for Warden.
Before EDMONDSON, BIRCH and COX, Circuit Judges.
PER CURIAM:
Petitioner-Appellant Ismael F. Arnaiz appeals the dismissal of his petition for a writ of habeas corpus under 28 U.S.C. § 2241, challenging solely the restitution ordered in connection with his convictions for conspiracy to commit money laundering and mail fraud. In this appeal we must decide whether Arnaiz can collaterally attack the restitution part of his sentence by seeking a writ of habeas corpus while he is imprisoned. We conclude that he can cannot get relief from the restitution *1327 and affirm the district court's dismissal of the habeas petition.

I. BACKGROUND
Arnaiz entered into a plea agreement with the United States Attorney for the Southern District of Florida in April 1996, well over a year before the grand jury returned its indictment in July 1997. Under the terms of the plea agreement, Arnaiz agreed to plead guilty to one count of mail fraud in violation of 18 U.S.C. § 1341 and one count of money laundering in violation of 18 U.S.C. § 1956(a)(1). The plea agreement listed the pertinent period of conduct as "the period June 1, 1994 through in or about January, 1996." The agreement also stipulated that restitution would be calculated under the Victim and Witness Protection Act of 1982 ("VWPA"), 18 U.S.C. § 3663(a), which authorizes discretionary restitution sentences.
Later, the indictment ultimately charged, and Arnaiz plead guilty to, conspiracy to commit money laundering under 18 U.S.C. § 1956(h). The indictment specified the pertinent period of conduct from "in or about May, 1994, and continuing to on or about the date of this Indictment [July 28, 1997]." Because of the enlarged window of relevant conduct in the indictment, Arnaiz's sentence was entered pursuant to the Mandatory Victims Restitution Act of 1996 ("MVRA"), 18 U.S.C. § 3664(f)(1)(A),[1] which required full restitution of the loss to victims. The sentencing court ordered Arnaiz to pay restitution in excess of $24 million.
Arnaiz contends that his counsel failed to bring the consequence of the time differences between the plea agreement and the indictment to Arnaiz's attention. As a result, no arguments were made to the sentencing court that the VWPA should apply and that the court could consider Arnaiz's ability to pay when ordering the amount of restitution.
Arnaiz is currently incarcerated serving his 144-month sentence. We affirmed his conviction on appeal, United States v. Arnaiz, 144 Fed.Appx. 27 (11th Cir.2005), although the specific issue of whether the MVRA or the VWPA should apply was not raised. In 2006, Arnaiz filed a motion to vacate his sentence and sought release from custody under 28 U.S.C. § 2255. In December 2007, the district court denied the motion.
In January 2007, while his section 2255 motion was pending, Arnaiz filed this petition for a writ of habeas corpus under 28 U.S.C. § 2241, challenging only the restitution part of his sentence. In this petition, Arnaiz advances this contention: his defense counsel was ineffective for not challenging the government's breach of the plea agreement; because of the ineffective assistance of counsel, the trial court imposed restitution in violation of the plea agreement; and his counsel was ineffective for failing to challenge the restitution order at sentencing and on direct appeal.
In the district court, Arnaiz argued that he appropriately styled his collateral attack as a petition for writ of habeas corpus (28 U.S.C. § 2241) because circuit case law foreclosed challenging restitution under section 2255. The district court disagreed, reading our case law as allowing Arnaiz to add his restitution challenge as part of his then-pending section 2255 claim seeking *1328 release from custody. Because the district court concluded that section 2255 could provide an adequate remedy, it dismissed Arnaiz's section 2241 petition for failing to meet the "savings clause" test of section 2255 that generally must be satisfied before the door is opened to habeas corpus under section 2241.
The district court decided this case without the benefit of Mamone v. United States, 559 F.3d 1209 (11th Cir.2009), which was decided after the parties' appellate briefs had been filed but before oral argument in this case. In Mamone, we concluded that section 2255 is an inappropriate vehicle for challenging the restitution part of a sentence, regardless of whether the claim is coupled with one seeking release from custody. Id. at 1210-11. Because the district court's reasoning cannot stand in the light of Mamone, both parties have narrowed their arguments to the remaining dispositive issue: Can a prisoner currently in custody obtain relief from the restitution part of his sentence by seeking a writ of habeas corpus per section 2241?

II. DISCUSSION
We have never decided, in a published opinion, whether a prisoner can collaterally attack just the restitution part of his sentence by seeking a writ of habeas corpus under section 2241.[2] Section 2241 is the statutory grant of authority to federal courts to issue the writ when certain jurisdictional prerequisites are satisfied. Medberry v. Crosby, 351 F.3d 1049, 1059 (11th Cir.2003). At issue here is section 2241(c)(1), which allows us to issue the writ if a prisoner is "in custody under or by color of the authority of the United States."
Arnaiz seeks to have his restitution sentence recalculated. He contends that he can satisfy the "in custody" jurisdictional prerequisite of section 2241 because he is currently incarcerated in federal prison. We agree that he, in fact, is in custody, but that is not the critical question. The question we must decide is, in the light of that custody, whether habeas corpus can provide the remedy Arnaiz seeks. The answer depends on the scope of the writ and its relationship to the asserted custody giving rise to our jurisdiction.
Because the statute itself does not define "habeas corpus," the Supreme Court has "generally looked to common-law usages and the history of habeas corpus both in England and in this country" to determine the writ's scope. See Jones v. Cunningham, 371 U.S. 236, 83 S.Ct. 373, 375, 9 L.Ed.2d 285 (1963). "At its historical core, the writ of habeas corpus has served as a means of reviewing the legality of Executive detention, and it is in that context that *1329 its protections have been strongest." I.N.S. v. St. Cyr, 533 U.S. 289, 121 S.Ct. 2271, 2280, 150 L.Ed.2d 347 (2001). "The typical remedy for such detention is, of course, release." Munaf v. Geren, ___ U.S. ___, 128 S.Ct. 2207, 2221, 171 L.Ed.2d 1 (2008). In recognition of this historical purpose and scope, the statutes controlling our jurisdiction to grant habeas relief all require some form of custody. See Carafas v. LaVallee, 391 U.S. 234, 88 S.Ct. 1556, 1560 & n. 10, 20 L.Ed.2d 554 (citing 9 W. HOLDSWORTH, HISTORY OF ENGLISH LAW 108-25 (1926)).
Federal courts have expanded the scope of what constitutes "custody" beyond literal physical confinement. E.g., Jones, 83 S.Ct. at 377 (parole is a form of custody). But whatever the expanded scope of our jurisdiction may be, the remedy that habeas corpus provides remains tied to some form of relief from the petitioner's custody. Cf. Munaf, 128 S.Ct. at 2221 ("[The] nature of the relief sought by the habeas petitioners suggests that habeas is not appropriate in these cases. Habeas is at its core a remedy for unlawful executive detention .... But here the last thing petitioners want is simple release." (internal citation omitted)). "It is clear, not only from the language of [the statutes], but also from the common-law history of the writ, that the essence of habeas corpus is an attack by a person in custody upon the legality of that custody ...." Preiser v. Rodriguez, 411 U.S. 475, 93 S.Ct. 1827, 1833, 36 L.Ed.2d 439 (1973) (emphasis added).
In Arnaiz's case, a successful challenge to the restitution part of his sentence would, in no way, provide relief for the physical confinement supplying the custody necessary for federal habeas jurisdiction. In other words, no significant connection exists between Arnaiz's factual custody and the legal relief he seeks. And because habeas corpus has traditionally required a relationship between a petitioner's custody and the relief sought, we do not understand section 2241 to extend to the facts of this case.[3]
For restitution, our decision today treats different people convicted of the same federal crime alike, regardless of whether they were or were not also sentenced to prison. In Mamone, we decided that a petitioner cannot challenge a restitution sentence with a motion to vacate his sentence  even when joined with a claim seeking release from custody  because the language of section 2255 limits its application to "a prisoner in custody ... claiming the right to be released." 559 F.3d at 1211. We noted that a contrary rule *1330 would result in incongruent access to the courts because it would allow prisoners sentenced to both imprisonment and restitution a collateral attack on restitution under 2255, but not defendants only sentenced to restitution. Id. We thought such an incongruent result was both "unwarranted by the language and purpose of § 2255." Id.
Our sister circuits agree with this congruence rationale in a similar context under section 2255. See, e.g., United States v. Segler, 37 F.3d 1131, 1137 (5th Cir.1994); Smullen v. United States, 94 F.3d 20, 25-26 (1st Cir.1996). We accept this line of reasoning and extend it so that such incongruent results will be avoided under section 2241. We see no good reason why Arnaiz  who was properly convicted and sentenced to a term of imprisonment, but was allegedly improperly sentenced to restitution  should be permitted a remedy under the federal habeas statute when someone else that was properly convicted and given only an improper restitution sentence is not.

III. CONCLUSION
We conclude that the district court was mistaken when it dismissed Arnaiz's petition for a writ of habeas corpus on the ground that he must first satisfy the savings clause test in 28 U.S.C. § 2255(e). But, we affirm the district court's dismissal of the petition because habeas corpus cannot be used to challenge just the restitution part of a sentence when the custody supporting our jurisdiction is actual imprisonment.
AFFIRMED.
NOTES
[1]  Briefly stated, under the MVRA, which became effective on 24 April 1996, the district court must order restitution in the full amount of the victim's loss, regardless of the defendant's ability to pay. 18 U.S.C. § 3664(f)(1)(A). Before the MVRA, restitution was discretionary and the district court was required to consider the defendant's ability to pay in determining the amount of restitution owed. United States v. Thayer, 204 F.3d 1352, 1357 (2000).
[2]  We declined to decide this issue in Dohrmann v. United States, 442 F.3d 1279 (11th Cir.2006), because the petitioner had defaulted his claim and "failed to demonstrate the exceptional circumstances required in order for this court to hear such an argument [for the first time] in a collateral proceeding." Id. at 1280-81. Although Arnaiz also defaulted his claim by failing to raise his restitution challenge at sentencing or on direct appeal, unlike Dohrmann, he has alleged cause (ineffective assistance of counsel) that would constitute exceptional circumstances if proved. See Murray v. Carrier, 477 U.S. 478, 106 S.Ct. 2639, 2645-46, 91 L.Ed.2d 397 (1986). The district court did not reach the issue of exceptional circumstances because it dismissed the petition on different grounds. But because we believe that habeas corpus cannot be used to challenge restitution on these facts, "a remand to the district court for a hearing on ... procedural default would be a waste of time." See Cain v. Redman, 947 F.2d 817, 820 (6th Cir.1991). By the way, to the degree that the district court on remand might have to decide constitutional questions dealing with ineffectiveness of counsel, we especially wish to avoid pressing the district court to make an unnecessary decision: Constitutional issues should be decided as a last resort.
[3]  Given the arguments presented to us, we do not decide whether, in some other circumstances, an order to pay restitution may itself be a restraint on liberty sufficient to constitute custody within the meaning of the habeas statutes that would allow relief from the restitution order. See Kaminski v. United States, 339 F.3d 84, 87 (2d Cir.2003) ("Whether a fine or restitution order could ever be such a restraint on the liberty of a petitioner as to amount to custody is a question we need not reach today ....") But see Mays v. Dinwiddie, 580 F.3d 1136, 1139 (10th Cir.2009) ("`[T]he payment of restitution or a fine, absent more, is not the sort of significant restraint on liberty contemplated in the custody requirement of the federal habeas statutes.'"); Westberry v. Keith, 434 F.2d 623, 624-25 (5th Cir.1970) (per curiam) (no custody where petitioner suffered fine and revocation of driver's license); Spring v. Caldwell, 692 F.2d 994, 996-99 (5th Cir.1982) ("We hold that an arrest warrant issued for willful refusal to pay a fine does not amount to custody within the meaning of 28 U.S.C. §§ 2241 and 2254 in habeas cases challenging the constitutionality of a statute that only imposes a fine."). We also express no opinion on the availability of other writs, such as a writ of coram nobis, to bring collateral attacks against restitution orders. See Kaminski, 339 F.3d at 89-90 & n. 4 (discussing but not deciding this issue).
