OPINION

SUTTON, Circuit Judge.

Garry James appealed from a judgment that gave him everything he wants, leaving him with no injury. We dismiss his appeal for lack of jurisdiction.

In 2005, seventeen days into his parole for a state drug conviction, the police caught James selling drugs while carrying a pistol. That proved doubly bad for James. Michigan revoked his parole, sending him back to state prison for five more years. And the federal government indicted him for carrying a firearm while drug trafficking, which comes with a mandatory minimum five-year prison term and potentially a life sentence. See 18 U.S.C. § 924(c)(1)(A)(i).

Less than a year into his state sentence, the State temporarily transferred James to federal custody to face his federal charge. James pleaded guilty, and a federal district court sentenced him to a below-guidelines fifteen-year sentence. The court chose to run the sentence concurrently to James' pre-existing state sentence, meaning James would serve the first part of his federal sentence in state prison. Before transferring James back to state prison, the court told James that he would receive "credit" for the time he had "been in custody of the federal marshal": from July 20, 2006, through January 4, 2007. R. 55 at 26-27.

As James' state prison term neared an end, the federal Bureau of Prisons told him that he would not receive any credit for his presentence time in federal custody. The Bureau reasoned that it could ignore what the district court said at sentencing because it, not the district court, calculates presentence credit. It thought that awarding James any such credit would impermissibly "double credit" him since Michigan had already given him state credit for the same time. Under its calculation, James would not be eligible for release as early as the district court said he would.

James preferred the district court's approach. Invoking Criminal Rule 36, James filed a motion in the district court to amend its judgment to make clear that it wanted him to receive presentence credit toward his federal sentence. The court complied, adding to the original judgment that James "shall get credit for time served beginning July 20, 2006, to January 4, 2007." R. 51 at 2. That was good but not good enough, thought James. He worried that the amended judgment failed to give him "credit" for his time spent in state prison after January 4, 2007 — until his state sentence ended on October 12, 2010. He appealed, asking us to clarify that he deserves "credit" for this time too.

The amended judgment gives James everything he wants. The Bureau of Prisons followed the amended judgment's instructions, giving James the "Jail Credit" he wanted from July 20, 2006, through January 3, 2007. See Addendum to Appellee's Br., Bureau of Prisons Sentence Computation (June 24, 2015). And the Bureau has not changed how it treated James' sentence from January 4, 2007, on: as a concurrent one beginning on that day and still running today. See id. The upshot is that James' federal-sentence clock has been ticking at all times since July 20, 2006 — and thus for all times that James requests on appeal.

But if that is true, James asks, why does the amended judgment say he receives "credit" only until January 4, 2007 (his federal sentencing date), and not until October 12, 2010 (the end of his state prison term)? The answer turns on the difference between credits and concurrent sentences. This kind of "credit" is by definition "awarded only for presentence restraints on liberty." Reno v. Koray, 515 U.S. 50, 56, 115 S.Ct. 2021, 132 L.Ed.2d 46 (1995); see 18 U.S.C. § 3585. The court's amended judgment thus properly recognizes that James can receive "credit" only for his presentence time in federal custody while leaving in place the fact that his concurrent federal sentence has been running at all times since January 4, 2007. For all relevant purposes, James has received the relief he requests — in the name of a concurrent sentence rather than any sort of credits.

James does not ask for, and thus cannot receive, anything more. When the appealing party obtains the relief he seeks, when he has no actual injury capable of redress, we must dismiss the appeal for lack of Article III jurisdiction. See Lujan v. Defenders of Wildlife, 504 U.S. 555, 560-61, 112 S.Ct. 2130, 119 L.Ed.2d 351 (1992); Fialka-Feldman v. Oakland Univ. Bd. of Trs., 639 F.3d 711, 713 (6th Cir.2011); United States v. Riley, 609 Fed.Appx. 837, 841-42 (6th Cir.2015).

For these reasons, we dismiss the appeal.