
606 F.3d 829 (2010)
Susan SWANSON, Petitioner-Appellee,
v.
Thomas DeSANTIS, Respondent-Appellant.
No. 09-1501.
United States Court of Appeals, Sixth Circuit.
Submitted: January 21, 2010.
Decided and Filed: June 4, 2010.
*830 ON BRIEF: Brian O. Neill, Office of the Michigan Attorney General, Lansing, Michigan, for Appellant. Lawrence J. Emery, Law Office, Lansing, Michigan, for Appellee.
Before: BATCHELDER, Chief Judge; SUTTON and KETHLEDGE, Circuit Judges.

OPINION
SUTTON, Circuit Judge.
Susan Swanson filed a federal habeas corpus petition challenging her state court conviction on two grounds. The district court concluded that Swanson had exhausted her state remedies for one of the claims but not the other, then allowed the exhausted claim to proceed in federal court but stayed the unexhausted claim pending its review in state court. The State appeals, arguing that the district court may not proceed with a partially exhausted petition. Because we do not have the power to review this non-final judgment, we dismiss the appeal for lack of jurisdiction.

I.
In 2002, Swanson hit and killed a pedestrian while driving on Grand River Avenue outside of Lansing, Michigan. The next year, a jury convicted her of (1) operating a motor vehicle under the influence and causing death, and (2) failing to stop at the scene of an accident involving a serious injury. See M.C.L. §§ 257.625(4), 257.617. She received a combined sentence of 54 to *831 180 months. The Michigan Court of Appeals and the Michigan Supreme Court denied her requests for relief. See People v. Swanson, 474 Mich. 1085, 711 N.W.2d 41 (2006).
In 2007, Swanson petitioned for federal habeas corpus relief on two grounds: (1) the trial court gave the jury constitutionally defective instructions; and (2) her sentence turned on judicial factfinding in violation of Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004). Michigan responded that Swanson did not exhaust the claims in state court. See 28 U.S.C. § 2254(b). The district court agreed in part, holding that Swanson had failed to exhaust her jury-instruction claim but had exhausted her Blakely claim.
At that point, the district court did not dismiss the entire petition. Nor did the court stay it. Nor did the court follow any of the other traditional paths for handling a mixed petition, one with exhausted and unexhausted claims. See Harris v. Lafler, 553 F.3d 1028, 1031-32 (6th Cir.2009); see also Rose v. Lundy, 455 U.S. 509, 510, 102 S.Ct. 1198, 71 L.Ed.2d 379 (1982). Instead, the court proceeded with the Blakely claim and stayed the jury-instruction claim, apparently with the idea that Swanson could then contest the jury-instruction claim in state court. In opting to proceed on part of the petition, the district court relied on a case that arises under the Prison Litigation Reform Act (PLRA), Jones v. Bock, 549 U.S. 199, 127 S.Ct. 910, 166 L.Ed.2d 798 (2007), which it interpreted to hold that "courts are no longer permitted to dismiss properly-exhausted habeas claims merely because the petition also contains unexhausted claims." R.45 at 19 n. 3. The State filed a motion for reconsideration. It asked the court to stay the whole petition, arguing (1) that a court may not grant relief on a petition containing an unexhausted claim and (2) that "Jones v. Bock applies to prisoner actions challenging the conditions of confinement, not . . . habeas actions." R.46 at 2. The court appears to have misunderstood the State's motion (not itself a paragon of clarity), treating it as a request to proceed on the exhausted Blakely claimthe opposite of what the State sought. The court denied the motion, and the State appealed.

II.
The State argues that the "total exhaustion" rule prohibits a district court from proceeding to address a petition that contains exhausted and unexhausted claims. See Rhines v. Weber, 544 U.S. 269, 273-74, 125 S.Ct. 1528, 161 L.Ed.2d 440 (2005); Lundy, 455 U.S. at 510, 102 S.Ct. 1198. When faced with a mixed petition, the State points out, the district court has four options: (1) stay the entire petition; (2) dismiss the entire petition without prejudice; (3) deny the entire petition on the merits; or (4) dismiss the unexhausted claims and proceed with the exhausted ones. See Harris, 553 F.3d at 1031-32. But here, the State adds, the court mistakenly thought it had a fifth optionstaying some claims and proceeding on the merits with the othersmisconstruing Jones v. Bock, which, in rejecting a total exhaustion rule for conditions-of-confinement cases under the PLRA, distinguished (and preserved) the total exhaustion rule for habeas corpus cases. See 549 U.S. at 221-22, 127 S.Ct. 910.
Before reaching the merits of the State's arguments, we must consider our power to hear them. Two potential obstacles exist. First: Is the district court's ruling a "final decision[]"? 28 U.S.C. § 1291. If not, we lack jurisdiction over the appeal. See Mohawk Indus., Inc. v. Carpenter, ___ U.S. ___, 130 S.Ct. 599, 604-05, ___ L.Ed.2d ___ (2009). Second: Have intervening events mooted the appeal? According to Swanson's brief, the State has released her *832 on parole, which suggests she would derive little, if any, benefit from a decision adopting her Blakely argument that the state court unconstitutionally extended her parole eligibility date. Because the State appeals only the district court's decision to proceed on the Blakely claim, the entire appeal would be moot if that claim is moot.
It takes just one jurisdictional defect to deprive a court of authority to hear a case. We will startand finishwith the final-order question.
Section 1291 empowers the courts of appeals to review "final decisions," those that "end[] the litigation on the merits and leave[] nothing for the court to do but execute the judgment." Cunningham v. Hamilton County, 527 U.S. 198, 204, 119 S.Ct. 1915, 144 L.Ed.2d 184 (1999). In the normal course, that means the losing party will "raise all claims of error in a single appeal following final judgment." Firestone Tire & Rubber Co. v. Risjord, 449 U.S. 368, 374, 101 S.Ct. 669, 66 L.Ed.2d 571 (1981). A typical "final decision[]" in the habeas context would include orders granting or denying petitions on the merits. See, e.g., Tucker v. Palmer, 541 F.3d 652, 655 (6th Cir.2008) (reviewing grant of writ); Coomer v. Yukins, 533 F.3d 477, 483 (6th Cir.2008) (reviewing denial of writ).
Today's appeal does not meet this definition. It is the epitome of a request for interlocutory relief, as the relevant order more closely resembles a routine claim-processing order than a decision leaving nothing more to do than "to execute the judgment." Cunningham, 527 U.S. at 204, 119 S.Ct. 1915. The court permitted Swanson to proceed with the merits of her Blakely claim, but it did not finally resolve the merits of that claim or for that matter even begin to resolve the merits of that claim. An order establishing that a courtat some pointwill resolve the merits of a claim is not a final order, and that would be so even if this were the only claim in the case. But it was not even that. Swanson raised another ground for relief, her jury-instruction claim, and the court did not resolve the merits of that claim either. It did just the opposite, staying resolution of the claim until Swanson exhausted her state court remedies. Whether these classically interim orders are considered singly or together, they do not amount to "final decisions" under § 1291.
Neither are the orders eligible for interim review as orders "granting, . . . refusing or dissolving injunctions." 28 U.S.C. § 1292(a)(1). Although some orders described as "stays" may have the practical effect of an injunction and thus qualify for appeal under § 1292(a)(1), see Workman v. Bredesen, 486 F.3d 896, 904 (6th Cir.2007), stay orders that merely regulate the course of proceedings do not qualify, see In re M.T.G., Inc., 403 F.3d 410, 414 (6th Cir.2005). "An order by a federal court that relates only to the conduct or progress of litigation before that court ordinarily is not considered an injunction and therefore is not appealable under § 1292(a)(1)." Gulfstream Aerospace Corp. v. Mayacamas Corp., 485 U.S. 271, 279, 108 S.Ct. 1133, 99 L.Ed.2d 296 (1989).
That leaves one more possibilitythe collateral-order doctrinea haven of last resort for litigants disappointed by interim-relief orders that do not terminate the litigation. Section 1291, as the Court has construed the statute since 1949, see Cohen v. Beneficial Indus. Loan Corp., 337 U.S. 541, 69 S.Ct. 1221, 93 L.Ed. 1528, allows us to hear not only decisions that terminate the litigation in full but also "a small class of collateral rulings that, although they do not end the litigation, are appropriately termed final." Mohawk Indus., 130 S.Ct. at 605 (quotation marks omitted). To file an interlocutory *833 appeal under the collateral-order doctrine, the decision (1) must be "conclusive" on the question it decides, (2) must "resolve important questions separate from the merits" and (3) must be "effectively unreviewable" if not addressed through an interlocutory appeal. Id. That is not as easy as it might sound. The courts have vigilantly preserved the narrow confines of the collateral order doctrine to promote "judicial efficiency" and to "avoid[] the obstruction to just claims that would come from permitting the harassment and cost of a succession of separate appeals." Will v. Hallock, 546 U.S. 345, 350, 126 S.Ct. 952, 163 L.Ed.2d 836 (2006). "The justification for immediate appeal must . . . be sufficiently strong to overcome the usual benefits of deferring appeal until litigation concludes." Mohawk Indus., 130 S.Ct. at 605.
The State does not satisfy this test. As to the first requirement, it is not clear that the court's order amounts to a "conclusive" resolution of the issue appealed. We need not resolve the point, however. Even if we treat the district court's order as conclusively resolving the court's authority to proceed with one claim of a petition containing other unexhausted claims, the State still runs into problems on the other prongs of the test.
As to the second requirement, the order does not "resolve important questions separate from the merits," at least not sufficiently urgent questions to merit an exception to the traditional final-judgment rule. The point of the total-exhaustion rule is to prevent piecemeal litigation in the district court over habeas petitions. That may be an important objective, but how strange to enforce it through interlocutory appeals. Avoiding piecemeal litigation in the district court does not justify piecemeal litigation in the court of appeals. Claim-by-claim litigation in the district and appellate courts "undermines [Congress'] goal of streamlining federal habeas proceedings," Rhines, 544 U.S. at 277, 125 S.Ct. 1528, and the latter scenario spreads the problem from one court to two.
As to the third consideration, States faced with Michigan's problem "have several potential avenues of review apart from collateral order appeal," and accordingly the issue is not "effectively unreviewable" if we dismiss the appeal. Mohawk Indus., 130 S.Ct. at 605, 607. If the district court grants the writ on one claim without reaching a different, unexhausted claim in the petition, we may review that order as a "final decision[]"whether because, as required in some circuits, the district court signs off on the finality of the ruling under Rule 54(b) of the Federal Rules of Civil Procedure, see Foxworth v. Maloney, 515 F.3d 1, 3 n. 1 (1st Cir.2008) (collecting cases), or because, as may be the case in other circuits, the order may be reviewed in the ordinary course under § 1291, see id.; cf. Miller v. Misfud, 762 F.2d 45, 46 (6th Cir. 1985) (per curiam). Even if the timing of the case allows the petitioner to exhaust all claims before final judgment by which point this court would have no easy way to undo the district court's decision to proceed with part of what was originally a mixed petitionthat does not deprive the State of all opportunity for review along the way. A State may seek mandamus review of such an order if it "amount[s] to a judicial usurpation of power or a clear abuse of discretion, or otherwise works a manifest injustice." Mohawk Indus., 130 S.Ct. at 607; see Gulfstream Aerospace, 485 U.S. at 288 n. 13, 108 S.Ct. 1133 (noting that mandamus is merited in "exceptional cases involving stay orders"). In appropriate circumstances, moreover, a district court may certify an issue for immediate appeal under 28 U.S.C. § 1292(b), which (with the court of appeals' approval) also may provide a useful "safety valve" for immediate review. Digital Equip. *834 Corp. v. Desktop Direct, Inc., 511 U.S. 863, 883, 114 S.Ct. 1992, 128 L.Ed.2d 842 (1994). There is no compelling need to stretch the collateral order doctrine to fit this case.
This conclusion accords with the general rule that a district court's decision to grant or deny a stay of its own proceedings "is not ordinarily a final decision for the purposes of § 1291." Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 10 n. 11, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983); see Charles Alan Wright, Arthur R. Miller & Edward H. Cooper, 15A Federal Practice & Procedure § 3914.13 (2d ed. 1992) ("Stays . . . used to regulate the court's own proceedings or to accommodate the needs of parallel proceedings. . . are no more appealable than other interlocutory procedural orders."). No doubt, there are exceptions to this general rule; there often are. But they do not apply here. Michigan invokes a line of cases premised on Moses H. Cone Memorial Hospital, where the Supreme Court permitted an appeal of a stay granted under the Colorado River abstention doctrine. But, in allowing the interlocutory appeal, the Court reasoned that the order in that case "amount[ed] to a refusal to adjudicate the merits." 460 U.S. at 12, 103 S.Ct. 927. Adding that the order had the "sole purpose and effect" of "surrender[ing] jurisdiction of a federal suit to a state court," the Court contrasted the order from one that, like today's order, merely has "the practical effect of allowing a state court to be the first to rule on a common issue." Id. at 10 n. 11, 103 S.Ct. 927.
Since Moses H. Cone Memorial Hospital, the Court has held that § 1291 does not grant automatic jurisdiction over an order denying a Colorado River stay. See Gulfstream Aerospace, 485 U.S. at 278, 108 S.Ct. 1133. That is the better analogy to our case. The order at issue is closest to a denial of a stay, because the State contests not the decision to stay one claim but the decision to proceed with the other, reinforcing the position that no review should be available here. We know of no precedent addressing this issue that permits the appeal on collateral-order grounds.
Not so, says Michigan, pointing to courts that have agreed to hear appeals by States challenging stays of unexhausted habeas petitions under the collateral order doctrine. See Carmichael v. White, 163 F.3d 1044, 1045 (8th Cir.1998); Christy v. Horn, 115 F.3d 201, 206 (3d Cir.1997); see also Johnson v. Texas, 878 F.2d 904, 906 (5th Cir.1989) (hearing appeal by petitioner). It is not clear, as an initial matter, whether Carmichael, Christy and Johnson remain good law after Mohawk Industries, in which the Court expressed reservations about expanding the doctrine. At least one court has suggested "no." See Thompson v. Frank, 599 F.3d 1088, 1090 (9th Cir.2010) (per curiam) (addressing the question after Mohawk Industries and concluding that § 1291 does not allow appeal from a stay of habeas proceedings). Be that as it may, we need not resolve the point. All three cases addressed a different scenario, one in which the State appealed a decision granting a stay of an entire case. Here, by contrast, the State appeals a decision denying a stay of part of the case. All three cases also relied on the distinction in Moses H. Cone Memorial Hospital and Gulfstream Aerospace between granting a stay and denying it, see Carmichael, 163 F.3d at 1045; Christy, 115 F.3d at 204-05; Johnson, 878 F.2d at 905-06a point that, as noted, cuts in the opposite direction from the path the State wishes us to take.
In the final analysis, § 1291 does not permit an appeal in this case. That leaves one lasttruly lastpotential form of interim appellate relief: a mandamus petition. *835 See 28 U.S.C. § 1651. We have the discretion to treat the State's appeal as a petition for mandamus relief, and we have done so before. See, e.g., Beard v. Carrollton R.R., 893 F.2d 117, 120 (6th Cir.1989). We decline to do so today. For one thing, the case may already be moot, as noted above. For another, the State's difficulty below seemed to stem largely from a misunderstanding about the State's legal position, and the district court should get another shot at the issueperhaps after it has been more clearly briefedbefore we consider interfering with its processing of the case.

III.
For these reasons, we dismiss the appeal for lack of jurisdiction.
