Before BARKSDALE, ELROD, and HO, Circuit Judges.* JAMES C. HO, Circuit Judge: District courts do not have discretion to ignore mandates issued by this court. A previous panel of this court ordered the district court to begin implementing the permanent injunction in this case “without further changes.” The district court made further changes anyway. We reverse and remand. * * * Plaintiffs are a certified class of minor children in the permanent managing conservatorship (PMC) of the Texas Department of Family Protective Services. About ten years ago, they brought a series of § 1983 claims alleging that the Texas foster-care system violated their substantive due process right “to be free from an unreasonable risk of harm.” M.D. ex rel. Stukenberg v. Abbott (“Stukenberg I“), 907 F.3d 237, 243 (5th Cir. 2018). The district court agreed and issued a wide-ranging permanent injunction imposing “sweeping changes” on the Texas foster-care system. Id. The state appealed. This court agreed with some of the district court’s constitutional holdings, but vacated and remanded the injunction to the district court for “modification consistent with this opinion.” Id. at 287–88. The district court accordingly made additional modifications to the injunction. The state appealed again. Once again, this court agreed with some of the district court’s changes, but disagreed with others. M.D. ex rel. Stukenberg v. Abbott (“Stukenberg II“), 929 F.3d 272, 275 (5th Cir. 2019). This time, however, we instructed the district court to “begin implementing, without further changes, the modified injunction with the alterations we have made.” Id. at 281. Notwithstanding our specific instruction not to make “further changes” to the injunction, the district court did just that. In Stukenberg II, we approved an injunction requiring all licensed PMC residences housing more than six children to provide 24-hour “awake-night” supervision—that is, at least one supervising adult awake at all times. Id. at 276–77. The rationale for this requirement is simple: The more unrelated foster children living in the same home at the same time, the greater the risk of harm. Not surprisingly, then, the injunction did not limit the state’s ability to move PMC children from overcrowded homes into less crowded homes. On remand, however, the district court expanded the injunction again—this time enjoining the state “from moving any PMC child from their current . . . placement as a result of enforcement of the Court’s requirement for 24-hour awake-night supervision unless application is made to the Court . . . prior to [the] proposed discharge.” This modification demonstrably constitutes a “further change” to the injunction. Before the modification, the state could move PMC children from larger homes to smaller homes at its discretion, without violating the injunction. After the modification, the state could no longer move PMC children “without permission” from the district court. It is black-letter law that a district court must comply with a mandate issued by an appellate court. See, e.g., Gen. Universal Sys., Inc. v. HAL, Inc., 500 F.3d 444, 453 (5th Cir. 2007) (“The mandate rule requires a district court on remand to effect our mandate and to do nothing else.”). We have underscored that the mandate rule is “essential to the orderly administration of justice” because it brings finality to disputes. United States v. Pineiro, 470 F.3d 200, 205 (5th Cir. 2006). The rule is “aimed at preventing obstinate litigants from repeatedly reasserting the same arguments and at discouraging opportunistic litigants from appealing repeatedly in the hope of acquiring a more favorable appellate panel.” Id. Plaintiffs claim that the district court did not violate the mandate rule because a court “invok[ing] equity’s power to remedy a constitutional violation by an injunction mandating systemic changes to an institution” generally has “the continuing duty and responsibility to assess the efficacy and consequences of its order.” Brown v. Plata, 563 U.S. 493, 542 (2011). As Plaintiffs point out, we recited this general principle in Stukenberg II, stating that “[a] district court undoubtedly has the equitable power to oversee compliance with its own injunction.” 929 F.3d at 278. “[E]quitable decrees that impose a continuing supervisory function on the court commonly . . . contemplate the subsequent issuance of specific implementing injunctions.” Moore v. Tangipahoa Parish Sch. Bd., 843 F.3d 198, 200 (5th Cir. 2016) (alterations in original) (citation omitted). But judges disagree on occasion over the proper exercise of equitable powers, just as judges disagree on occasion over the proper interpretation of statutes. When that happens, appellate courts must make the final decision—and once the decision is made, it must be followed. And that, of course, is the whole purpose of the mandate rule: “A district court on remand . . . may not disregard the explicit directives of [the appellate] court.” Perez v. Stephens, 784 F.3d 276, 280 (5th Cir. 2015) (quotations omitted). To elevate general equitable principles over the mandate rule is to challenge the very principle of appellate review—including any number of other doctrines inherent in our judicial hierarchy, such as vertical stare decisis. We do not question the good faith of the district judge in this case. But make no mistake: Accepting Plaintiffs’ approach would replace judicial hierarchy with judicial anarchy. Plaintiffs alternatively contend that the modification was a necessary “administrative measure” to prevent Defendants from “evad[ing] the 24-hour supervision requirement by shuffling PMC children around on the fly” “so that a given facility remains below the seven-child threshold at a given moment.” Put another way, Plaintiffs disagree that our prior mandate adequately protects them from harm. But a district court cannot ignore the terms of a mandate it disagrees with any more than we can ignore the words of a federal statute that we disagree with. If it is necessary to modify an injunction in the face of a mandate that forbids all further changes, the solution is not for the district court to update the injunction on its own—but for the parties to litigate the matter to the extent our procedures permit. See, e.g., Deutsche Bank Nat’l Trust Co. v. Burke, 902 F.3d 548, 551 (5th Cir. 2018) (“[W]e will only reexamine issues of law addressed by a prior panel opinion in a subsequent appeal of the same case if (i) the evidence on a subsequent trial was substantially different, (ii) controlling authority has since made a contrary decision on the law applicable to such issues, or (iii) the decision was clearly erroneous and would work a manifest injustice.”) (quotations omitted). Relief of this kind may be “rarely” granted, to be sure. Id. But if that seems like strong medicine, the lesson is for appellate courts to draft their mandates carefully, not for district courts to ignore established rules of appellate procedure. * * * We repeat what we said in Stukenberg II. “The case is remanded to the district court to begin implementing, without further changes, the modified injunction with the alterations we have made.” 929 F.3d at 281. We reverse and remand.