ORDER

Peter Prostyakov and Masco Corporation have been litigating for the last 20 years over an embittered business relationship, which the parties attempted to resolve through arbitration. For details of their litigation history, see Prostyakov v. Masco Corp., 513 F.3d 716 (7th Cir. 2008) and Masco Corp. v. Prostyakov, 558 Fed.Appx. 685 (7th Cir. 2014). This is now the parties’ third appeal related to their arbitration. In the last appeal, we upheld the district court’s decision to confirm an arbi-tral award for Masco. We also upheld the court’s decision “to fine Prostyakov” because “of the legion of meritless motions he made” in the district court. But we remanded so that the court could explain how it “arrived at the substantial and oddly precise amount of $25,500” for that fine. Masco, 558 Fed.Appx. at 688-89.

After the case was remanded, both parties filed statements (as directed by S.D. IND. L.R. 16-2) providing the district court with their positions on what action the court should take. In his statement Prostyakov attacked the court’s decision to impose sanction as well as the court’s underlying decision in favor of Masco. He invoked Rule 60(b)(4) of the Federal Rules of Civil Procedure and argued that the judgment was void for lack of subject-matter jurisdiction. Masco asserted that our remand order limited the district court to one issue: explaining its rationale for choosing the $25,500 sanction.

The district court explained its reason for the sanction amount. As a starting point, it began with $25,000 because that figure modestly reflected a mere one-half of one percent of the $5 million that Pros-tyakov unreasonably demanded during their latest settlement negotiations. When the negotiations collapsed, Prostyakov then frivolously contested in court Masco’s efforts to confirm the arbitral decision that had awarded Prostyakov nothing. The re *571 maining $500 was added to the sanction because, the court explained, that amount is our “common and evidently presumptive fine on litigants who abuse the court’s processes.” The court also denied Pros-tyakov’s Rule 60(b) motion.

On appeal Prostyakov generally contests the district court’s order reimposing the sanction, but the district court’s detailed rationale persuades us that the $25,500 sanction is reasonable. We have recently observed that excessive demands are sanc-tionable when they produce needless litigation. See Smith v. Greystone Alliance, LLC, 772 F.3d 448, 450 (7th Cir. 2014). And we have repeatedly warned parties not to raise baseless challenges to arbitral awards, emphasizing that we will uphold sanctions against parties who do so frivolously, as Prostyakov did here. See Cuna Mut. Ins. Soc’y v. Office & Prof'l Emps. Int’l Union, Local 39, 443 F.3d 556, 561 (7th Cir. 2006). Moreover, sanctions “may exceed the amount of fees incurred by the opposing party” in order to protect “the court itself’ and other litigants, whose day in court is delayed by needless motions. Frantz v. U.S. Powerlifting Fed’n, 836 F.2d 1063, 1066 (7th Cir. 1987). Here, the district court reasonably estimated that the cumulative harm arising from Prostya-kov’s outrageous demand was roughly comparable to a tiny percentage of that demand. It then reasonably considered the need to deter similar misconduct. Thus we conclude that the court did not abuse its discretion by imposing its sanction. See Chambers v. NASCO, Inc., 501 U.S. 32, 55, 111 S.Ct. 2123, 115 L.Ed.2d 27 (1991); Schmude v. Sheahan, 420 F.3d 645, 650 (7th Cir. 2005); Kapco Mfg. Co. v. C&O Enters., Inc., 886 F.2d 1485, 1496 (7th Cir. 1989).

Prostyakov also presses his Rule 60(b)(4) collateral challenge to the ruling affirming the arbitral award for Masco. Prostyakov frames his argument in terms of jurisdiction. But a party may not attack subject-matter jurisdiction collaterally. Travelers Indem. Co. v. Bailey, 557 U.S. 137, 152, 129 S.Ct. 2195, 174 L.Ed.2d 99 (2009); In re Lodholtz, 769 F.3d 531, 534 (7th Cir. 2014). In any case, his argument, to the extent it is decipherable, actually attacks the merits of the district court’s underlying order. And as Masco correctly points out, had the district court dived back into the merits of the lawsuit, it would have violated the mandate rule. That rule limits the scope of the district court’s power on remand to the specific directions in the remand order and bars the court from revisiting issues disposed of by the appellate court. See 28 U.S.C. § 2106; United States v. White, 406 F.3d 827, 831 (7th Cir. 2005); Moore v. Anderson, 222 F.3d 280, 283 (7th Cir. 2000).

AFFIRMED.