POSNER, Chief Judge.

This procedurally remarkable case began life innocently enough as a routine contract suit brought in federal district court under the diversity jurisdiction. The principal (and we shall assume only) plaintiff, DDI, manufactures the metal cylinders used in fire extinguishers. The defendant, General Fire, manufactures the extinguishers themselves. General Fire agreed to purchase a large quantity of cylinders from DDI. But after DDI had tooled up to produce the cylinders for the contract and begun producing them, General Fire repudiated the contract. It complained that the cylinders were defective and, perhaps more to the point, that "the fire extinguisher market has been on a slide downward and frankly, the market is no longer here." In 1989 DDI brought suit for breach of contract, seeking damages of more than $400,000. The case was assigned to Judge Aspen, who suggested the name of a law professor to mediate the parties' dispute. After the professor failed and after the district court's champion settler, Judge (now ex-Judge) Bua, failed too, the parties, concerned that Judge Aspen's crowded docket would require them to wait a year or more for trial, agreed to have the case tried before a magistrate judge. The case was assigned to Magistrate Judge Bobrick. He also thought the case should be settled rather than tried. Protracted efforts at settlement ensued but were unsuccessful. Then the lawyers had a brainstorm: appoint Judge Bobrick the arbitrator of their dispute.

He agreed, and on April 6, 1992, issued an order, which the lawyers had drafted, establishing the agreed procedure for settling the case. An independent auditor selected by the parties would determine the actual losses sustained by both parties and "the Court will retain jurisdiction to act as the arbitrator if any impasse arises as to any of the elements of loss, and shall make a decision binding upon the parties regarding such issue. Upon the conclusion of the audit, the final determination of the actual losses will be reported to the Court and the parties will be enter a stipulation and order for payment of the losses and following payment a stipulation to dismiss the lawsuit, with prejudice and without legal costs and fees. It is so ordered." The order was signed by Judge Bobrick and also (under the legend "agreed to") by the lawyers for the parties. He set a deadline for the parties to submit to him any objections they might have to the auditor's report.

The auditor's report, submitted to Judge Bobrick on February 25, 1993, found that DDI had sustained a net loss of $38,000. Both parties submitted objections. Hearings (the first by telephone conference call) on the objections were held on March 17 and 26, 1993, before the magistrate judge, who at the conclusion of the second hearing issued a document, captioned "judgment," which states that "Defendant shall pay the sum of $124,860 to the Plaintiff and its attorney within 10 days from the date of this Order. In the event of the failure of the Defendant to pay this amount within the time provided, Plaintiff shall have liquidated damages in the amount of one hundred and fifty ($150.00) per day for each day the payment [sic] remains unpaid." It is from this order that General Fire has appealed. DDI, arguing that the appeal is frivolous because, by agreeing to have the magistrate judge arbitrate the parties' dispute and make a binding decision on any matters on which the parties disagreed, General Fire waived its right to appeal, asks us not only to dismiss the appeal but also to impose sanctions on General Fire under Fed.R.Civ.P. 11 and Fed.R.App.P. 38. We cannot, however, award sanctions under Rule 11 of the civil rules; unlike Rule 38 of the appellate rules, it is inapplicable to appellate proceedings. Cooter Gell v. Hartmarx Corp., 496 U.S. 384, 406-07, 110 S.Ct. 2447, 2461-62, 110 L.Ed.2d 359 (1990); Mortell v. Mortell Co., 887 F.2d 1322, 1328 (7th Cir. 1989); Partington v. Gedan, 923 F.2d 686 (9th Cir. 1991) (en banc) (per curiam). We shall take up the question of Rule 38 sanctions at the end of this opinion.

Even after questioning General Fire's counsel closely at argument, we are uncertain what relief he seeks from this court. But he seems to want us to rule that the parties had no power to appoint a magistrate judge to arbitrate their dispute and that the judgment (if that is what it is) which the magistrate judge issued on March 26 should therefore be treated as if it were an ordinary civil judgment rather than an arbitrator's award and should be reversed because the magistrate judge's findings of fact with regard to DDI's damages were clearly erroneous, or alternatively because General Fire had a right to an evidentiary hearing.

General Fire is correct that arbitration is not in the job description of a federal judge, including (see 28 U.S.C. § 636) a magistrate judge. It is true that there are part-time as well as full-time magistrate judges, and the former we suppose could serve as arbitrators when they were not doing their magistrate-judge work. Cf. 28 U.S.C. § 632(b). But Judge Bobrick is a full-time magistrate judge. Federal statutes authorizing arbitration, such as 9 U.S.C. § 1 et seq. and 28 U.S.C. § 651 et seq., do not appear to authorize or envisage the appointment of judges or magistrate judges as arbitrators, and it is suggestive that when the consent of the parties to proceed before a magistrate judge is required he is authorized to "order the entry of judgment in the case" — not to make an arbitration award. 28 U.S.C. § 636(c)(1); see also (c)(3), which makes clear that the judgment to which (c)(1) refers is an appealable judgment.

An arbitration award must be confirmed by the district court to be enforceable. 9 U.S.C. § 13. So if judges or magistrate judges could double as arbitrators, Judge Aspen, say, might issue an arbitration award and the winner might take it to Judge Zagel for an order of confirmation. It's an ingenious idea and since "alternative dispute resolution" is all the rage these days — since at least one state (Connecticut) already authorizes its judges to moonlight as arbitrators, Kirk Johnson, "Public Judges as Private Contractors: A Legal Frontier, N.Y. Times, Dec. 10, 1993, p. B9 — the day may not be distant when federal judges will be recommissioned (or issued supplementary commissions) as arbitrators. But it has not arrived.

Even more curious, ingenious, and economical would be a procedure by which a judge or magistrate judge would on day 1, wearing his judge's hat, encourage the parties to submit their dispute to arbitration; would on day 2, wearing his arbitrator's hat, arbitrate the parties' dispute; and on day 3, wearing his judge's hat once more, would confirm the arbitration award. That is one possible characterization of what Judge Bobrick did. Were it the correct characterization we probably would lack appellate jurisdiction. For the procedure we have sketched is so remote from the procedures that federal judicial officers are authorized to use that the final order emanating from it might well be void — as if a judge issued an order directing President Clinton to go on a pilgrimage to Mecca. Having no legal effect, the order would not affect the defendant's interests and Article III would therefore preclude an appeal. We have encountered this problem before, in cases in which an injunction, being too vague to be enforced by contempt or any other sanction, has no binding effect and is therefore unappealable. See United States v. Board of Education, 11 F.3d 668, 672 (7th Cir. 1993). It may seem a considerable paradox that if the judge's error is so flagrant as to make his order void, the appellate court loses jurisdiction. But a void order has no bite, and Article III precludes an appeal from a harmless order. And in a case in which the district judge's order was unenforceable because he exceeded the outer bounds of the federal judicial power, the appeal could be recharacterized as a request for mandamus and in that way the jurisdiction of the appellate court preserved. Mallard v. United States District Court, 490 U.S. 296, 308-09, 109 S.Ct. 1814, 1821-22, 104 L.Ed.2d 318 (1989).

An alternative characterization to ultra vires of what the magistrate judge did is possible. It is that the parties stipulated to an abbreviated, informal procedure for his deciding the case in his judicial capacity. Parties are free within broad limits to agree on simplified procedures for the decision of their case. They can agree for example to waive the right to present oral testimony and instead to treat the summary judgment proceeding as the trial on the merits. Brotherhood Shipping Co. v. St. Paul Fire Marine Ins. Co., 985 F.2d 323, 327 (7th Cir. 1993). They can agree that the hearing on a preliminary injunction shall be deemed the trial on the merits as well. Fed.R.Civ.P. 65(a)(2); Planned Parenthood Association/Chicago Area v. Chicago Transit Authority, 767 F.2d 1225, 1228 n. 3 (7th Cir. 1985). They can agree to a trial on stipulated facts. United Automobile Workers v. Randall Division, 5 F.3d 224, 227 (7th Cir. 1993); Peterson v. Lindner, 765 F.2d 698, 700 (7th Cir. 1985). They can, of course, agree to binding arbitration, albeit before an arbitrator rather than a judge. They can agree to waive appeal: that is possible even in criminal cases, by a plea agreement. One way to describe what the parties and the judge did in this case is that they agreed that the judge would make a decision on a record consisting of the auditor's report plus the parties' objections, after oral argument by the parties conducted (as is increasingly common in federal district courts) over the telephone, Lucien v. Breweur, 9 F.3d 26, 28 (7th Cir. 1993), and that they would not appeal the decision. So viewed, the procedure was not improper. Of course the parties should have avoided reference to "arbitration," a mode of dispute settlement distinct from adjudication. They should simply have said that this was the procedure they had agreed upon.

One of the big differences between arbitration and adjudication is that unless the parties provide otherwise, an arbitrator's award is not appealable. It is, however, subject to limited judicial review. Under the federal arbitration code, a party can seek to vacate an award by showing that it is based on fraud, or that the arbitrator had a serious conflict of interest, or that he exceeded the terms of his reference, or that his award is too indefinite to enforce. 9 U.S.C. § 10(a); Barbier v. Shearson Lehman Hutton Inc., 948 F.2d 117, 120 (2d Cir. 1991). We may assume that by talking the language of arbitration the parties in this case intended to reserve to themselves that much, but no more, right of judicial review, just as a criminal defendant who pleads guilty and by doing so is said to waive his right of appeal can nevertheless appeal in order to argue that his plea was involuntary.

So we must consider whether General Fire's appeal falls within the narrow limits of permissible judicial review available to a party who has waived his right of appeal. We think not. Once the challenge to the magistrate judge's authority and to the agreed-upon procedure is set to one side, all that is left is a complaint that his findings of fact were clearly erroneous, which is precisely the kind of complaint that cannot be used to upset an award or judgment that the loser had agreed in advance not to appeal. Hill v. Norfolk Western Ry., 814 F.2d 1192, 1195 (7th Cir. 1987). Clear error is the standard of appellate review when the appellant has not agreed to limit his ordinary right of appeal.

We are given some pause by the provision for liquidated damages in the magistrate judge's final order. Remember that on the view we take of this case the judgment that he issued on March 26, 1993, really was a judgment, and not an arbitrator's award. It is unusual, to say the least, for a judge to issue an order directing the payment of a judgment within ten days under threat of sanctions — there is no other way to describe the "liquidated damages" provision, which so far as appears bears no relation to any reasonable estimate of the cost to DDI of a one day's delay in payment of the judgment — if the order is disobeyed. Indeed, in the usual case such an order would clearly be ultra vires. Not only is there no statutory authority for it; there is no room for an exercise of inherent judicial power. The ground is occupied by statutes and rules already. A plaintiff who obtains a money judgment is entitled to post-judgment interest, 28 U.S.C. § 1961, at an interest rate (the T-bill rate, currently about 3 percent per annum) much lower than the implicit interest rate (43.8 percent per annum!) reflected in the "liquidated damages" provision imposed by the magistrate judge. And the collectibility of a judgment is secured by the requirement that the defendant post a supersedeas bond if he wants to stave off execution pending appeal, Fed.R.Civ.P. 62(d), so that the astronomical interest rate implied by Judge Bobrick's order not only is unauthorized but also is unnecessary to compensate the plaintiff for the risk of nonpayment. If for some extraordinary reason these provisions were insufficient to protect the plaintiff against the consequences of delay in being able to collect the judgment, he could ask the judge for additional relief. Philips Medical Systems Int'l B.V. v. Bruetman, 8 F.3d 600, 604 (7th Cir. 1993). No case has been made for regarding the liquidated-damages provision in this light.

Section 1961 is inapplicable to a real arbitrator's award until the award is confirmed. So a post-award, preconfirmation interest award by an arbitrator is appropriate — but not at punitive rates. J.M. Owen Building Contractors, Inc. v. College Walk, Ltd., 101 N.C. App. 483, 400 S.E.2d 468, 470-71 (1991); Napoleon Steel Contractors, Inc. v. Monarch Construction Co., 3 Ohio App.3d 410, 3 OBR 476, 445 N.E.2d 743, 745 (1982) (per curiam). And Judge Bobrick, to repeat, is not an arbitrator.

It could we suppose be argued that because the defendant had relinquished its right of appeal, any appeal it tried to take would have to be frivolous, and the liquidated-damages provision imposed by the magistrate judge was merely a conditional sanction under Rule 11 for filing a frivolous appeal. But the premise is wrong. The procedure employed was sufficiently irregular to give General Fire more than a long shot at an appeal based on the argument that the magistrate judge had exceeded his authority; more on this below. And in any event the imposition of sanctions requires a statement of the ground, Automatic Liquid Packaging, Inc. v. Dominik, 909 F.2d 1001, 1006 n. 3 (7th Cir. 1990), unless the ground is obvious, Teamsters Local No. 579 v. B M Transit, Inc., 882 F.2d 274, 279-80 (7th Cir. 1989), which it was not. So exotic a mode of sanctioning a party as employed here required more than the announcement of the sanction — not represented as such, either, since "liquidated damages" is conventionally, though not invariably, Trans World Airlines, Inc. v. Thurston, 469 U.S. 111, 125, 105 S.Ct. 613, 623-24, 83 L.Ed.2d 523 (1985); Fortino v. Quasar Co., 950 F.2d 389, 397 (7th Cir. 1991), a compensatory rather than a punitive remedy.

An alternative possibility is that General Fire's promise not to appeal, a promise embodied in the original order specifying the procedure for resolving the parties' dispute, implied consent to an award of liquidated damages. That we doubt too, because the charge to the auditor in that order told him to "cut off" the parties' losses as of February 6, 1992, and if the liquidated damages compensate for anything it is for losses from delay in paying a judgment rendered more than a year later. The order authorized the magistrate judge to resolve disagreements over the auditor's report, not to add items of loss that the auditor had been ordered to ignore.

Although the magistrate judge may well not have been authorized to award these liquidated damages, General Fire has forfeited any challenge in this court to the magistrate judge's authority. Its opening brief devotes a single sentence to the issue, contending without citing any authority (or explaining the absence of authority) that the provision was "totally unwarranted." That was not enough to preserve the issue for our review. United States v. Dunkel, 927 F.2d 955, 956 (7th Cir. 1991) (per curiam). An issue must be pressed, must be argued and supported; a bare conclusion is not enough.

So the appeal fails; but not so badly as to be sanctionable under Fed.R.App.P. 38. Granted there is an element of bad faith in General Fire's appeal. It agreed to the procedure that the magistrate judge followed and only when it lost decided that it had agreed to something improper. But issues of subject-matter jurisdiction are not waived until all appellate remedies are exhausted, and one characterization of the appeal is that the defendant was challenging, however belatedly, the jurisdiction of the magistrate judge. The lawyer for General Fire who took the appeal was not the same one who had signed the order establishing the procedure for resolution of the parties' dispute, and we can understand how he might have thought that the order had attempted to vest the magistrate judge with powers that Congress has not authorized federal judicial officers to exercise, though in that event he should have asked for mandamus, rather than just trying to appeal from what he believed to be a void order.

Although we prefer the alternative characterization of the order, under which the parties' right to appeal was greatly curtailed, we shall not pretend that our characterization is inevitable. Maybe the parties and the magistrate judge really did intend him to step out of his judicial role and become an arbitrator, albeit, unlike his Connecticut cousins, an unpaid one. When at one point Judge Bobrick said, "Once we determine . . . what the losses are in this matter, then we can reduce that to a judgment form," one of the lawyers interrupted to say, "We don't want to have a judgment entered. We want a stipulation to dismiss." Judge Bobrick replied, "Yes." Yet the order which established the procedure provides for the entry of an "order for payment of the losses" as well as for a stipulation to dismiss the suit. And if there were no such order but just an arbitration award enforceable only by obtaining a confirmation order, we would have the spectacle of Judge Bobrick being asked to confirm his own arbitration award, or, what would be no less weird, of one judge being asked to confirm another's arbitration award. On balance we think it slightly more plausible to suppose that the parties and the magistrate judge were agreeing to an abbreviated judicial procedure rather than an unauthorized arbitral one. But only slightly.

The judgment is affirmed — so General Fire had better hurry up and pay it because it's growing by $150 every day — but the motion for sanctions is denied.