SELYA, Circuit Judge.
Patrick McCarthy's stock went up when an arbitral decision came down against Advest, Inc., a brokerage house. Advest moved in federal district court to vacate the award, but the court refused because the motion "does no more than allege an erroneous result, which does not support an inference of any of the circumstances authorizing the vacation of an award contained in 9 U.S.C. § 10."1 Advest appeals, arguing that since the arbitration award was in "manifest disregard of the law" and without "rational basis in fact or law," vacation was appropriate. But the bases for review of arbitration awards outside of 9 U.S.C. § 10 are very limited, no matter how colorfully a given petitioner may package and label its motion to vacate - and those bases are inapplicable in the case at hand. We therefore affirm the judgment below.
The Essential Facts
Stripped to essentials, the facts in this case are straightforward. McCarthy opened a margin account with Advest's predecessor in interest and purchased securities over a period of time.2 In May 1984, he owned shares in three companies: Avco, Amdahl, and Recognition Equipment. At that time, Advest sent him at least one mailgram requesting that he post additional funds to meet his margin requirements. Upon inquiry, he was told that the request was due to a computer error and could be ignored. In January 1985, McCarthy tendered his Avco shares to an acquiring company, using the proceeds in April to purchase 12,500 additional shares of Amdahl.
At that juncture, the customer-broker relationship began to sour. By virtue of McCarthy's latest transaction, his position in Amdahl amounted to 16,000 shares and comprised more than 60 percent of the value of his account. Due to this increased concentration, Advest's margin requirement jumped from 30 percent to 45 percent. It launched a series of mailgrams demanding that McCarthy deposit incremental funds to meet the increased margin. When McCarthy failed to do so, Advest unilaterally liquidated portions of his holdings, selling all the Recognition Equipment stock (4000 shares) in June 1985 and 3400 shares of Amdahl in the fall of that year.
McCarthy maintained his account with Advest through March 1987 when he switched brokers. In January 1988, he filed an arbitration claim with the National Association of Securities Dealers. McCarthy's complaint was that Advest's serial requests for further funds were misleading in that they stated Advest was "required by federal regulation" to secure additional margin for a concentrated account when, in fact, the applicable regulations merely allowed Advest to do so. See generally 12 C.F.R. §§ 220.1-220.130. McCarthy claimed that, had he known the truth, he would simply have shifted his margin account to a more accommodating broker; instead, his reliance on Advest's misrepresentation caused part of his holdings to be liquidated, contrary to his best interests.
The three member arbitration panel found for McCarthy, awarded him $22,500, and ordered Advest to "restore the 6800 shares of Amdahl stock to [McCarthy] adjusting for any and all splits and dividens [sic] through the date of [the] award." In the district court, Advest challenged this award on two fronts, (1) that the arbitrators could not rationally have found the mailgrams to be misleading and the ensuing sell-offs improper, and (2) even if Advest was liable, the measure of damages was bizarre. In oral argument before us, however, appellant conceded that the arbitration panel could conceivably have found that the mailgrams were misleading, thereby effectively undermining its first assignment of error.3 Accordingly, we limit our discussion to whether the district court erred in not vacating the award because the decreed remedy had no rational basis and was in manifest disregard of the law.
Standard of Review
The bases for review of arbitration awards are enumerated in 9 U.S.C. § 10, supra note 1. The statute does not allow courts to roam unbridled in their oversight of arbitral awards, but carefully limits judicial intervention to instances where the arbitration has been tainted in certain specific ways. In fine, section 10 authorizes vacatur of an award in cases of specified misconduct or misbehavior on the arbitrators' part, actions in excess of arbitral powers, or failures to consummate the award.4 See Carte Blanche (Singapore) Pte., Ltd. v. Carte Blanche Int'l Ltd., 888 F.2d 260, 264-65 (2d Cir. 1989). The statute contains no express ground upon which an award can be overturned because it rests on garden-variety factual or legal bevues. To the precise contrary, courts "do not sit to hear claims of factual or legal error by an arbitrator as an appellate court does in reviewing decisions of lower courts." United Paperworkers Int'l Union v. Misco, Inc., 484 U.S. 29, 38, 98 L. Ed. 2d 286, 108 S. Ct. 364 (1987). Even where such error is painfully clear, "courts are not authorized to reconsider the merits of arbitration awards. . . ." S. D. Warren Co. v. United Paperworkers' Int'l. Union, Local 1069, 845 F.2d 3, 7 (1st Cir.), cert. denied, 488 U.S. 992, 109 S. Ct. 555, 102 L. Ed. 2d 582 (1988).
Courts do, however, retain a very limited power to review arbitration awards outside of section 10. "The considerable deference due an arbitrator's decision 'does not grant carte blanche approval to any decision that the arbitrator might make. . . .'" Challenger Caribbean Corp. v. Union General de Trabajadores, 903 F.2d 857, 861 (1st Cir. 1990) (quoting International Bhd. of Firemen Local 261 v. Great N. Paper Co., 765 F.2d 295, 296 (1st Cir. 1985)). Nevertheless, non-reviewability remains the general rule - and exceptions are few and far between. See Bettencourt v. Boston Edison Co., 560 F.2d 1045, 1049 (1st Cir. 1977). In the main, a successful challenge to an arbitration award, apart from section 10, depends upon the challenger's ability to show that the award is "(1) unfounded in reason and fact; (2) based on reasoning so palpably faulty that no judge, or group of judges, ever could conceivably have made such a ruling; or (3) mistakenly based on a crucial assumption that is concededly a non-fact." Local 1445, United Food and Commercial Workers v. Stop & Shop Cos., 776 F.2d 19, 21 (1st Cir. 1985); Bettencourt, 560 F.2d at 1050. Put differently, "as long as the arbitrator is even arguably construing or applying the contract and acting within the scope of his authority," a court's conviction that the arbitrator made a serious mistake or committed grievous error will not furnish a satisfactory basis for undoing the decision. See Misco, 484 U.S. at 38; see also Georgia-Pacific Corp. v. Local 27, United Paperworkers Int'l Union, 864 F.2d 940, 944 (1st Cir. 1988).
This standard of judicial review has taken on various hues and colorations in its formulations in this, and other, circuits. See, e.g., Raiford v. Merrill Lynch, Pierce, Fenner & Smith, Inc., 903 F.2d 1410, 1412 (11th Cir. 1990) (arbitration award may be set aside if "arbitrary and capricious"); Merrill Lynch, Pierce, Fenner & Smith, Inc. v. Bobker, 808 F.2d 930, 933 (2d Cir. 1986) (arbitration award may be set aside if made in "manifest disregard of the law");5 French v. Merrill Lynch, Pierce, Fenner & Smith, Inc., 784 F.2d 902, 906 (9th Cir. 1986) (arbitration award may be set aside if "completely irrational"); Stop & Shop, supra, Slip. Op. at p.6-7; see also United Steelworkers of America v. Enterprise Wheel & Car Corp., 363 U.S. 593, 597, 4 L. Ed. 2d 1424, 80 S. Ct. 1358 (1960) (holding arbitration award to be impregnable "so long as it draws its essence" from the underlying agreement). Although the differences in phraseology have caused a modicum of confusion, we deem them insignificant. We regard the standard of review undergirding these various formulations as identical, no matter how pleochroic their shadings and what "terms of art have been employed to ensure that the arbitrator's decision relies on his interpretation of the contract as contrasted with his own beliefs of fairness and justice." Jenkins v. Prudential-Bache Securities, Inc., 847 F.2d 631, 634 (10th Cir. 1988). However nattily wrapped, the packages are fungible.
Our purpose here is not to wave a magic wand and produce some new, better, or more definitive formulation of the proper standard; even if that were within our linguistic ken, it would be supererogatory under the circumstances. Rather, we propose merely to point out that the determinant of this array of alternatively worded formulations consists of two classes of cases where an arbitral award is subject to review. One category, usually involving labor arbitration, is where an award is contrary to the plain language of the collective bargaining agreement. See, e.g., Strathmore Paper Co. v. United Paperworkers Int'l Union, 900 F.2d 423, 427 (1st Cir. 1990); Berklee College of Music v. Berklee Chapter of the Massachusetts Federation of Teachers, Local 4412, 858 F.2d 31, 32-33 (1st Cir. 1988), cert. denied, 493 U.S. 810, 107 L. Ed. 2d 22, 110 S. Ct. 53 (1989); S. D. Warren Co., 845 F.2d at 8. The second category embraces instances where it is clear from the record that the arbitrator recognized the applicable law - and then ignored it. See, e.g., Carte Blanche (Singapore), 888 F.2d at 265; Stroh Container Co. v. Delphi Industries, Inc., 783 F.2d 743, 750 (8th Cir.), cert. denied, 476 U.S. 1141, 90 L. Ed. 2d 695, 106 S. Ct. 2249 (1986).6 Advest is making a claim of the second type, asserting that the relief granted in this case was chimerical: the law regarding damages was so clear and the arbitrators' award so irreconcilable with it that the panel must have disregarded the law and embarked on a flight of fancy.
Having set the parameters of our inquiry, we turn now to the merits of the appeal. To amplify slightly, Advest argues that when shares of stock are wrongfully liquidated, compensation for actual loss is the proper measure of damages, the loss to be gauged by "the highest intermediate value reached by the stock between the time of the wrongful act complained of and a reasonable time thereafter, to be allowed to the party injured to place himself in the position he would have been in had not his rights been violated." Galigher v. Jones, 129 U.S. 193, 200, 32 L. Ed. 658, 9 S. Ct. 335 (1889). See also Schultz v. Commodity Futures Trading Comm'n, 716 F.2d 136, 139 (2d Cir. 1983); Letson v. Dean Witter Reynolds, Inc., 532 F. Supp. 500, 503 (N.D. Cal. 1982) (applying Galigher principle by measuring damages as difference between  highest intermediate value of the securities within a reasonable time after wrongful liquidation and  value obtained upon liquidation), aff'd, 730 F.2d 769 (9th Cir. 1984). An award of shares rather than monetary damages, appellant's thesis runs, cannot comport with this rule of law since the shares' actual value on the award date will have no necessary correlation with the shares' highest value within a reasonable period following the wrongful act.
Although this asseveration might have some force if we were reviewing the district court's findings in a jury-waived trial, the level of deference accorded an arbitrator's selection of remedies is much greater than that accorded a constitutional court. See Misco, 484 U.S. at 38 ("where it is contemplated that the arbitrator will determine remedies . . . courts have no authority to disagree with his honest judgment in that respect"); Georgia-Pacific Corp., 864 F.2d at 944; Taunton Mun. Light Plant Comm'n v. Paul L. Geiringer & Assocs., 560 F. Supp. 1249, 1251-52 (D. Mass.), aff'd, 725 F.2d 664 (1st Cir. 1983) (table).
No argument is advanced that the agreement to arbitrate restricted the arbitrators' remedial powers. Thus, in order to prevail, Advest by its own admission must prove that the arbitrators' choice of redress was in manifest disregard of the law. The hurdle is a high one, especially since there is nothing talismanic about the phrase "manifest disregard." The configuration merely means that, to vacate an arbitration award, "there must be some showing in the record, other than the result obtained, that the arbitrators knew the law and expressly disregarded it." O.R. Securities, Inc. v. Professional Planning Assoc., Inc., 857 F.2d 742, 747 (11th Cir. 1988). In this context, then, "disregard" implies that the arbitrators appreciated the existence of a governing legal rule but wilfully decided not to apply it. See Bobker, 808 F.2d at 933. As arbitrators need not explain their award, see Raytheon Co. v. Automated Business Systems, Inc., 882 F.2d 6, 8 (1st Cir. 1989), and did not do so here, it is no wonder that appellant is hard pressed to satisfy the exacting criteria for invocation of the doctrine. Compare, e.g., O.R. Securities, 857 F.2d at 747 & n.4 (recognizing that a showing of manifest disregard is "extremely difficult" where the arbitrators have opted not to state reasons).
In certain circumstances, the governing law may have such widespread familiarity, pristine clarity, and irrefutable applicability that a court could assume the arbitrators knew the rule and, notwithstanding, swept it under the rug. The case at bar, however, is not cut to so rare a pattern: appellant has utterly failed to show that the arbitrators inevitably must have recognized that the measure of damages adumbrated in Galigher v. Jones, supra, was the controlling rule of law.
To be sure, Advest presented this authority to the panel, and McCarthy, we are told, articulated no cohesive alternative. But arbitrators' remedial choices are not restricted to the array of anodynes proposed during the hearing. In actuality, the opposite is true: subject to the terms of the empowering clause, arbitrators possess latitude in crafting remedies as wide as that which they possess in deciding cases. See Challenger Caribbean, 903 F.2d at 869; see also S. D. Warren Co., 845 F.2d at 8. That leeway is at its zenith when, as here, the arbitration clause imposes no limitations on choice of remedies. See, e.g., Carte Blanche (Singapore), 888 F.2d at 266; Raytheon, 882 F.2d at 12. "If the parties do not pre-negotiate remedies, the arbitrator can fashion them as part of his decisional discretion." S. D. Warren Co., 845 F.2d at 8.
In this case, particularly, eschewal of a narrowly tailored compensatory remedy was well within the arbitrators' discretion. The panel might understandably have felt that restoration of McCarthy's stake in Amdahl, an essentially restitutionary measure of damages,7 represented the fairest, most concinnous resolution of the dispute. Whether this judgment was accurate is as much beside the present point as whether the restitutionary remedy would ultimately survive the scrutiny of a legion of legists. Because the panel chose a remedy "in the realm of what a judge might decide," Stop & Shop, 776 F.2d at 22, we cannot object to it here. After all, "there is often more than one satisfactory method for ascertaining the quantum of damages." Northern Heel Corp. v. Compo Indus., Inc., 851 F.2d 456, 473 (1st Cir. 1988).
We need go no further.8 Advest, having failed to find a bull market for its dubious legal wares, must bear with the consequences of the arbitral award. The district court's denial of appellant's motion to vacate conformed to the law.
* The Honorable Edward D. Re, Chief Judge of the United States Court of International Trade, sitting by designation.
1. The statute provides: In either of the following cases the United States court in and for the district wherein the award was made may make an order vacating the award upon the application of any party to the arbitration - (a) Where the award was procured by corruption, fraud, or undue means. (b) Where there was evident partiality or corruption in the arbitrators, or either of them. (c) Where the arbitrators were guilty of misconduct in refusing to postpone the hearing, upon sufficient cause shown, or in refusing to hear evidence pertinent and material to the controversy; or of any other misbehavior by which the rights of any party have been prejudiced. (d) Where the arbitrators exceeded their powers, or so imperfectly executed them that a mutual, final, and definite award upon the subject matter submitted was not made. (e) Where an award is vacated and the time within which the agreement required the award to be made has not expired the court may, in its discretion, direct a rehearing by the arbitrators. 9 U.S.C. § 10 (1988).
2. A margin account is a device used to extend credit to investors who buy securities. Initially, the investor pays only a percentage of the purchase price, borrowing the difference from the brokerage firm. The purchased securities are themselves used as collateral for the loan. The arrangement is a dynamic one, however, because the value of stock fluctuates. If the market price of the securities decreases, the collateral's value is diminished and the broker may demand that the investor deposit incremental funds.
3. To ensure that this aspect of the appeal requires no deeper inquiry, we have studied the pertinent regulations, the text of the mailgrams, and the associated parts of the record. The regulations were, as appellant now admits, precatory. On the other hand, the wording of the mailgrams was, as McCarthy claims, infelicitous, quite obviously suggesting the exact interpretation which McCarthy reached. That being so, ancillary issues related to liability - whether McCarthy's reliance was genuine, reasonable, and detrimental; whether his remonstrance was timely - were plainly grist for the arbitrators' mill.
4. In addition, 9 U.S.C. § 11 provides for correction of "evident" and "material" arithmetic or descriptive errors. Appellant has not attempted to invoke section 11 in this case.
5. The "manifest disregard" language derives directly from dicta employed by the Court in Wilko v. Swan, 346 U.S. 427, 436-37, 98 L. Ed. 168, 74 S. Ct. 182 (1953). The lane of review that has opened out of this language is a judicially created one, not to be found in 9 U.S.C. § 10. See Bobker, 808 F.2d at 933; see also Jenkins v. Prudential-Bache Securities, Inc., 847 F.2d 631, 634 (10th Cir. 1988).
6. While we understand the temptation to recognize a third, residual category for cases which are "completely irrational," French, 784 F.2d at 906, "arbitrary and capricious," Raiford, 903 F.2d at 1412, or "unfounded in reason and fact," Stop & Shop, 776 F.2d at 21, we resist it. In our view, any case which purports to fall into this residual category involves an award made contrary to the plain meaning of the contract authorizing arbitration or one made in manifest disregard of the law.
7. The cash portion of the award, presumably intended to compensate for liquidation of the Recognition Equipment shares, has not been seriously challenged on appeal. The controversy centers around the order that McCarthy's Amdahl holdings must be replenished. That element of the award was restitutionary despite the fact that only 3400 shares of Amdahl stock were liquidated and 6800 were awarded. Because Amdahl shares split 2-for-1 between the time of the sell-off and the award date, the 6800 shares represented no more than the restoration of appellee's stake in the company.
8. Appellant makes passing mention of the award's vulnerability because the arbitrators did not accept Advest's proffer of a closing brief on the measure of damages. This contention, weak to begin with, is an obvious afterthought, presented in bare bones fashion. We dismiss it summarily. First, we are unable to see how, given Advest's other opportunities to present its position against a non-lawyer adversary who represented himself at the arbitration, this declination compromised the fundamental fairness of the arbitral proceeding. Cf., e.g., Rivera-Gomez v. de Castro, 843 F.2d 631, 634 (1st Cir. 1988) ("A district court unquestionably has broad authority to dam the flow of endless torrents of briefs."). Second, the cursory manner in which the point was presented in this court eliminates any need for an exegetic response. See, e.g., United States v. Zannino, 895 F.2d 1, 17 (1st Cir.) (issues adverted to on appeal, without any attempt at developed argumentation, are waived), cert. denied, 494 U.S. 1082, 108 L. Ed. 2d 944, 110 S. Ct. 1814 (1990); Collins v. Marina-Martinez, 894 F.2d 474, 481 n.9 (1st Cir. 1990) (same).