Under the Multiemployer Pension Plan Amendments Act of 1980, an employer that withdraws from a multiemployer pension plan can be forced to pay the plan a sum approximating the vested but unfunded benefits of the employer’s employees. 29 U.S.C. §§ 1381 et seq. The purpose of this “withdrawal liability,” which is enforceable in a suit by the pension plan with issues of fact[*727] resolved by an arbitrator subject to review by the district court for clear error (see 29 U.S.C. §§ 1401(b)(2), (c), 1451, as glossed in Chicago Truck Drivers, Etc. Pension Fund v. Louis Zahn Drug Co., 890 F.2d 1405, 1411 (7th Cir.1989)), is to protect the other employers in the multi-employer plan from having to pay for those benefits. Central States, Southeast & Southwest Areas Pension Fund v. Lady Baltimore Foods, Inc., 960 F.2d 1339, 1340 (7th Cir.1992). A parent and its subsidiaries are treated as one employer for this purpose, 29 U.S.C. § 1301(b)(1); so if a subsidiary withdraws from the plan, its withdrawal liability can be assessed against the parent. § 1381(a). If, however, rather than causing the subsidiary to withdraw the parent sells the subsidiary, the parent is not liable for withdrawal liability of the subsidiary unless “a principal purpose” of the transaction was to “evade or avoid” parental liability. § 1392(c).

In 1984, in a leveraged buyout, Santa Fe Pacific Corporation sold a trucking subsidiary — the Santa Fe Trails Transportation Company (SFTT) — that was a member of the Central States multiemployer pension plan. The purchaser, a rail freight consolidator, went broke a year later, whereupon Central States assessed a withdrawal liability of $7.6 million against Santa Fe to fund the vested pension benefits of SFTT’s employees. Santa Fe challenged the assessment and the matter was referred to arbitration. The arbitrator, a nonlawyer selected by the parties from a panel, established by the American Arbitration Association, of specialists in withdrawal-liability arbitrations, thrice found that avoidance of withdrawal liability had not been a principal purpose of the sale. The first two times the district judge remanded the case to the arbitrator, finding the opinions he had written in support of his conclusion utterly unsatisfactory. The third time the judge, with evident reluctance, upheld the arbitrator, precipitating this appeal.

The issue is purpose, a state of mind inferred from testimony and other evidence. The arbitrator heard testimony for fifteen days and reviewed innumerable documents, and even if the statute did not require the district court (and this court) to accord substantial deference to the arbitrator’s judgment, such deference would be the counsel of prudence. But despite the impression that may have been conveyed by some colorful language in Parts & Electric Motors, Inc. v. Sterling Electric Inc., 866 F.2d 228, 233 (7th Cir.1988), where we said that a finding to be deemed clearly erroneous must stink like a “five-week-old, unrefrigerated dead fish,” the clear-error standard is not a rub-berstamp, even when the trier of fact is called an arbitrator rather than a judge. (The review of an arbitrator’s findings is normally much more limited than that of a judge’s findings, see, e.g., DDI Seamless Cylinder Int’l, Inc. v. General Fire Extinguisher Corp., 14 F.3d 1163, 1166-67 (7th Cir.1994); Brotherhood of Locomotive Engineers v. Atchison, Topeka & Santa Fe Ry., 768 F.2d 914, 921-22 (7th Cir.1985), but Congress departed from the norm in the Multiemployer Pension Plan Amendments Act.) A finding is clearly erroneous if the reviewing court, after duly acknowledging the superior proximity of the factfinder to the witnesses, is firmly convinced that the finding is erroneous. Concrete Pipe & Products of California, Inc. v. Construction Laborers Pension Trust, — U.S.-,-, 113 S.Ct. 2264, 2279-80, 124 L.Ed.2d 539 (1993); Anderson v. City of Bessemer City, 470 U.S. 564, 573-75, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518 (1985).

The imposition of withdrawal liability in a sale of business situation requires only that a principal purpose of the sale be to escape withdrawal liability. It needn’t be the only purpose; it need only have been one of the factors that weighed heavily in the seller’s thinking. We can find no decisions discussing situations in which there is more than one principal (major, weighty, salient, important) purpose, but we would be doing violence to the language and the purpose of the statute if we read “a principal” as “the principal.” The clear import of “a principal” is to let the employer off the hook even if one of his purposes was to beat withdrawal liability, provided however that it was a minor, subordinate purpose, as distinct from a major purpose. To let the employer off even if avoiding such liability was a major purpose[*728] would ill serve the statute’s goal of preventing one employer from unloading his pension obligations onto the other employers in a multiemployer plan.

There can be no serious doubt that withdrawal liability was one of the principal considerations in the decision to sell SFTT. It is true that officials of Santa Fe denied this in their testimony before the arbitrator, yet his three opinions contain only one finding with respect to credibility; he believed the testimony of Santa Fe’s president that concern with the effect on morale of firing the rest of SFTT’s employees incident to a sale of all its assets and with difficulties in making asset sales weighed heavily in the decision to sell the stock rather than assets of the subsidiary. But the arbitrator’s judgment that therefore avoiding withdrawal liability was not “a principal purpose” of the transaction is an inference from the testimony (and other evidence), not the testimony itself. We therefore need not decide whether this is one of those rare cases in which irreconcilable conflict between oral testimony on the one hand and indubitable documentary evidence and admissions on the other entitles the reviewing court to reject the credibility determinations of the trier of fact. Bullard v. Sercon Corp., 846 F.2d 463, 466 (7th Cir.1988); Winchester Packaging, Inc. v. Mobil Chemical Co., 14 F.3d 316, 319 (7th Cir.1994). We can reject the district judge’s factual inferences from testimony only if they are clearly erroneous, but they do not have the additional insulation from appellate review that determinations of credibility enjoy.

Proper analysis of the case requires distinguishing between two different desires of Santa Fe. One was to rid itself of SFTT. The other was to sell SFTT. These sound alike but are different. There is no doubt that for reasons unrelated to withdrawal liability Santa Fe wanted to get rid of the subsidiary, which it described as being “among the living dead” because of the seismic changes in the transportation industry caused by deregulation. But the sale of the subsidiary as a going concern, as by selling the stock of SFTT, was only one possible method of getting rid of the subsidiary. The other was to sell off its assets, either piecemeal or in a lump. Santa Fe had set forth on this road, closing down a large part of SFTT, selling 57 percent of SFTT’s trucks and discharging 44 percent of its employees in the process (thus already incurring a risk of withdrawal liability, for the risk arises whenever an employer discharges a substantial fraction of its employees who have vested but unfunded benefits in a multiemployer pension plan, see 29 U.S.C. § 1385, and later SFTT actually rehired some of these discharged employees to avoid the risk of withdrawal liability), when in 1982 it began a systematic consideration of the fate of what remained of SFTT. The options were quickly narrowed to two: sell the assets; sell the stock. The first route, it was estimated, would bring in more money. The subsidiary had been losing money (the president of Santa Fe called SFTT “a perennial loser”); the prospects for a turnaround were not good; its value as a going concern was therefore less than its salvage value. The difference in the estimated yields of the alternative methods of disposition would have provided a strong, perhaps a compelling, inducement to go the liquidation route but for the prospect of withdrawal liability. One consultant advised Santa Fe in 1981 that “pension fund liability,” which the consultant estimated at $10.5 mihion, “is a major stumbling block in implementing the liquidation of SFTT’s operation.” The president of Santa Fe testified that this report was “my first sort of hit with a 2 by 4 about MPAA.” We know that the vested but unfunded pension benefits of SFTT’s employees would later be estimated by Central States at $7.6 million, and this is the estimate of the liability to Central States alone; SFTT had some, though much less, withdrawal liability to other multiemployer pension plans. When the fate of SFTT was being discussed within Santa Fe, the amount of the potential withdrawal liability was uncertain but it was believed to be at least several million dollars and possibly more than $11 million, so that if it could be avoided by sale of the stock of SFTT rather than its assets this might be the more profitable route to take after all, even though it would have been the less profitable route in the absence of any danger of withdrawal liability.

[*729] Internal documents that cannot be explained away make clear that Santa Fe’s management was both aware of the company’s potential withdrawal liability (the “spec-tre of the Multi-Employer Pension Plan Act, which imposes liability for withdrawal from the teamster retirement plan,” as one document describes it) and aware that a sale of the company might avoid it. As Santa Fe’s president wrote the chairman of the board in 1983, “If a purchaser [for SFTT] can be located, there is a good possibility of transferring part or all of a rather substantial liability which the company is incurring under the Multiemployer Pension Plan Amendments Act.” A lawyer for Santa Fe reminded the company’s general counsel that “Due to MPPAA considerations among other things, you advised him [a prospective purchaser of SFTT] that we were seeking a large, financially strong purchaser.” This lawyer’s notes of one meeting of the selling team report that the team was considering “desperation moves,” including “selling it [SFTT] to someone in trouble.”

The situation, in short, was that by selling the stock rather than the assets of the subsidiary Santa Fe stood to avoid millions of dollars in withdrawal liability, whereas without that potential liability the sale of the assets would have brought a higher price. In this situation the inference that withdrawal liability figured heavily in the company’s decision to sell the stock is well-nigh irresistible. Obviously a purpose for the sale of stock is “principal” if, were it absent, the sale would not have taken place. It follows that a principal purpose of the sale of SFTT’s stock must have been to avoid withdrawal liability unless, somehow, the other considerations favoring a sale of stock over a sale of assets were so compelling that they reduced the avoidance of withdrawal liability to a minor consideration because the sale of stock would have taken place even if the MPPAA had never been passed. Certainly if SFTT had had much greater value as a going concern than on the auction block, and if a sale of stock as in a leveraged buyout was a much more feasible method of preserving the subsidiary as an intact concern than a cash sale of the assets or a merger (which is a form of asset acquisition), it might be reasonable to infer that withdrawal liability was only a minor factor in Santa Fe’s thinking. But on the contrary, the subsidiary was worth considerably more as a conglomeration of assets than as a going concern.

Santa Fe’s president testified, as we mentioned, that despite the difference in yields he preferred the stock sale because he feared the impact on the morale of Santa Fe’s remaining workers if it fired all of SFTT’s employees, as it planned to do when the terminals and other assets that these workers worked in or with were sold. The testimony was not backed up by any of the extensive documentary evidence generated in Santa Fe’s protracted consideration of alternative methods of disposing of the subsidiary. Having already discharged almost half its work force, SFTT could not plausibly be considered overly concerned with employee morale. But even if the president’s testimony is taken at face value, at most it establishes that the avoidance of withdrawal liability was not the only consideration in the structuring of the transaction, not that avoidance did not play an important role in the decision.

At oral argument Santa Fe’s able counsel emphasized a second factor — that the yield from a piecemeal liquidation could not be known for sure in advance, could not in fact be known for sure until the last asset had been sold. This is a plausible point, but since it was not mentioned in any of the planning documents, it can hardly be thought a purpose for the sale that either by itself or in conjunction with the concern about employee morale assumed such transcendent importance in the minds of Santa Fe’s managers as to push those millions of dollars of potential withdrawal liability into the shade.

The arbitrator’s treatment of these issues was entirely inadequate. Most of his third opinion, the one the district judge reluctantly upheld, is devoted to irrelevant questions, such as whether Santa Fe had reasons independent of withdrawal liability to divest itself of SFTT and whether it knew that the purchaser of SFTT was likely to flop. The issue is not whether Santa Fe had compelling reasons independent of withdrawal liability to divest itself of SFTT; that is a given. The issue is the form the divestiture took — a sale of stock rather than of assets. The statutory[*730] criterion is not whether the transaction is a sham, having no purpose other than to defeat the goals of the Multi-employer Pension Plan Amendments Act by leaving the other employers in the multiemployer pension plan holding the bag. It is whether the avoidance of withdrawal liability by the seller (not necessarily by the purchaser as well) is one of the principal purposes of the transaction. To that central issue the arbitrator devoted a single, short paragraph, in which he remarks that if SFTT had been closed down “there would have been a serious loss of jobs” and that “selling of assets causes numerous problems that can go on for some time.” That is the whole meat of the opinion — of the three opinions in fact. It does not justify the arbitrator’s conclusion that the avoidance of withdrawal liability was not one of the principal purposes of the transaction.

At argument the question arose whether a reviewing court has the inherent power, corresponding to the power that our circuit rule 36 gives us in remanding cases to district courts, to direct that an arbitral matter that must be remanded be remanded to a different arbitrator. This was done in Stroehmann Bakeries, Inc. v. Local 776, International Brotherhood of Teamsters, 969 F.2d 1436, 1446 (3d Cir.1992), but without discussion of the court’s power to do so. The issue is moot. The arbitrator has died, and Rule 14 of the American Arbitration Association (under whose auspices the arbitration was conducted) establishes a mechanism for the appointment of a new arbitrator in such a case. If necessary. The record permits only one conclusion concerning the issue under appeal — that a principal purpose of the sale of SFTT’s stock was to avoid withdrawal liability — and we are not aware that Santa Fe is contesting the amount of withdrawal liability that Central States determined or the method of assessing interest on it, but this is a matter that can be straightened out in the district court.

The judgment of the district court is reversed and the case remanded for further proceedings consistent with this opinion.