BAUER, Circuit Judge.
Eljer Manufacturing, Inc., seeks to modify an arbitration order entered against it. The district court reduced part of the award and affirmed the remainder. 822 F.Supp. 505. Kowin Development Corp. cross-appeals, arguing that the district court’s reduction of the award should be reversed and the order of the arbitrator reinstated in full. We affirm in part and modify the award in part.
I. Facts
Eljer was, during the relevant period, the parent corporation of the Simonds Division, a producer of metal files. In 1984, Simonds along with Kowin formed Kowin-Simonds, Inc. The agreement creating Kowin-Si-monds provided that Kowin-Simonds would participate in a joint venture with a Chinese company to manufacture files in China. The Chinese joint venture would then agree to supply Simonds with a certain proportion of Simonds’s file requirements every year for twenty years. Kowin and Simonds agreed to submit any disputes arising under the agreement to arbitration.1
To aid the Chinese joint venture, Simonds agreed to sell its excess manufacturing equipment for a total price of $3.5 million. Kowin-Simonds bought some of this equipment with the proceeds of a $2.5 million loan from the Bank of America. Kowin and Eljer each guaranteed $1.25 million of the loan. The rest of the necessary equipment was purchased for $1 million by the Bank of China which in turn leased the equipment back to the Chinese joint venture. Pursuant to the Kowin-Simonds agreement, Simonds paid Kowin a $500,000 commission which the [1253]*1253arbitrator determined to be in return for arranging all the financing.
In June of 1985, the Beijing Steel Files Plant agreed to be Kowin-Simonds’s Chinese partner in the joint venture and operations began soon thereafter. For a variety of reasons, not relevant for purposes of our review, the venture failed miserably. As a result of the failure, Kowin-Simonds was unable to meet its obligations on the Bank of America loan and, as guarantors, Eljer and Kowin were each forced to pay the bank $1.25 million plus accrued interest.
On March 17, 1988, Kowin sued Eljer and Simonds in the United States District Court for the Central District of California. Kow-in’s complaint listed fraud, breach of contract, and federal securities claims,2 and alleged that Eljer and Simonds fraudulently misrepresented and concealed facts concerning the equipment it sold and the market conditions for steel files.
Eljer moved to compel arbitration pursuant to the Kowin-Simonds agreement and the district court granted the motion. The parties proceeded to arbitration in Chicago, and on October 30, 1992, the arbitrator awarded Kowin a total of $14,844,858 in damages, $4 million in prejudgment interest and attorneys’ fees. The arbitrator divided the damages into three separate awards: (1) $2,960,542; (2) $8,384,316; and (3) $3,500,000. The arbitrator neglected, however, to articulate his findings any further. Eljer filed a motion to vacate or modify the award in the United States District Court for the Northern District of Illinois.
On March 1, 1993, the district court partially affirmed the arbitrator’s award. Because each award duplicated precisely the amounts requested by Kowin in the damages section of its post-hearing brief, the court was easily able to determine what injury each of the three damage awards was intended to compensate. Once it had discerned the bases for each award, the court reduced two of the three awards.
The first award of $2,960,542 represented the $2.5 million principal of the Kowin-Si-monds loan plus $460,542 of accrued interest.3 As guarantor on $1.25 million of the loan, Eljer had already paid this sum to the bank. Including this in the award would have required Eljer to make the same payment twice. The district court, therefore, reduced this award by $1.25 million.
The arbitrator’s second damages award of $8,384,316 represented lost profits projected over the twenty year term of the contract plus Kowin’s $250 capital contribution to the venture. The district court refused to modify this award because in its view the arbitrator did not deliberately' disregard the law.
As for the third award of $3.5 million, the court concluded it represented what Kowin alleged to be Simonds’s unjust enrichment from the sale of its equipment. Recognizing that $2.5 million of this, the Bank of America proceeds, was included in the first award, the court reduced the award to $1 million to avoid double recovery.
II. Standard of Review
Our scope of review of a commercial arbitration award is grudgingly narrow. Sections 10 and 11 of the Federal Arbitration Act provide statutory grounds for the modification of an arbitrator’s decision.4 In addi[1254]*1254tion to the reasons set out in the statute, we will set aside an arbitrator’s decision if in reaching his result, the arbitrator deliberately disregards what he knows to be the law. Health Servs. Mgmt. Corp. v. Hughes, 975 F.2d 1253, 1267 (7th Cir.1992). Errors in the arbitrator’s interpretation of law or findings of fact do not merit reversal under this standard. National Wrecking Co. v. International Brotherhood of Teamsters, Local 731, 990 F.2d 957 (7th Cir.1993); Moseley, Hallgarten, Estabrook, & Weeden v. Ellis, 849 F.2d 264 (7th Cir.1988). Nor does an insufficiency of evidence supporting the decision permit us to disturb the arbitrator’s order. Arbitration does not provide a system of “junior varsity trial courts” offering the losing party complete and rigorous de novo review. National Wrecking, 990 F.2d at 960. It is a private system of justice offering benefits of reduced delay and expense. A restrictive standard of review is necessary to preserve these benefits and to prevent arbitration from becoming a “preliminary step to judicial resolution.” E.I. DuPont de Nemours v. Grasselli Employees Indep. Ass’n, 790 F.2d 611, 614 (7th Cir.), cert. denied, 479 U.S. 853, 107 S.Ct. 186, 93 L.Ed.2d 120 (1986).
III. Kowin’s Cross-Appeal
We deal first with the cross-appeal. Kowin argues that the court’s reduction of the award rests on impermissible speculation as to what each of the arbitrator’s three awards was attempting to redress. We disagree. Kowin confuses a narrow standard of review with a nonexistent standard of review. The basis for each of the arbitrator’s awards is no mystery. As the district court noted, the figures were identical to certain amounts requested by Kowin in the damages section of its post-hearing brief. It was hardly speculative for the district court to base its analysis on Kowin’s own explanation of its damages. We agree with the district court’s breakdown of the awards and its subsequent review in that light.
We also agree with the district court’s reduction of the first and third award.
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BAUER, Circuit Judge.
Eljer Manufacturing, Inc., seeks to modify an arbitration order entered against it. The district court reduced part of the award and affirmed the remainder. 822 F.Supp. 505. Kowin Development Corp. cross-appeals, arguing that the district court’s reduction of the award should be reversed and the order of the arbitrator reinstated in full. We affirm in part and modify the award in part.
I. Facts
Eljer was, during the relevant period, the parent corporation of the Simonds Division, a producer of metal files. In 1984, Simonds along with Kowin formed Kowin-Simonds, Inc. The agreement creating Kowin-Si-monds provided that Kowin-Simonds would participate in a joint venture with a Chinese company to manufacture files in China. The Chinese joint venture would then agree to supply Simonds with a certain proportion of Simonds’s file requirements every year for twenty years. Kowin and Simonds agreed to submit any disputes arising under the agreement to arbitration.1
To aid the Chinese joint venture, Simonds agreed to sell its excess manufacturing equipment for a total price of $3.5 million. Kowin-Simonds bought some of this equipment with the proceeds of a $2.5 million loan from the Bank of America. Kowin and Eljer each guaranteed $1.25 million of the loan. The rest of the necessary equipment was purchased for $1 million by the Bank of China which in turn leased the equipment back to the Chinese joint venture. Pursuant to the Kowin-Simonds agreement, Simonds paid Kowin a $500,000 commission which the [1253]*1253arbitrator determined to be in return for arranging all the financing.
In June of 1985, the Beijing Steel Files Plant agreed to be Kowin-Simonds’s Chinese partner in the joint venture and operations began soon thereafter. For a variety of reasons, not relevant for purposes of our review, the venture failed miserably. As a result of the failure, Kowin-Simonds was unable to meet its obligations on the Bank of America loan and, as guarantors, Eljer and Kowin were each forced to pay the bank $1.25 million plus accrued interest.
On March 17, 1988, Kowin sued Eljer and Simonds in the United States District Court for the Central District of California. Kow-in’s complaint listed fraud, breach of contract, and federal securities claims,2 and alleged that Eljer and Simonds fraudulently misrepresented and concealed facts concerning the equipment it sold and the market conditions for steel files.
Eljer moved to compel arbitration pursuant to the Kowin-Simonds agreement and the district court granted the motion. The parties proceeded to arbitration in Chicago, and on October 30, 1992, the arbitrator awarded Kowin a total of $14,844,858 in damages, $4 million in prejudgment interest and attorneys’ fees. The arbitrator divided the damages into three separate awards: (1) $2,960,542; (2) $8,384,316; and (3) $3,500,000. The arbitrator neglected, however, to articulate his findings any further. Eljer filed a motion to vacate or modify the award in the United States District Court for the Northern District of Illinois.
On March 1, 1993, the district court partially affirmed the arbitrator’s award. Because each award duplicated precisely the amounts requested by Kowin in the damages section of its post-hearing brief, the court was easily able to determine what injury each of the three damage awards was intended to compensate. Once it had discerned the bases for each award, the court reduced two of the three awards.
The first award of $2,960,542 represented the $2.5 million principal of the Kowin-Si-monds loan plus $460,542 of accrued interest.3 As guarantor on $1.25 million of the loan, Eljer had already paid this sum to the bank. Including this in the award would have required Eljer to make the same payment twice. The district court, therefore, reduced this award by $1.25 million.
The arbitrator’s second damages award of $8,384,316 represented lost profits projected over the twenty year term of the contract plus Kowin’s $250 capital contribution to the venture. The district court refused to modify this award because in its view the arbitrator did not deliberately' disregard the law.
As for the third award of $3.5 million, the court concluded it represented what Kowin alleged to be Simonds’s unjust enrichment from the sale of its equipment. Recognizing that $2.5 million of this, the Bank of America proceeds, was included in the first award, the court reduced the award to $1 million to avoid double recovery.
II. Standard of Review
Our scope of review of a commercial arbitration award is grudgingly narrow. Sections 10 and 11 of the Federal Arbitration Act provide statutory grounds for the modification of an arbitrator’s decision.4 In addi[1254]*1254tion to the reasons set out in the statute, we will set aside an arbitrator’s decision if in reaching his result, the arbitrator deliberately disregards what he knows to be the law. Health Servs. Mgmt. Corp. v. Hughes, 975 F.2d 1253, 1267 (7th Cir.1992). Errors in the arbitrator’s interpretation of law or findings of fact do not merit reversal under this standard. National Wrecking Co. v. International Brotherhood of Teamsters, Local 731, 990 F.2d 957 (7th Cir.1993); Moseley, Hallgarten, Estabrook, & Weeden v. Ellis, 849 F.2d 264 (7th Cir.1988). Nor does an insufficiency of evidence supporting the decision permit us to disturb the arbitrator’s order. Arbitration does not provide a system of “junior varsity trial courts” offering the losing party complete and rigorous de novo review. National Wrecking, 990 F.2d at 960. It is a private system of justice offering benefits of reduced delay and expense. A restrictive standard of review is necessary to preserve these benefits and to prevent arbitration from becoming a “preliminary step to judicial resolution.” E.I. DuPont de Nemours v. Grasselli Employees Indep. Ass’n, 790 F.2d 611, 614 (7th Cir.), cert. denied, 479 U.S. 853, 107 S.Ct. 186, 93 L.Ed.2d 120 (1986).
III. Kowin’s Cross-Appeal
We deal first with the cross-appeal. Kowin argues that the court’s reduction of the award rests on impermissible speculation as to what each of the arbitrator’s three awards was attempting to redress. We disagree. Kowin confuses a narrow standard of review with a nonexistent standard of review. The basis for each of the arbitrator’s awards is no mystery. As the district court noted, the figures were identical to certain amounts requested by Kowin in the damages section of its post-hearing brief. It was hardly speculative for the district court to base its analysis on Kowin’s own explanation of its damages. We agree with the district court’s breakdown of the awards and its subsequent review in that light.
We also agree with the district court’s reduction of the first and third award. When an arbitration award orders a party to pay damages that have already been paid or which are included elsewhere in the award, a court may modify the award. Double recovery constitutes a materially unjust miscalculation which may be modified under section 11 of the Federal Arbitration Act. Transnitro, Inc. v. M/V Wave, 943 F.2d 471 (4th Cir.1991); Ellis, 849 F.2d at 272.
IV. Eljer’s Appeal
Eljer attacks three aspects of the arbitrator’s award. First, Eljer argues that the arbitrator’s failure to explain the basis for his award requires that we remand the case to him with instructions to clarify the grounds for the award. Second, Eljer claims that the arbitrator made several miscalculations in his damage awards. Third, Eljer contends that the arbitrator’s award of attorneys’ fees was improper. We consider these arguments in turn.
A. Arbitrator’s Failure to Explain the Award
Eljer argues that the arbitrator’s failure to articulate the grounds for his award prevented “meaningful judicial review” of his claim. Eljer’s concern is that the arbitrator erroneously rejected some of its defenses and by shielding his decision from scrutiny, prevented reviewing courts from exposing those errors. Eljer asks that we remand the case to the arbitrator with instructions to clarify his award.
This argument fails for two reasons. First and most fundamentally, an arbitrator is simply not required to state the reasons for his decision. Randall v. Lodge No. 1076, Int’l Ass’n of Machinists and Aerospace Workers, 648 F.2d 462, 468 (7th Cir.1981). Such a requirement would serve only to perpetuate the delay and expense which arbitration is meant to combat.
[1255]*1255Eljer’s requested remand must also be denied because errors of law alone do not constitute a sufficient basis for remanding the case. In its brief, Eljer goes to great lengths in trying to persuade us that yarious legal defenses it presented to the arbitrator should have prevailed. Eljer misses the point. Even if its legal defenses were dis-positive, the fact that the arbitrator erroneously rejected them does not, by itself, provide grounds for a remand. The arbitrator must have deliberately disregarded what he knew to be the law. ' Eljer has not shown such disregard here.
B. Damage Awards
Eljer challenges the arbitrator’s three awards, alleging that each contains flaws in its calculation. Claiming that the cumulative award constitutes a triple recovery, Eljer also contests the award as a whole.
1. Award of $1,710,542. Eljer’s objection to the first award is that even after the reduction by the district court, the award exceeds Kowin’s damages by $500,000. As it stands, this award is comprised of the principal and interest on Kowin’s share of its guarantee on the Bank of America loan.
In the Letter of Intent which was later incorporated into the Kowin-Simonds agreement, the parties agreed that Kowin would receive a $500,000 commission. The parties dispute however for what service that commission was to be paid. Eljer claims that the commission was paid to Kowin in exchange for entering into the venture. Eljer insists that the commission must be offset against the damages incurred by Kowin in making its loan payment.
Not surprisingly, Kowin disputes this explanation for the commission. According to Kowin, the commission was compensation for Kowin’s role in arranging the financing necessary to purchase Simonds’s machinery and not as an inducement to enter the transaction. From this perspective, the commission was in essence a separate agreement and should not impact the damages Kowin suffered from having to satisfy Kowin-Si-monds’s loan.
We refuse to reduce this award further. Eljer’s argument merely asserts that the arbitrator reached the wrong result from conflicting evidence. Our scope of review does not permit us to disturb the arbitrator’s findings as to the relative credibilities of each side’s evidence. We therefore yield to the decision of the arbitrator.
2. Award of $8,384,316. This award represented Kowin’s share of the profits which Eljer projected the joint venture would generate in its first five years, extrapolated over the twenty year term of the contract. Eljer advances three theories for vacating or reducing this award. First, Eljer contends the award should be vacated because under the relevant law, future lost profits are not recoverable. Second, Eljer requests that we vacate the award because it was based on insufficient evidence. Alternatively, Eljer asks us to limit the award to profits projected over the first five years and to vacate the portion of the award which represents the extrapolation over the remaining fifteen years. Eljer claims that this extrapolation is too tenuous on which to base an award.
Eljer’s first claim essentially asks us to vacate the award because the arbitrator made an error of law. Kowin asserted violations of federal securities laws as well as California and Illinois tort law. Since federal securities law does not permit the recovery of future lost profits, Madigan, Inc. v. Goodman, 498 F.2d 238, 289 (7th Cir.1974), Eljer reasons that the award could only have been granted pursuant to the California and/or Illinois claims. Neither California nor Illinois law, however, permit awards of lost profits to “unestablished” ventures because profit projections are usually too speculative. Maggio, Inc. v. United Farm Workers of America, 227 Cal.App.3d 847, 278 Cal.Rptr. 250, 264 (1991); Drs. Sellke & Conlon v. Twin Oaks Realty, 143 Ill.App.3d 168, 96 Ill.Dec. 633, 638, 491 N.E.2d 912, 917 (Ill.App.1986). Eljer concludes that because the arbitrator’s second award was barred by the applicable law, the arbitrator exceeded his powers under section 10(a)(4) of the Federal Arbitration Act.
Contrary to Eljer’s reading, a court can modify an arbitrator’s decision under [1256]*1256section 10(a)(4) only if the arbitrator exceeds the powers delegated to him by the parties. Ethyl Corp. v. United Steelworkers of America, 768 F.2d 180, 184 (7th Cir.1985). In this case, whether or not the claim is permitted under-the applicable law is irrelevant under 10(a)(4). Nor can we hold that the arbitrator’s award was in deliberate disregard of the law. As we have stated repeatedly, mere error in the interpretation of the law (as opposed to failure to decide in accordance with relevant provisions of law) does not provide grounds for disturbing an arbitration award. Health Services, 975 F.2d at 1267.
Even if an arbitrator’s mistake of law permitted us to modify his decision, we still would not do so here. The premise of the so-called “new business” rule is that the success of a new enterprise is ordinarily uncertain. Where, however, the enterprise is simply an absorption or extension of a previously established successful operation and the venture’s future is less in doubt; the awarding of future lost profits is not, as a matter of law, forbidden. GHK Assocs. v. Mayer Group, Inc., 224 Cal.App.3d 856, 274 Cal.Rptr. 168 (1990); Hallmark Ins. Admin’rs v. Colonial Penn. Life Ins., 697 F.Supp. 319, 327 (N.D.Ill.1988), aff'd, 990 F.2d 984 (7th Cir.1993). Kowin argued that the Chinese venture fell under this exception and the arbitrator could have made his decision on this basis.
This brings us to Eljer’s second argument for vacating the award of lost profits: that the evidence supporting the award was insufficient. We have set out above the circumstances in which we are empowered to set aside an arbitration award. 9 U.S.C. § 10. Insufficiency of the evidence is not one of those grounds and we see no reason to adopt it as such here. In fairness to the arbitrator, even if we could vacate the award we would not do so because the evidence was clearly sufficient to support the award. Kowin’s claim for lost profits was based on Eljer’s own representations about the venture’s profitability and based on Eljer’s commitment to purchase a certain number of files every year.
For identical reasons, we reject El-jer’s request that we limit the award to profits over five years instead of the twenty year term of the contract. The evidence submitted to the arbitrator projected profits for the first five years of the joint venture. Kowin arrived at the figure it requested by extrapolating those profits over the twenty year term of the contract. Eljer asserts that this extrapolation was insufficient to sustain the lost profits award. A question as to the sufficiency of the evidence before the arbitrator simply does not trigger the review powers of this court. For all of the foregoing reasons, we affirm the arbitrator’s award of lost profits.
3. Award of $1,000,000. This award represents the amount by which Eljer was alleged to have been unjustly enriched. The arbitrator originally awarded $3.5 million but the district court reduced the amount after determining that the $2.5 million loan was included in both this award and the first award.
In its reduced form, the award is comprised solely of the fee which Eljer received from the Bank of China for some of Si-monds’s equipment. The Bank of China has sued Eljer in China for fraud in connection with this sale. Kowin claims that Eljer should be required to disgorge the proceeds of this sale. While we agree that Eljer should not be permitted to benefit from any fraudulent activity, it is unclear why Eljer should pay Kowin for losses suffered by the Bank of China.
Eljer argues here that the remaining $1 million should be vacated because in awarding Kowin damages for a loss it did not suffer, the arbitrator exceeded his powers under the contract. We agree. The test for vacating an award under section 10(a)(4) of the Arbitration Act is whether the arbitrator exceeded the powers delegated to him by the parties. Ethyl Corp., 768 F.2d at 184. Though the arbitration clause is broadly worded, it cannot be construed to delegate to the arbitrator the power to arbitrate disputes between Eljer and a third party. The language of the clause limits arbitration to disputes arising under the contract. The transaction between the Bank of China and Eljer was completely separate from the Kowin-[1257]*1257Simonds agreement and was therefore outside the scope of the arbitration clause. Because the arbitrator exceeded the scope of his powers, we vacate the third damage award of $1 million.
4. The damage award as a whole. Eljer asserts that the most significant miscalculation by the arbitrator was his granting of three separate measures of damages. El-jer claims that the award as a whole gave Kowin a triple recovery and asks that we modify the awards so that Kowin is granted only one measure of damages. Although we have already vacated the third award, we presume that Eljer’s objection still stands with respect to the two remaining awards.
Eljer errs in characterizing the two awards as alternative measures of Kowin’s damages. Each award represents a separate and distinct injury which Kowin suffered as a result of Eljer’s actions. The first award compensates Kowin for having to pay off a loan that otherwise would have been paid by Kowin-Simonds. The second award gives Kowin the benefit of the bargain which Kowin would have realized had Eljer not breached the contract. The two awards are not incompatible. We therefore affirm the arbitrator’s granting of the two awards.
C. Attorneys’ Fees
Apparently in reliance on the “American Rule” for attorneys’ fees, Eljer submits that in arbitration, as in court, each side must pay its own legal expenses absent an express statutory or contractual provision to the contrary. Eljer argues that in this case the arbitrator had no statutory or contractual basis for awarding Kowin attorneys’ fees and requests that we vacate the award. We find otherwise and affirm the arbitrator’s decision.
At the outset, we point out that at least one other jurisdiction has rejected extension of the “American Rule” to arbitration. Tennessee Dep’t of Human Servs. v. United States Dep’t of Educ., 979 F.2d 1162, 1169 (6th Cir.1992). We need not decide whether such an approach is merited in this circuit because we find that the arbitrator’s award was within his authority. First, as Eljer acknowledges, Kowin’s Illinois securities law claim, if successful, permits recovery of attorneys’ fees. 815 ILCS § 5/13(2) (1993). This claim was submitted to the arbitrator for resolution pursuant to the arbitration clause as a claim arising under the terms of the contract. In passing on this claim, the arbitrator was well within his powers to award attorneys’ fees.
Eljer argues in rebuttal that the arbitrator could not have awarded fees' pursuant to Illinois securities law because those claims were time barred. Once again, Eljer attempts to have us review the arbitrator’s decision for errors in law. We emphasize yet again that on factual and legal questions falling within the arbitrator’s authority, we defer to his decision.
The arbitrator’s decision could have been based on other state law as well. It is completely possible that the arbitrator awarded attorneys’ fees as damages for fraud or misrepresentation and not pursuant to a statute. Illinois law permits the recovery of attorneys’ fees as damages if the plaintiff proves that the fees resulted from the defendant’s misconduct and the fees, are reasonable. Tan v. Boyke, 156 Ill.App.3d 49, 108 Ill.Dec. 229, 236, 508 N.E.2d 390, 397 (1987). Attorneys’ fees “may be recovered under the common law as an element of compensatory damages in cases where the defendant’s tor-tious conduct proximately caused the plaintiff to incur them.” Calcagno v. Personalcare Health Mgmt., 207 Ill.App.3d 493, 152 Ill. Dec. 412, 421, 565 N.E.2d 1330, 1339 (1991).
V. Conclusion
■ For the foregoing reasons, we vacate the arbitrator’s third award, reducing the total award by $1,000,000. In all other respects, the district court’s decision reducing part of the arbitrator’s award and enforcing the remainder, is affirmed.