Hayden Mcllroy, Plaintiff below, appeals the district court’s denial of his motion to modify or vacate an arbitration award handed down by an arbitration panel of the National Association of Securities Dealers (“NASD”). Mcllroy argues that the district court erred in failing to modify or vacate the award under the Federal Arbitration Act, 9 U.S.C. § 1 et seq. (“Arbitration Act”), and that it erred in excluding his submission of supplemental authority. For the reasons that follow, we affirm.

I. Facts

Appellant Mcllroy, an experienced investor, purchased 40,000 shares of stock in Sooner Federal Savings & Loan Association (“Sooner”) in 1987, through a broker at the Tulsa, Oklahoma office of Kidder, Peabody & Company. In March, 1988, Appel-lee PaineWebber, Incorporated (“Paine-Webber”) took over Kidder Peabody’s Tulsa office and Mcllroy became a Paine-Webber client.

In June, 1988, after Sooner had reported several quarterly losses, Mcllroy informed his PaineWebber broker, F. Stephen Allen, that he wanted to sell his Sooner stock, if possible without taking a discount on the price. Allen reminded Mcllroy that Sooner stock was held by only a few investors and was, in consequence, difficult to sell. Mcll-roy did not enter a formal sell order and Allen did not locate a buyer for the stock.

In September, 1988, Allen informed Mcll-roy that another Sooner shareholder was preparing to sell a substantial amount of stock. Such a sale would force short sellers of Sooner stock to cover, driving the stock price up and allowing Mcllroy to liquidate his shares at a favorable price. Mcllroy purchased an additional 10,000 shares but the stock sale never occurred. In October, 1988, Mcllroy again asked Allen to sell his Sooner shares.

In November, 1988, some short sellers of Sooner stock entered the market. Paine-Webber sold them 47,397 shares, and then an additional 1,600 shares, out of its own inventory, for a total price of $893,395.25. Allen assured Mcllroy that he would sell Mcllroy’s stock in the next short cover transaction, which he believed would occur immediately. No short cover transactions occurred in November or December, 1988, and Sooner stock declined precipitously in value. In November, 1989, the Federal Savings and Loan Insurance Corporation placed Sooner into receivership. Paine-Webber eventually sold Mcllroy’s stock at a price which left a $70,000.00 deficit in his trading account.

Mcllroy submitted a claim for $1,033,-750.00 in damages and costs to the National Association of Securities Dealers. PaineWebber counterclaimed for the deficit in Mcllroy’s account and moved to dismiss Mcllroy’s claim. After a hearing, a NASD arbitration panel found PaineWebber liable and awarded Mcllroy $40,875.00. The panel dismissed PaineWebber’s counterclaim and ordered each party to bear its own costs.

Mcllroy filed a motion in Texas state court seeking either an upward modification of the award to $911,323.88 1 or vacation of the award. PaineWebber removed the action to federal court. While the motion was pending, Mcllroy submitted to the court a letter and supplemental caselaw dealing with modification of arbitration awards. PaineWebber moved to strike the documents on the basis that Mcllroy had not complied with local filing rules. The court granted PaineWebber’s motion to strike and ruled on the merits that Mcllroy failed to meet any of the grounds for modification or vacation of an award specified in the Arbitration Act. Mcllroy filed this appeal.

II. Discussion

We review de novo the district court’s order denying Mcllroy’s motion to vacate or modify Forsythe Int’l, S.A. v. Gibbs Oil Co., 915 F.2d 1017, 1020 (5th *820 Cir. 1990). Contrary to Petitioner’s suggestion, this de novo review does not leave us “free to correct the arbitration award” App.Br. at 10; rather, it is intended to reinforce the strong deference due an arbi-trative tribunal. Forsythe, supra at 1021 (“In the arbitration context, granting the deference ordinarily due the district court risks forgetting the prior and critical deference ■ due the findings of the arbitration panel.”). Mindful of the limitations on our review of the arbitration award itself, we consider each of Mcllroy’s arguments in turn.

A. Vacation

Title 9 U.S.C. § 10(a) provides that a district court may vacate an award:

(1) Where the award was procured by corruption, fraud or undue means.

(2) Where there was evident partiality or corruption in the arbitrators....

(3) Where the arbitrators were guilty of misconduct in refusing to postpone the hearing ... 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.

(4) Where the arbitrators exceeded their powers, or so imperfectly executed them that a mutual, final and definite award upon the subject matter was not made.

9 U.S.C. § 10(a).

In this circuit, section 10 of the Arbitration Act describes the only grounds upon which a reviewing court may vacate an arbitration award. R.M. Perez & Associates, Inc. v. Welch, 960 F.2d 534 (5th Cir. 1992); accord Robbins v. Day, 954 F.2d 679 (11th Cir. 1992). 2

Mcllroy urged the district court to vacate the arbitration award on grounds that the award “was the product of such gross mistake as to imply failure to exercise honest judgment.” D.Ct. Op. at 5. He offered no evidence of a “gross mistake” save the discrepancy between his claim and the panel’s award. Without deciding whether Mcllroy’s allegation was true, the district court found that he failed to meet any of the grounds for attacking an award listed in section 10 and denied the motion. We agree with the district court that Mcllroy’s allegations, standing alone, do not entitle him to vacation of the award under section 10 of the Arbitration Act.

B. Modification

Section 11 of the Arbitration Act governs judicial modification of arbitration awards and provides, in relevant part:

[The] court ... may make an order modifying or correcting [an] award upon the application of any party to the arbitration—

(a) Where there was an evident material miscalculation of figures or an evident material mistake in the description of any person, thing or property referred to in the award.

(b) Where the arbitrators have awarded upon a matter not submitted to them, unless it is a matter not affecting the merits of the decision upon the matter submitted.

(c) Where the award is imperfect in matter of form not affecting the merits of the controversy.

The order may modify and correct the award, so as to effect the intent thereof and promote justice between the parties.

9 U.S.C. §. 11.

Mcllroy argued below that the panel had committed an “evident material miscalcula *821 tion” under 11(a) because it was “impossible to calculate damages of only $40,875.00 arising out of the evidence presented at the hearing.” The district court declined to modify the award “absent a specific showing of miscalculation of figures.” D.Ct.Op. at 6.

In our recent decision in Valentine Sugars, Inc. v. Donau Corp., 981 F.2d 210 (5th Cir. 1993), we adopted from the Sixth Circuit the following definition of an “evident material miscalculation” under section 11:

“[W]here the record that was before the arbitrator demonstrates an unambiguous and undisputed mistake of fact and the record demonstrates strong reliance on that mistake by the arbitrator in making his award, it can fairly be said that the arbitrator ‘exceeded [his] powers....’” National Post Office v. United States Postal Service, 751 F.2d 834, 843 (6th Cir. 1985). We interpret the term “undisputed” to mean we should look to see whether there is any rational basis for disputing the truth of the fact, (citations omitted).

981 F.2d at 214.

On appeal, Mcllroy offers no support for his contention that the arbitration panel committed an “evident miscalculation” except to point again to the discrepancy between the award he requested and the one he received. Receipt of less than one requests in an arbitration proceeding does not, standing alone, constitute a miscalculation under section 11 of the Arbitration Act. See, e.g., Merrill, Lynch, Pierce, Fenner & Smith, Inc. v. Burke, 741 F.Supp. 191, 193 (N.D.Cal. 1990).

The arbitration panel did not explain the rationale behind its award but it was not required to do so. Antwine v. Prudential-Bache Securities, Inc., 899 F.2d 410, 412 (5th Cir. 1990). The panel did list Mcllroy’s allegations, which included breach of duty, failure to execute a sell order, violation of federal and state securities laws, and breach of contract. The panel also noted PaineWebber’s counterclaim for the balance owing on Mcllroy’s brokerage account. During two days of hearings, the panel heard PaineWebber’s contentions that Mcllroy’s calculation of damages was speculative and that Mcllroy had failed to mitigate his losses. Accordingly, the panel had several grounds upon which to base an award in Mcllroy’s favor and a wealth of data from which to calculate an appropriate award. , We find no miscalculation evident in this record. As the Eleventh Circuit has remarked: “When ... parties agree[ ] to arbitration, they agree[ ] to accept whatever reasonable uncertainties might arise from the process,” Raiford v. Merrill, Lynch, Pierce, Fenner & Smith, Inc., 903 F.2d 1410, 1413 (11th Cir. 1990). The size of an award is one such uncertainty, and a claimant’s dissatisfaction alone will not support judicial modification of that award. We affirm the district court’s denial of Mcllroy’s motion to vacate or modify the award.

C. Excluded Material

While Mcllroy’s motion was pending before the district court, he sent the judge, under a cover letter, a copy of new and arguably relevant caselaw. Local Rule 2.1(b) of the United States District Court for the Northern District of Texas concerns the form and filing of legal documents and provides that “all legal documents except discovery materials shall be filed directly with the Clerk’s office for the appropriate Division and shall not be sent directly to the Judge for filing.’’ Rule 2.1(b). “Legal document” is broadly defined in Rule 2.1(a) to include “every pleading, petition, application, motion, brief, notice, demand, offer, request, proposed order, and any other paper to be made a part of the record in any civil or criminal case.” Rule 2.1(a). PaineWebber moved to strike Mcllroy’s submission for failure to comply with Rule 2.1(b). Concerned that the submission included new legal argument, the district judge granted. PaineWebber’s motion. Mcllroy argues that the court erred in characterizing the submission as a legal document and in failing to accept and consider it.

We note, parenthetically, that the opinion at issue was subsequently reversed, such that prejudice to Mcllroy is doubtful at best. In any event, we are satisfied that *822 the district court acted well within its discretion in excluding the material.

For the foregoing reasons, we AFFIRM the judgment of the district court.