FEINBERG, Circuit Judge:

Plaintiffs Stanley Hill, as Executive Director of District Council 37, American Federation of State, County and Municipal Employees, AFL-CIO, and George Psaltis, as President of its affiliated Local 1665 (together, the Union) appeal from an order of the United States District Court for the Southern District of New York, Shir a A. Scheind-lin, J., entered in September 1996. The order denied the Union’s motion to confirm an arbitrator’s award made pursuant to a collective bargaining agreement (the Agreement) between the Union and defendants Staten Island Zoological Society, Inc. and its president John D. Kearney (together, the Society). The district court’s order also granted the Society’s cross-motion to vacate the award. The arbitrator found that the Society had not proven an alleged pattern of theft by Psaltis and that there was not “just cause” for his discharge, but that the Society had proven an “irregular purchase” by Psal-tis justifying a 30-day suspension. The basis of the district court’s decision to vacate the award was that the arbitrator had no authority to substitute a different penalty for the one imposed by the Society. For the reasons stated below, we reverse.

I. Background

A. Facts

Psaltis was employed by the Society for 24 years as a maintenance worker, and served as President of the local union. In 1991, Society Director Gattullo warned Psaltis that he suspected Psaltis was billing the Society for gasoline for his personal use, and told him that any employee caught stealing would be discharged. In January 1995, Gattullo received a phone call from Kris Reiman, the owner of a hardware store with which the Society had an account. Reiman told Gattul-lo that Psaltis had charged three cans of “weld-crete” bonding compound to the Society’s account, but that Psaltis had actually taken only two cans of weld-crete and some items for his personal use (apparently worth about $23.) Also in January 1995, Psaltis’s *211ex-girlfriend Rose Edwards came to Gattullo with a drill and pictures of other property which she alleged had been stolen from the Society by Psaltis and stored in Psaltis’s basement. Shortly thereafter, Gattullo gave Psaltis a week to resign. Receiving no response, Gattullo discharged Psaltis.

The Union initiated a grievance under the Agreement. Gattullo refused to reinstate Psaltis, and the Union submitted the grievance to arbitration. Article 10 of the Agreement described the procedure for adjusting

[a] grievance or complaint of an employee involving the interpretation of or compliance with this Agreement, which shall include disciplinary action without just cause....

Article 11 provided for submitting an unresolved grievance to an arbitrator whose decision “shall be final and conclusively binding.” The Agreement also contained a “management’s rights clause” in Article 8, which provided, among other things, that

[t]he Union and the employees agree that the right to operate and manage the affairs of the Society, and the right to select and direct the working forces ... are vested exclusively in the Society. These rights include ... [the rights] to employ, assign, promote, discipline, discharge, lay off, transfer and retire the employees ----

(emphasis added). Finally, Article 11 provided that “[t]he arbitrator shall be bound by the specific terms of this Agreement and he shall not have authority to change or modify the express terms ... of this Agreement.”

B. Arbitration Proceeding

Arbitrator Barbara Zausner Tener held three hearings in the summer of 1995. On the first hearing day, after the attorneys for the parties had made opening statements, the arbitrator said:

Let’s make sure we have the issue framed. Number one is, is the grievance arbitrable and if so, was there just cause for the discharge?

The arbitrator issued her written award on December 12, 1995. At the outset, her opinion stated:

ISSUE

Is the grievance arbitrable?

Did the Employer have cause to dismiss

George Psaltis?

If not, what shall be the remedy?

The arbitrator found the grievance arbitra-ble, and neither party challenges that holding on appeal.

On the merits, the arbitrator found in a thorough opinion that the Society had failed to prove “the bulk of the charges” against Psaltis and ordered that Psaltis be reinstated with backpay, except for a 30-day period. As to the 1991 allegations of gasoline theft, the arbitrator found there had been no formal disciplinary action at the time and there was no proof now, and noted that the warning to Psaltis in 1991 was not evidence of later thefts. With regard to the 1995 charge by Psaltis’s former girlfriend Edwards, the arbitrator found that it could not be determined that Psaltis had stolen the drill or items in his basement. The arbitrator found that the testimony of Edwards was completely unreliable because of clear signs that Edwards “had an ax to grind” with Psaltis, e.g., Edwards’s daughter-in-law testified that she heard Edwards threaten to “get George” and that Edwards admitted having lied about Psaltis at the hearings. The arbitrator found that even as to those items from Psaltis’s basement that could be identified as Society property, credible witnesses had testified some items were given to Psaltis, and there was evidence that the Society allowed employees to borrow property but insufficient evidence that it enforced an alleged policy requiring advance permission for such loans. As to the 1995 weld-erete transaction, although the arbitrator found that Psaltis’s testimony had been “evasive and contradictory,” and raised “questions about his honesty,” she concluded that “proof of a pattern of theft is not established through [this] incident.” She ultimately held that “[i]n light of the ... prior warning [in 1991] about irregular purchases, it would be reasonable to impose a thirty calendar day suspension----”

C. District Court Proceeding

The Society refused to reinstate Psaltis, and the Union petitioned in state court to *212confirm the arbitrator’s award. The Society removed the case to the district court. The district judge held that the arbitrator had authority to decide only whether there was cause to discipline and, once that was shown, the form or degree of discipline was in the Society’s discretion, i.e., the arbitrator’s finding that Psaltis had handled the weld-crete transaction dishonestly “implicitly recognizes” that there was just cause for any discipline the employer chose to impose. The judge also held that the Agreement was silent as to the arbitrator's authority to modify a disciplinary penalty and that if the arbitrator had this authority “it is likely that this would be explicitly stated in the Agreement.” Finally, the judge said that there was a “discrepancy regarding exactly what the arbitrator believed her authority to be under the Agreement.” Accordingly, the district court refused to confirm the arbitrator’s award, and vacated it. This appeal followed.

II. Standard of Review

When an arbitrator is given the power under a collective bargaining agreement to adjudicate the propriety of employer disciplinary action, the award is accorded broad deference. The Supreme Court has stated in this context that an arbitrator’s award will not be disturbed as long ás it “draws its essence from the collective bargaining agreement” and is not merely the arbitrator’s “own brand of industrial justice.” United Paperworkers Int’l Union v. Misco, 484 U.S. 29, 36, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987) (internal quotation marks and citations omitted). In other words, “as long as the arbitrator is even arguably construing or applying the contract and acting within the scope of his authority, that a court is convinced he committed serious error does not suffice to overturn his decision.” Id. at 38, 108 S.Ct. 364. Our cases have consistently acknowledged the broad deference due to arbitrators’ awards in this context. See, e.g., First Nat’l Supermarkets, Inc. v. Retail, Wholesale & Chain Store Food Employees Union Local 338, 118 F.3d 892, 896 (2d Cir.1997) (hereinafter Edwards Foods); Saint Mary Home, Inc. v. Service Employees Int’l Union, Dist. 1199, 116 F.3d 41, 44 (2d Cir.1997); Local 153, Int’l Union of Elec., Radio & Mach. Workers v. Otis Elevator Co., 314 F.2d 25, 28 (2d Cir.1963).

III. Discussion

In this court, appellant Union argues that the district court exceeded its authority when it refused to confirm the arbitrator’s award modifying a disciplinary penalty of termination to a 30-day suspension pursuant to the provision of the Agreement providing for arbitral review of disciplinary action taken without just cause. The Union also, contends that, contrary to the district court’s decision, the arbitrator had the power to modify the penalty when-she found no just cause unless the Agreement expressly limited that power, which is not the case here. Finally, the Union argues that the district court’s reliance on a “discrepancy” in the framing of the issues between the hearing.transcript and the arbitrator’s opinion is misplaced, because any doubt as to the extent of the arbitrator’s authority should have been resolved in favor of coverage.

The Society argues principally that the arbitrator’s finding that Psaltis handled the weld-crete transaction dishonestly is an implicit finding of “just cause” for some form of discipline, and that once the arbitrator made that finding she had no power to impose a penalty different from that chosen by the Society. It also argues that even if the arbitrator would otherwise have had the authority to modify the discipline imposed, the arbitrator limited her authority by fi’aming the issues more narrowly at the outset of the hearings.

The Society rests its argument almost entirely on the arbitrator’s implicit finding that a portion of the evidence (concerning the third weld-crete can) was sufficient cause for some discipline even if it did not amount to just cause for discharge. But in the context of this appeal, we are not sure what the implications of the Society’s argument are meant to be. Perhaps the Society is arguing that now that the arbitrator has found Psaltis at fault in the weld-crete incident, the Society has (or had) the unreviewablé right to discharge him. But that is not so. Under the *213Agreement, the discharge would still have to be for just cause, and the arbitrator has already ruled that the weld-crete incident even in conjunction with the other evidence did not justify that penalty. A fortiori, that incident alone could not provide just cause for discharge. Whether we or the district court would have come to the same conclusion is not determinative, or even particularly significant. The parties gave the responsibility for deciding that issue to the arbitrator, not to us or to the district court. If the Society is arguing that the arbitrator did not have the power to fix any remedy after finding that the Society did not have just cause for the discharge, we reject that contention. The arbitrator clearly had the power to order reinstatement with full back pay for a wrongful discharge. It may be — although we doubt it — that the Society is saying that if no just cause existed, the arbitrator had to award back pay for the full period and could not deduct 30 days’ pay from the amount awarded. If so, the Society is complaining only of an “error” that benefits it. Vacating the entire award, at the Society’s instance, because of an “error” that only benefited it does not make any sense.

The district court’s decision accepting the Society’s arguments that the arbitrator had exceeded her authority was apparently based on two premises: (1) Article 8 of the Agreement effectively limited the arbitrator’s power to determining' only whether there was just cause to impose any discipline against the employee, not whether there was just cause for the particular disciplinary penalty imposed by the Society; and (2) if the Arbitrator had authority to modify a disciplinary penalty, “it is likely that this would be explicitly stated in the ' Agreement.” However, well-settled law on both propositions is to the contrary.

Article 8 does not limit the arbitrator’s power to determining whether there was just cause for some disciplinary action without considering the penalty. Article 8 contains a general statement that the Society has the right to manage its affairs, including the right to “discipline” and “discharge” its employees. This right is, however, subject to Articles 10 and 11, which call for arbitration of grievances concerning “disciplinary action without just cause.” The meaning of “just cause,” as frequently is the case, is not defined anywhere in the Agreement, but it is certainly reasonable to construe it to mean just cause for the particular “disciplinary action” taken by the Society. It is well-established that the district court was bound to defer to the arbitrator’s interpretation as long as she was “even arguably ... acting within the scope of [her] authority,” Misco, 484 U.S. at 38, 108 S.Ct. 364, as was surely the case here. The interpretation urged by the Society would allow any infraction, no matter how minor or what the other circumstances involved, to serve as “just cause” for any discipline, no matter how disproportionate. The potential for abuse in such an interpretation is obvious, so much so that an arbitrator could obviously conclude, in the absence of more explicit language, that it must be rejected.

The cases cited to us by the Society, primarily from other circuits, would not compel another result even if we were inclined to agree with them (about which we express no view). For example, in Delta Queen Steamboat Co. v. District 2 Marine Engineers Beneficial Ass’n, 889 F.2d 599 (5th Cir.1989) and E.I. DuPont de Nemours & Co. v. Local 900, Int’l Chem. Workers Union, 968 F.2d 456 (5th Cir.1992) (per curiam), the courts vacated the awards of arbitrators who found the employer had actually proven its charges against the employee but imposed a different penalty anyway. Here, however, the arbitrator found that the Society failed to prove the bulk of the charges against Psaltis and expressly found no cause for discharge.

As for the arbitrator’s power to substitute a lesser penalty after determining that the Society’s proposed penalty was not supported by just cause, the district court was incorrect in believing that such a power needs to be mentioned expressly in the Agreement. Our past cases have uniformly upheld the arbitrator’s determination in similar situations, and those decisions did not depend on any express grant to the arbitrator of the power to substitute a remedy. Both the Supreme Court and this court have said that a limitation on the arbitrator’s ability to substitute a *214lesser penalty where he or she has found that just cause did not exist must be stated expressly. In Misco, 484 U.S. at 41, 108 S.Ct. 364, the Supreme Court said:

Normally, an arbitrator is authorized to disagree with the sanction imposed for employee misconduct---- [The arbitrator] is to bring his [or her] informed judgment to bear in order to reach a fair solution of a problem. This is especially true when it comes to formulating remedies. The parties, of course, may limit the discretion of the arbitrator in this respect....

(emphasis in original; internal quotation marks and citations omitted). In Edwards Foods, 118 F.3d at 896, we said that “[i]f [the employer] wished to have an unquestionable right to discharge an employee for any specified conduct, it needed to negotiate for recognition of that right in the [collective bargaining agreement].” Likewise, in Otis Elevator Co., 314 F.2d at 28, we said:

If the employer wanted - the automatic right to discharge an employee for violation of certain company ■ rules ... it had the opportunity to seek such an explicit exclusion.... In the absence of such a clause, the decision of the arbitrator ... must be taken as conclusively establishing ... that the discharge of [the employee] was not for just cause and as foreclosing judicial review____

As for Article 8, it says nothing- whatsoever about remedies, and cannot be construed as a limitation on this routine power of the arbitrator. Thus, in Edwards Foods, we distinguished the Fifth Circuit decision in General Drivers, Warehousemen & Helpers Local Union 968 v. Sysco Food Servs., Inc., 838 F.2d 794 (5th Cir.1988), by pointing out that the arbitration clause there provided “[t]he only-question which may be the subject of a ‘grievance’ is whether or not the disciplined employee did or did not engage in the specific conduct .... ” Edwards Foods, 118 F.3d at 897 (quoting Sysco Foods, 838 F.2d at 796; change in original; internal quotation marks omitted).

Finally, the Society attempts to make much of the “discrepancy” noted by the district court, that is, the arbitrator’s failure to include the sentence “If not, what shall the remedy be?” in her preliminary oral statement on the first day of the arbitration hearing. Such language is often employed, but it is not a ritual formula upon which the arbitrator’s power depends. The extent of the arbitrator’s power is determined primarily by the collective bargaining agreement, and there is a presumption of arbitrability which may only be overcome if “it may be said with positive assurance that the arbitration clause is not susceptible of an interpretation that covers the asserted dispute.” Associated Brick Mason Contractors of Greater New York, Inc. v. Harrington, 820 F.2d 31, 35 (2d Cir.1987) (quoting AT & T Technologies, Inc. v. Communications Workers of America, 475 U.S. 643, 650, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986)). Parties to an arbitration may stipulate the issues they want determined and increase or limit, the arbitrator’s contractual authority by their express submission. Ottley v. Schwartzberg, 819 F.2d 373, 376 (2d Cir.1987) (arbitrator’s authority “determined by the agreement or submission.”) (internal quotation.marks and citations omitted). But that is not what occurred here. The arbitration clause in the Agreement is broad, and the parties neither disputed the arbitrator’s power to fashion a remedy at the hearing nor stipulated that the arbitrator had no such authority. The Society never contested the arbitrator’s authority in this regard even though in this context it was easily foreseeable that the arbitrator might, as is commonplace, determine a substitute penalty. Indeed, as the Union points out, the Society in its post-hearing brief gave the arbitrator reasons why the discharge imposed should not be modified, which indicates that the Society was well aware that the arbitrator might impose a substitute penalty if it found no just cause for discharge.

For the foregoing reasons, the order of the district court is reversed, and we remand with instructions to confirm the arbitrator’s award.