A rule for determining the winner in a sealed ceiling bid in which a contract for providing services is offered to a set of qualified bidders is proposed. This rule is, in fact, an economic mechanism encouraging the bidders to submit their bids for the contract that are close to a (calculated) price desired by the auctioneer while discouraging the bidders to submit both damping prices and too high prices. Under the proposed rule, for each participating bidder, the probability of winning the contract at a particular price desirable by the auctioneer turns out to be higher than that under the traditional rule – when the contract is awarded to a bidder offering the lowest price for providing services stipulated in the contract. At the same time, the probability of winning the contract by each bidder at a price exceeding this particular price (desirable by the auctioneer) turns out to be lower than that of winning the contract at the desirable price, which makes the proposed rule mutually beneficial for both the auctioneer and the bidders.