Unverifiable quality may affect the enforcement of procurement contracts even when the award procedure is able to select the most efficient firm in the market. In this paper, we show that a discriminatory competitive mechanism – which awards the contract on the basis of price and (firms') past performance – yields an efficient allocation of the contract and allows the buyer to implement her desired quality. Quality enforcement arises out of relational contracting whereby the buyer ‘handicaps' a contractor in future competitive tendering processes if it fails to provide the required quality. We study an infinitely repeated procurement model with two firms and one buyer imperfectly informed on the firms' cost, in which, in each period, the buyer runs a discriminatory auction. We restrict our analysis to the case of a buyer committed to her handicapping strategy, a case which captures some of the features of a public buyer. When players use either grim trigger or stick-and-carrot strategies, we find that the buyer can induce the delivery of optimal (unverifiable) quality with a variety of handicap levels and, when applicable, durations of the punishment period; for some values of the handicap and the length of the punishment period, both firms remain active in the market even when punished