Competitive bidding is often advocated as an effective procedure to select the most effi- cient firm in procurement markets. However, when procurement contracts mostly comprise unverifiable quality dimensions efficiency at the award stage does not ensure quality provision at the execution stage. In this paper, we show that an appropriately modified competitive mechanism – which awards the contract on the basis of price and (firms’) past performance – allows the buyer to yield an efficient allocation of the contract and to implement the desired level of quality. Quality enforcement arises out of a “relational” contract whereby the buyer threatens to “handicap” any contractor in future competitive tendering processes if it failed to provide high quality. We study an infinitely repeated procurement model with two firms and one buyer imperfectly informed on the firms’ cost. In each period, the procurement contract is awarded through a discriminatory competitive tender, where discrimination is based on the firms’ past performance. We analyse both the case of a committed and uncommitted buyer, which may capture some of the features of a public or private buyer. A committed buyer may induce the delivery of unverifiable quality provided that she sets a sufficiently large handicap; only very large values of the handicap imply also the debarment the cheating firm from the procurement market. An uncommitted buyer, instead, need not debar a cheating firm to en- force quality. Depending also on the nature of the tiebreaking rule, she may not be able to enforce the provision of quality when the latter is too high.