One solution to limit the contractor’s default risk in first-price procurement auctions is to audit the winning firm in order to assess the reliability of its bid, and, in case of an unsatisfactory response, move to the firm that ranked second, and so on. Focussing on a situation in which firms with cheaper technologies have a higher risk of default ex-post, we provide conditions that ensure that a first-price auction with audit is indeed optimal. These conditions are likely to be satisfied when the relation between firms’ cost and default risk is not too steep and when the cost of performing the audit is not too large. We also characterize the optimal threshold that determines which firms are to be audited and which are not. We finally discuss cases in which, instead, a first-price auction with audit is dominated by a mechanism in which the allocation (and the audit) is done randomly, at least at some point of the awarding process.