Laffont and Tirole's [Laffont, J., Tirole, J., 1986. Using cost observation to regulate firms. Journal of Political Economy 94, 614–641.] classic model of procurement under asymmetric information predicts that optimal contracts will always entail some cost sharing and that payments will be a convex function of realized cost. In contrast, pure cost-reimbursement contracts are common in practice, as are contracts in which payments are a concave function of realized cost. We consider a straightforward extension of Laffont and Tirole's model that admits optimal contracts of the forms that prevail in practice. The extension simply allows the supplier to be able to reduce production costs more easily when costs are initially high than when they are initially low.