We study a quantity discount problem under stochastic demand. For a single period problem, we derive the optimal policy for a buyer, which is a three-index   policy. In an experimental analysis, we investigate the structure of the optimal policy for the infinite horizon problem, and show that higher index policies with complex order structures may turn out to be optimal. We characterize the conditions under which such order structures are observed. We study the performance of the best three-index policy. We analytically show how a supplier can create discounts where two- or three-index policies are optimal for the buyer. We suggest discount schemes that a supplier may use to moderate the buyer's ordering policy to achieve specific objectives of operational efficiency.