Abstract: This paper studies the problem of an agent that needs to buy a fixed amount of units from multiple firms with private information regarding their costs of production. We characterize the optimal —cost minimizing— mechanism using the classical mechanism design approach and it turns out to be diffcult to implement in practice. Consequently, we present two alternatives of a sequential nature that are more easily implementable: the familiar sequential posted prices scheme and a novel “sequentially optimal” mechanism. We characterize these mechanisms and show through numerical analysis that the latter tends to closely approximate the expected cost of the optimal mechanism, while the former performs much worse. The results have natural applications to several issues faced by a government, for example, the problem of buying back (“expropriating”) pollution permits in order to meet an international environmental agreement.