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Peer-to-peer (P2P) file distribution is a scalable way to disseminate content to a wide audience. This paper presents an algorithm by which download times are sequentially minimized; that is, the first peer's download time is minimized, and subsequent peers' times are minimized conditional on their predecessors' times being minimized. This objective gives robustness to the file distribution in the case that the network may be partitioned. It is also an important step towards the natural objective of minimizing the average download time, which is made challenging by the combinatorial structure of the problem. This optimality result not only provides fundamental insight to scheduling in such P2P systems, but also can serve as a benchmark to evaluate practical algorithms and illustrate the scalability of P2P networks.