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The peer-to-peer (P2P) file-sharing applications are becoming increasingly popular and account for more than 70% of the Internet's bandwidth usage. Measurement studies show that a typical download of a file can take from minutes up to several hours depending on the level of network congestion or the service capacity fluctuation. In this paper, we consider two major factors that have significant impact on average download time, namely, the spatial heterogeneity of service capacities in different source peers and the temporal fluctuation in service capacity of a single source peer. We point out that the common approach of analyzing the average download time based on average service capacity is fundamentally flawed. We rigorously prove that both spatial heterogeneity and temporal correlations in service capacity increase the average download time in P2P networks and then analyze a simple, distributed algorithm to effectively remove these negative factors, thus minimizing the average download time. We show through analysis and simulations that it outperforms most of other algorithms currently used in practice under various network configurations.