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Video on demand systems are going to be important services of the future Internet. To achieve scalability and fault tolerance, these systems should rely on distributed video delivery schemes, using peer-to-peer (P2P) networks built among the clients. However, generic P2P data sharing protocols cannot guarantee timely arrival of the video segments. Therefore, they must be adapted to video streaming by restricting P2P delivery into a download window. In this paper we investigate the effect of the frequently occurring phenomenon of incomplete sessions on the efficiency of stored video streaming via P2P data distribution. Through theoretical considerations and a simulation study, we've found that with a P2P download window placed at a fixed distance from the playback position the superfluous downloads can be avoided, and the efficiency of the P2P distribution can be increased.