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This paper considers the problem of adapting the BitTorrent protocol for on-demand streaming. BitTorrent is a popular peer-to-peer file sharing protocol that efficiently accommodates a large number of requests for file downloads. Two components of the protocol, namely the rarest-first piece selection policy and the tit-for-tat algorithm for peer selection, are acknowledged to contribute toward the protocol's efficiency with respect to time to download files and its resilience to free riders. Rarest-first piece selection, however, is not suitable for on-demand streaming. In this paper, we present a new adaptive window-based piece selection policy that balances the need for piece diversity, which is provided by the rarest-first algorithm, with the necessity of in-order piece retrieval. We also show that this simple modification to the piece selection policy allows the system to be efficient with respect to utilization of available upload capacity of participating peers, and does not break the tit-for-tat incentive scheme which provides resilience to free riders.