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The volume of multimedia data, including video, served through peer-to-peer (P2P) networks is growing rapidly. Unfortunately, high bandwidth transfer rates are rarely available to P2P clients on a consistent basis, making it difficult to use P2P networks to stream video for on-line viewing. In this paper, we develop and evaluate on-line algorithms that coordinate the pre-fetching of scalably-coded variable bitrate video. These algorithms are ideal for P2P environments in that they require no knowledge of the future variability or availability of bandwidth, yet produce a playback whose average rate and variability are comparable to the best off-line prefetching algorithms that have total future knowledge. To show this, we develop an off-line algorithm that provably optimizes quality and variability metrics. Using simulations based on actual P2P traces, we compare our on-line algorithms to the optimal off-line algorithm and find that our novel on-line algorithms exhibit near-optimal performance and significantly outperform more traditional pre-fetching methods.