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Peer-to-peer streaming is a novel, low-cost, paradigm for large-scale video multicast. Viewers contribute their resources to an overlay network to act as relays for a real-time media stream. Early implementations fall short of the requirements of major content owners in terms of quality, reliability, and latency. In this work we show how adding a limited number of servers to a peer-to-peer streaming network can be used to enhance performance while preserving most of the benefits in terms of bandwidth cost savings. We present a theoretical model which is useful to estimate the number of servers needed to ensure fast connection times and improved error resilience. Experimental results show the proposed approach achieves 10times to 100times bandwidth cost savings compared to a content delivery network, and similar performance in terms of quality and startup latency.