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Due to their widespread popularity, peer-to-peer (P2P) live streaming systems have become a great challenge for Internet service providers (ISPs) as they consume huge amount of Internet bandwidth. By observing that different users may watch a channel with different window sizes, we propose a cooperative scheme called partial participation scheme (PPS) in which different peers request a video stream at different rates based on their window sizes, and a subset of peers viewing the video stream using a small window work as helpers to forward extra data to help other peers using a large window. By reducing streaming rate received by small-window peers, the total amount of consumed bandwidth decreases without sacrificing users' satisfaction. PPS includes peer cooperative bandwidth allocation algorithms and neighbor maintenance mechanisms to achieve short resizing delay when a peer changes its window between different sizes. We evaluate the performance of PPS via a comprehensive set of metrics generated from extensive simulations. Our simulation results show that PPS greatly reduces the bandwidth consumption, achieves short resizing delay, and maintains high and stable streaming quality.