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Layered streaming in P2P networks has become a hot topic recently. However, the "layered" feature makes the data scheduling quite different from that for nonlayered streaming, and it hasn't been systematically studied yet. In this paper, first, according to the unique characteristics caused by layered coding, we present four objectives that should be addressed by scheduling: throughput, layer delivery ratio, useless packets ratio, and subscription jitter prevention; then a three-stage scheduling approach LayerP2P is designed to request data, where the min-cost flow model, probability decision mechanism, and multiwindow remedy mechanism are used in Free Stage, Decision Stage, and Remedy Stage, respectively, to collaboratively achieve the above objectives. With the basic version of LayerP2P and corresponding experiment results achieved in our previous work, in this paper, more efforts are put on its mechanism details and analysis to its unique features; besides, to further guarantee the performance under sharp bandwidth variation, we propose the enhanced approach by improving the Decision Stage strategy. Extensive experiments by simulation and real network implementation indicate that it outperforms other schemes. LayerP2P has also been deployed in PDEPS Project in China, which is expected to be the first practical layered streaming system for education in P2P networks.