In a peer-to-peer (P2P) live streaming system, peer requests collide when multiple peers request data pieces from the same peer (or media server). When collisions occur, some of the peers' requests fail and retries have to be taken, which delays peer's receipts of pieces. This paper shows that request collisions occur frequently at both media servers and peers, and have big impact on system performance. It then proposes two algorithms to address this issue. The first is a novel admission control algorithm at the media server. The second is a peer selection algorithm in which peer requests pieces from neighbors with low collision probability. Simulation results show that the proposed algorithms improve system performance significantly.1