To provide live streaming services based on peerto- peer overlays is popular now. Previous researches put their emphasis on how to improve overlays efficiency with single overlay optimizations. These optimizations have drawbacks such as low resources utilization, high startup delay and source-to-end delay, and unreasonable resources assignment in global P2P network. To solve these problems, we propose an Intersecting-overlays optimizations scheme in this paper. This new idea has the following characteristics: 1) basically it can improve resources utilization of global P2P network; 2) resources can be assigned reasonably with the consideration of locality and delay; 3) streaming services qualities, such as delay and playback continuity, can be improved greatly. To prove the idea, we carry out several simulations and compare with traditional system. Results from simulations are quite encouraging, high resources utilization and good QoS of streaming services.