Most of the literature on peer-to-peer (P2P) live streaming focuses on how to provide best-effort streaming quality by efficiently using the system bandwidth; however, there is no guarantee about the provided streaming quality. This paper considers how to provide statistically guaranteed streaming quality to a P2P live streaming system. We study a class of admission control algorithms which statistically guaran-tee that a P2P live streaming system has sufficient overall bandwidth. Our results show that there is a tradeoff be-tween the user blocking rate and user-behavior insensitivity (i.e., whether the system performance is insensitive to the fine statistics of user behaviors). We also find that the sys-tem performance is more sensitive to the distribution change of user inter-arrival times than to that of user lifetimes.