Peer-to-peer (P2P) systems are quite attractive due to their ability to deliver large amounts of data at a reduced deployment cost. They offer an interesting paradigm for media streaming applications that can benefit from the inherent self organization and resource scalability made available by participating peers. However, most studies on P2P live video streaming deal mainly with the feasibility of such an approach with a focus on maximizing throughput and resiliency. Little has been done to investigate the impact of the characteristics of the streaming source and of the participating peers on the P2P system performance and more specifically, on the playback delays experienced by peers. Through the use of an integer linear programming model, this paper investigates several related trade offs we need to consider, to fully exploit the potential of a P2P streaming system.