In a P2P VoD system, the rate at which peers receive video fluctuates due to peer churn. Although scalable video coding has the potential to adapt to long-term rate variations, existing scalable video schemes have not been tailored for P2P systems for which substreams emanate from churning peers. In this paper we propose a new multi-stream coding and transmission scheme, Redundancy-Free Multiple Description (RFMD) Coding and Transmission, that has been designed for P2P VoD systems. Unlike layered video, with RFMD all substreams have equal importance. Thus, video quality gracefully degrades as substreams are lost, independently of which particular substreams are lost. Furthermore, only the source bits are collectively transmitted by the supplying peers. Thus, all transmitted bits contribute to improve video quality. Finally, RFMD can be used to create any number of descriptions. We conduct an extensive simulation study, comparing single layer coding with high-rate erasure codes, layered coding, multiple description coding (MD-FEC) and RFMD. The simulations show that RFMD performs best in a variety of representative scenarios.