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We consider the design of an open P2P live-video streaming system. When designing a live video system that is both open and P2P, the system must include mechanisms that incentivize peers to contribute upload capacity. We advocate an incentive principle for live P2P streaming: a peerpsilas video quality is commensurate with its upload rate. We propose substream trading, a new P2P streaming design which not only enables differentiated video quality commensurate with a peerpsilas upload contribution but can also accommodate different video coding schemes, including single-layer coding, layered coding, and multiple description coding. Extensive trace-driven simulations show that substream trading has high efficiency, provides differentiated service, low start-up latency, synergies among peers with different Internet access rates, and protection against free-riders.