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 peer's 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 peer's upload contribution but can also accommodate different video coding schemes, including single-layer coding, layered coding, and multiple description coding. Extensive tracedriven simulations show that substream trading has high ef-ciency, provides differentiated service, low start-up latency, synergies among peers with different Internet access rates, and protection against free-riders.