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Peer-to-peer live streaming systems involve complex engineering and are difficult to test and to deploy. To cut through the complexity, we advocate such systems be designed by composing ingredients: a novel abstraction denoting the smallest interoperable units of code that each express a single design choice. We present a system, STREAMAID, that provides tools for designing protocols in terms of ingredients, systematically testing the impact of every design decision in a simulator, and deploying them in a wide-area testbed such as PlanetLab for evaluation. We show how to decompose popular P2P live streaming systems, such as CoolStreaming, BitTorrent Live and others, into ingredients and how STREAMAID can help optimize and adapt these protocols. By experimenting with the essential building blocks of which P2P live streaming protocols are comprised, we gain a unique vantage point of their relative quality, their bottlenecks and their potential for future improvement.