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When there is more than one application server in the signaling path between IP media endpoints, and the servers manipulate media flow, media flow must be controlled com-positionally. This paper presents a protocol, signaling architecture, API, and API implementation for distributed, compositional media control. The semantics of the API is specified in linear temporal logic, and the implementation has been partially verified by model checking. The principles developed to solve this problem may be useful for making other network applications compositional.