The behavioral service composition problem arises when no available service can achieve a target behavior. The composition problem consists in building a special service, an orchestrator, which schedules the actions of the services to produce a behavior equivalent to the target one. In this paper, services are modeled as nondeterministic transition systems and the behavior of the composition realizes the behavior of the target. We propose an algorithm that avoids the full computation of the product of services, and instead constructs the orchestrator incrementally. Unlike most algorithms where the whole state space, which is exponential in the number of services, is visited, the proposed algorithm can find a solution by visiting only the pertinent portion of the state space. We also show that this on-the-fly behavior can be paired with a heuristic to speed up the synthesis.