Abstract The Web Service Composition (WSC) problem with respect to behavioral descriptions deals with the automatic synthesis of a coordinator web service, c, that controls a set of web services to reach a goal state. Despite its importance, however, solving the WSC problem for a general case (when c has only partial observations) remains to be doubly exponential in the number of variables in web service descriptions, rendering any attempts to compute an exact solution for modest size impractical. Toward this challenge, in this paper, we propose two novel (signature preserving and subsuming) approximation-based approaches using abstraction and refifinement. We empirically validate that our proposals can solve realistic problems effificiently