This paper proposes a heuristic algorithm for state minimization of incompletely specified finite state machines (FSMs). The strategy is similar to that in ESPRESSO, a wellknown heuristic algorithm for two-level logic minimization. It consists of generating an initial solution, the set of maximal compatibles, and attempting to apply a series of transformations to the solution. The main transformation is to reduce each compatible in the solution and delete unnecessary compatibles by iterative improvements. Other transformations, such as expansion and merging of compatibles, are also introduced for further reduction. When the number of compatibles is likely to be too large to handle explicitly, they are represented by a Binary Decision Diagram. Experimental results show that the proposed method finds better solutions in shorter CPU times for most of the examples than conventional methods.