We propose an improved algorithm for computing support sets for icompletely specified boolean functions. The problem to compute a compatible function with minimal support set, with respect to various criteria, arises in many applications, for example FPGA synthesis. By incorporating new lookup techniques together with lazy evaluation, we are able to prune the search space for possible mappings of the don't care set. We also suggest a new approach to the problem of support set minimization. The new algorithm computes the least specified compatible functions for all possible support sets up to 20 times faster than previous algorithms.