Studying the computation of orbits of some given group acting on a set, we show how successive refinements of a simple program provide a speedup factor of up to 200. The initial program cannot solve the problem at all, it is first converted into a program which needs one c.p.u. week and after all the optimizations have been performed, the computation takes only four hours. Although the problem is pecific, we shall show that many of the optimizations we use are of interest for other problems as well.