A new algorithm (CS-MC) for computing the minimal cuts of s-coherent fault trees is presented. Input events of the fault tree are assumed classified into classes, where events of the same class are indistinguishable. This allows capturing some symmetries which some systems exhibit. CS-MC uses a decision tree. The search implemented by the decision tree is guided by heuristics which try to make CS-MC as efficient as possible. In addition, an irrelevance test on the inputs of the fault tree is used to prune the search. The performance of CS-MC is illustrated and compared with the basic top-down and bottom-up algorithms using a set of fault trees, some of which are very difficult. The CS-MC performs very well even in the difficult examples, and the memory requirements of CS-MC are small.