We discuss the computation of the suppression distance between two hierarchical clusterings of the same set. It is defined as the minimum number of elements that have to be removed so the remaining clusterings are equals. The problem of distance computing was studied by Gusfield (2002) for partitions. We prove it can be solved in polynomial time in the case of hierarchies as it gives birth to a class of perfect graphs. We also propose an algorithm based on recursive maximum assignments.