Several algorithms [Cas92, MS89, Run92, DDHL94a, DDHL95, GMM95] have been proposed to automatically insert a class into an inheritance hierarchy. But actual hierarchies all include overriden and overloaded properties that these algorithms handle either very partially or not at all. Partially handled means handled provided there is a separate given function f able to compare overloaded properties [DDHL95, GMM95].In this paper, we describe a new version of our algorithm (named Ares) which handles automatic class insertion more efficiently using such a function f. Although impossible to fully define, this function can be computed for a number of well defined cases of overloading and overriding. We give a classification of such cases and describe the computation process for a well-defined set of nontrivial cases.The algorithm preserves these important properties:- preservation of the maximal factorization of properties- preservation of the underlying structure (Galois lattice) of the input hierarchy- conservation of relevant classes of the input hierarchy with their properties.