Abstract. Concept approximation is an inference service for Description Logics that provides “translations” of concept descriptions from one DL to a less expressive DL. In [4] a method for optimizing the computation of ALC-ALE-approximations of ALC-concept descriptions was introduced. The idea is to characterize a certain class of concept descriptions for which conjuncts can be approximated independently. In this paper we provide relaxed conditions for this class of ALC-concept descriptions, extend this notion to number restrictions and report on a first implementation of this method for ALCN -ALEN-approximation. 1 Motivation Approximation is a non-standard inference service in Description Logics (DLs) introduced in [3]. Approximating a concept description, defined in one DL, means to translate this concept description to another concept description, defined in a second, typically less expressive DL, such that both concepts are as closely related as possible with respect to subs...