In this paper we address the principle of modularity of ontologies in description logics. It turns out that with existing accounts of modularity of ontologies we do not completely avoid unforeseen interactions between module components, and modules designed in those ways may be as complex as whole theories. We here give a more fine-grained paradigm for modularizing descriptions. We propose algorithms that check whether a given terminology is modular and that also help the designer making it modular, if needed. Completeness, correctness and termination results are demonstrated for a fragment of ALC. We also present the properties that ontologies that are modular in our sense satisfy w.r.t. reasoning services.