Description Logics (DLs) are a family of knowledge representation formalisms used for terminological reasoning. They have a wide range of applications such as medical knowledge-bases, or the semantic web. Research on DLs has been focused on the development of sound and complete inference algorithms to decide satisfiability and subsumption for increasingly expressive DLs. Non-standard inferences are a group of relatively new inference services which provide reasoning support for the building, maintaining, and deployment of DL knowledge-bases. So far, non-standard inferences are not available for very expressive DLs. In this paper we present first results on non-standard inferences for DLs with transitive roles. As a basis, we give a structural characterization of subsumption for DLs where existential and value restrictions can be imposed on transitive roles. We propose sound and complete algorithms to compute the least common subsumer (lcs).