Abstract We investigate the problem of conservative rewritability of a TBox T in a description logic (DL) L into a TBox T 0 in a weaker DL L0 . We focus on model-conservative rewritability (T 0 entails T and all models of T are expandable to models of T 0 ), subsumption-conservative rewritability (T 0 entails T and all subsumptions in the signature of T entailed by T 0 are entailed by T ), and standard DLs between ALC and ALCQI. We give model-theoretic characterizations of conservative rewritability via bisimulations, inverse p-morphisms and generated subinterpretations, and use them to obtain a few rewriting algorithms and complexity results for deciding rewritability.