Distributed Description Logics (DDLs) is a KR formalism that enables reasoning with multiple ontologies interconnected by directional semantic mapping (bridge rules). DDLs capture the idea of importing and reusing concepts between ontologies and thus combine well with intuitions behind Semantic Web. We modify the original semantics of DDLs in order to cope with a modeling discrepancy that has been pointed out in the literature. We do so by introducing a new kind of bridge rules, which we call conjunctive. Using conjunctive bridge-rules instead of the normal ones solves the problem. All the basic properties that have been established for DDLs hold also for the adjusted framework. We also provide a transformational semantics for conjunctive bridge rules, and thus, at least theoretically, a decision procedure for the new semantics.