The use of ontologies in various application domains, such as Data Integration, the Semantic Web, or ontology-based data management, where ontologies provide the access to large amounts of data, is posing challenging requirements w.r.t. the trade-off between the expressive power of a Description Logic and the efficiency of reasoning. The logics of the DL-Lite family were specifically designed to meet such requirements and optimized w.r.t. the data complexity of answering complex types of queries. In this paper, we propose DL-Litebool, an extension of DL-Lite with full Booleans and number restrictions, and study the complexity of reasoning in DL-Litebool and its significant sub-logics. We obtain our results, together with useful insights into the properties of the studied logics, by a novel reduction to the one-variable fragment of firstorder logic. We study the computational complexity of satisfiability and subsumption, and the data complexity of answering positive existential que...