Ontology-mediated query answering (OMQA) consists in asking database queries on knowledge bases (KBs); a KB is a set of facts called the KB's database, which is described by domain knowledge called the KB's ontology. A widely-investigated OMQA technique is FO-rewriting: every query asked on a KB is reformulated w.r.t. the KB's ontology, so that its answers are computed by the relational evaluation of the query reformulation on the KB's database. Crucially, because FO-rewriting compiles the domain knowledge relevant to queries into their reformulations, query reformulations may be complex and their optimization is the crux of efficiency. We devise a novel optimization framework for a large set of OMQA settings that enjoy FO-rewriting: conjunctive queries, i.e., the core select-project-join queries, asked on KBs expressed using datalog±, description logics, existential rules, OWL, or RDFS. We optimize the query reformulations produced by state-of-the-art FO-rewriting algorithms by computing rapidly, with the help of a KB's database summary, simpler (contained) queries with the same answers that can be evaluated faster by RDBMSs. We show on a well-established OMQA benchmark that time performance is significantly improved by our optimization framework in general, up to three orders of magnitude.