Abstract Querying large databases while taking ontologies into account is currently a very active domain research. In this paper, we consider ontologies described by existential rules (also known as Datalog+/-), a framework that generalizes lightweight description logics. A common approach is to rewrite a conjunctive query w.r.t an ontology into a union of conjunctive queries (UCQ) which can be directly evaluated against a database. However, the practicability of this approach is questionable due to 1) the weak expressivity of classes for which efficient rewriters have been implemented 2) the large size of optimal rewritings using UCQ. We propose to use semi-conjunctive queries (SCQ), which are a restricted form of positive existential formulas, and compute sound and complete rewritings, which are union of SCQ (USCQ). A novel algorithm for query rewriting, C OMPACT, is presented. It computes sound and complete rewritings for large classes of ontologies. First experiments show that USCQ are both efficiently computable and more efficiently evaluable than their equivalent UCQ.