Ontology-based data access is a powerful form of extending database technology, where a classical extensional database (EDB) is enhanced by an ontology that generates new intensional knowledge which may contribute to answer a query. Recently, the Datalog+/- family of ontology languages was introduced; in Datalog+/-, rules are tuple-generating dependencies (TGDs), i.e., Datalog rules with the possibility of having existentially-quantified variables in the head. In this paper we introduce a novel Datalog+/- language, namely sticky sets of TGDs, which allows for a wide class of joins in the body, while enjoying at the same time a low query-answering complexity. We establish complexity results for answering conjunctive queries under sticky sets of TGDs, showing, in particular, that ontological conjunctive queries can be compiled into first-order and thus SQL queries over the given EDB instance. We also show some extensions of sticky sets of TGDs, and how functional dependencies and so-called negative constraints can be added to a sticky set of TGDs without increasing the complexity of query answering. Our language thus properly generalizes both classical database constraints and most widespread tractable description logics.