We address the issue of Ontology-Based Data Access, with ontologies repre-sented in the framework of existential rules, also known as Datalog±. A well-known approach involves rewriting the query using ontological knowledge. We focus here on the basic rewriting technique which consists of rewriting the initial query into a union of conjunctive queries. First, we study a generic breadth-first rewriting algorithm, which takes any rewriting operator as a parameter, and de-fine properties of rewriting operators that ensure the correctness of the algorithm. Then, we focus on piece-unifiers, which provide a rewriting operator with the de-sired properties. Finally, we propose an implementation of this framework and report some experiments.