Several database areas such as data exchange and integration share the problem of fixing database instance violations with respect to a set of constraints. The chase algorithm solves such violations by inserting tuples and setting the value of nulls. Unfortunately, the chase algorithm may not terminate and the problem of deciding whether the chase process terminates is undecidable. Recently there has been an increasing interest in the identification of sufficient structural properties of constraints which guarantee that the chase algorithm terminates. In this paper we propose an original technique which allows to improve current conditions detecting chase termination. Our proposal consists in rewriting the original set of constraints Σ into an ‘equivalent’ set Σα and verifying the structural properties for chase termination on Σα. The rewriting of constraints allows to recognize larger classes of constraints for which chase termination is guaranteed. In particular, we show that if Σ satisfies chase termination conditions T , then the rewritten set Σα satisfies T as well, but the vice versa is not true, that is there are significant classes of constraints for which Σα satisfies T and Σ does not.