Constrained frequent patterns and closed frequent patterns are two paradigms aimed at reducing the set of extracted patterns to a smaller, more interesting, subset. Although a lot of work has been done with both these paradigms, there is still confusion around the mining problem obtained by joining closed and constrained frequent patterns in a unique framework. In this paper we shed light on this problem by providing a formal definition and a thorough characterization. Wealso study computational issues and show how to combine the most recent results in both paradigms, providing a very efficient algorithm which exploits the two requirements (satisfying constraints and being closed) together at mining time in order to reduce the computation as much as possible.