The weighted CSP framework is a soft constraint framework with a wide range of applications. Most current state-of-the-art complete solvers can be described as a basic depth-first branch and bound search that maintain some form of arc consistency during the search. In this paper we introduce a new stronger form of arc consistency, that we call existential directional arc consistency and we provide an algorithm to enforce it. The efficiency of the algorithm is empirically demonstrated in a variety of domains.