Abstract When applied to numerical CSPs, the branch and prune algorithm (BPA) computes a sharp covering of the solution set. The BPA is therefore impractical when the solution set is large, typically when it has a dimension larger than four or fifive which is often met in underconstrained problems. The purpose of this paper is to present a new search tree exploration strategy for BPA that hybridizes depth- fifirst and breadth-fifirst searches. This search strategy allows the BPA discovering potential solutions in different areas of the search space in early stages of the exploration, hence allowing an anytime usage of the BPA. The merits of the proposed search strategy are experimentally evaluated