Backtrack search is a classical complete approach for exploring the search space of a constraint optimization problem. % when optimality is sought to be proved. Each time a new solution is found during search, its associated bound is used to constrain more the problem, and so the remaining search. An extreme (bad) scenario is when solutions are found in sequence with very small differences between successive bounds. In this paper, we propose an aggressive bound descent (ABD) approach to remedy this problem: new bounds are modified exponentially as long as the searching algorithm is successful. We show that this approach can render the solver more robust, especially at the beginning of search. Our experiments confirm this behavior for constraint optimization.