Providing efficient black-box search procedures is one of the major concerns for constraint-programming solvers. Most of the contributions in that area follow the fail-first principle, which is very useful to close the search tree or to solve SAT/UNSAT problems. However, for real-life applications with an optimization criterion, proving optimality is often unrealistic. Instead, it is very important to compute a good solution fast. This paper introduces a value selector heuristic focusing on objective bounds to make the first solution good. Experiments show that it improves former approaches on a wide range of problems.