Since the batteries in a wireless sensor networks cannot be replaced, efficient power management becomes an important research issue. If we can largely reduce the overlaps among detection ranges and decrease the amount of duplicate data then we can save energy more efficiently. In [6], Meguerdichian et al. exploit the coverage problems in wireless ad-hoc sensor networks in terms of Voronoi diagram and Delaunay triangulation. In this paper, we propose a Voronoi dEtection Range Adjustment (VERA) method that utilizes distributed Voronoi diagram to delimit the area of responsibility for each sensor. We then use Genetic Algorithm to optimize the most suitable detection range for each sensor. Simulations show that VERA outperforms Maximum Detection Range, K-covered [4], and Greedy [2] methods in terms of reducing the overlaps among detection ranges, minimizing energy consumption, and prolonging the lifetime of the whole network.