Scene registration of a pair of three-dimensional (3D) range images is a 6D optimization problem usually required in mobile robotics. This problem is different from object registration, since all scan directions and depths may contain relevant data, and because farther regions are sampled with lower densities. The paper proposes an efficient scene matching method based on the concept of coarse binary cubes. An integer objective function is defined as the number of coincident cubes between both scans. This is a metric of the degree of overlap that does not employ point distances. Its value is obtained without actually using any 3D grid data structure, with a computational complexity of order O(n), where n represents the number of laser points. This objective function is optimized with a globalized version of the downhill Simplex algorithm to avoid local minima. Experimental results are presented from indoor and outdoor environments with different degrees of structuring. The effect of cube size and the number of vertices on registration performance has been analyzed. Besides, experiments show that the proposed method achieves similar accuracy as iterative closest points (ICP) and normal distribution transform (NDT), while it improves both computation time and robustness against initial misalignments.