Some thinning algorithms for 3D objects, or generalizations of existing ones for 2D, have been proposed in recent years. The one given herein is surprisingly simple and very fast compared to most of them, and still it has theoretically favorable properties. Actually, it provides a connected surface skeleton that allows shapes to be reconstructed with bounded error. In addition, it is also very attractive because it allows discrete skeletons to be obtained directly from volumes in many representations without converting them to a voxel-based representation. Our algorithm is a generalization of the one presented in [2] for 2D objects. It is based on the application of directional erosions, while retaining those voxels that introduce disconnections.