We present a method to simplify the structure of the surface skeleton of a 3D object, such that loss of information can be kept under control. Our approach is to prune surface border jaggedness by removing peripheral curves. The surface border is detected and all curves belonging to it are identified. Then, distance information is used to distinguish the short curves, whose voxels are possibly deleted, provided that the topology is not changed. Our method is simple, fast, and can be applied also to two-voxel thick surface skeletons. It prunes only curves which correspond to minor features of the object, without shortening the remaining more significant curves. The structure of the surface skeleton becomes significantly simplified. The simplified set can be used directly for shape representation, or as input to curve skeleton computation. If we extract the curve skeleton from the simplified set, its structure is more manageable than if the curve skeleton is obtained from the non-simplified set.