Skeletonization using the Constrained Delaunay Triangulation technique has proven very effective, with respect to efficiency, accuracy and robustness against noise. This paper presents three algorithms that further improve this successful skeletonization method. Each of the three algorithms presented here deals with the refinement of the three types of triangles produced by triangulation, namely end triangles, normal triangles and junction triangles. Results show that these algorithms produce a skeleton that complies much better to a human?s perception of the underlying image, without detracting from the superior efficiency inherent in the original triangulation method.