A new method for determining skeletons of 3D shapes is described. It is a combination of the approach based on the “grass-fire” technique and Zhu's approach based on first finding portions of the shape where its width is approximately constant. The method specifically does not require presmoothing of the shape and is robust in the presence of noise. In an appendix, a method based on variational calculus is formulated for determining pruned, smoothed shape skeletons by minimizing a functional.