Computing a skeleton for a discretized boundary typically produces a noisy output, with a skeletal branch produced for each boundary pixel. A simplification step often follows to reduce these noisy branches. As a result, generating a clean skeleton is usually a 2-step process. In this article, we propose a skeletonization process that produces a clean skeleton in the first step, avoiding the creation of branches due to noise. The resulting skeleton compares favorably with the most common pruning methods on a large database of shapes. Our process also reduces execution time and requires only one parameter, ε, that designates the desired boundary precision in the Hausdorff distance.