The skeleton is an efficient and complete shape descriptor often used for matching. However, existing skeleton-based shape matching methods are computationally intensive. To reduce the algorithmic complexity, we propose to exploit the natural hierarchy of the skeleton. The aim is to quantify the importance of skeleton branches to guide the shape matching algorithm, in order to match branches having the same order of importance. Our method is based on successive shape smoothing operations and on the deformability of the skeleton to adapt it to each smoothed shape. Moreover, we show that our method is independent from the initial skeleton.