Wavelets play a similar role to Fourier series, in that they give an orthogonal basis for expanding quite general functions. Moreover, compactly supported wavelets are much more efficient in practice. Such wavelets must necessarily have only finite differentiability and Cohen and Dauberchies studied the problem of estimating their regularity. In joint work with Howard Weiss (Penn State University) we present a simple algorithm which leads to much more accurate numerical estimates.