We propose a powerful wavelet method to identify structural breaks in the mean of a process. If there is a structural change in the mean the sum of the squared scaling coefficients absorbs more variation leading to unequal weights for the variances of the wavelet and scaling coefficients. We use this feature of wavelets to design a statistical test for changes in the mean of an independently distributed process. We establish the limiting null distribution of our test and demonstrate that our test has good empirical size and substantive power relative to the existing alternatives especially for multiple breaks. (C) 2014 Elsevier Inc. All rights reserved.