We describe a new method for recovering the blur kernel in motion-blurred images based on statistical irregularities their power spectrum exhibits. This is achieved by a power-law that refines the one traditionally used for describing natural images. The new model better accounts for biases arising from the presence of large and strong edges in the image. We use this model together with an accurate spectral whitening formula to estimate the power spectrum of the blur. The blur kernel is then recovered using a phase retrieval algorithm with improved convergence and disambiguation capabilities. Unlike many existing methods, the new approach does not perform a maximum a posteriori estimation, which involves repeated reconstructions of the latent image, and hence offers attractive running times. We compare the new method with state-of-the-art methods and report various advantages, both in terms of efficiency and accuracy.