A method to extend low-resolution phases has been developed using histogram matching not only of the electron density itself but also of histograms obtained from the different levels of detail provided by the wavelet transform of the electron density. It is shown that the method can extend phases from 10 A to around 6-7 A on a wide range of trial structures differing in size, space group and solvent content. This level of phase extension can improve the electron-density map from little more than a molecular envelope to one in which secondary structure can often be identified.