A density-modification procedure for improving maps from single-particle electron cryogenic microscopy (cryo-EM) is presented. The theoretical basis of the method is identical to that of maximum-likelihood density modification, previously used to improve maps from macromolecular X-ray crystallography. Key differences from applications in crystallography are that the errors in Fourier coefficients are largely in the phases in crystallography but in both phases and amplitudes in cryo-EM, and that half-maps with independent errors are available in cryo-EM. These differences lead to a distinct approach for combination of information from starting maps with information obtained in the density-modification process. The density-modification procedure was applied to a set of 104 datasets and improved map-model correlation and increased the visibility of details in many of the maps. The procedure requires two unmasked half-maps and a sequence file or other source of information on the volume of the macromolecule that has been imaged.