Solvent flattening is a powerful tool for improving crystallographic phases for macromolecular structures obtained at moderate resolution, but uncertainties in the optimal weighting of experimental phases and modified phases make it difficult to extract all the phase information possible. Solvent flattening is essentially an iterative method for maximizing a likelihood function which consists of (i) experimental phase information and (ii) information on the likelihood of various arrangements of electron density in a map, but the likelihood function is generally not explicitly defined. In this work, a procedure is described for reciprocal-space maximization of a likelihood function based on experimental phases and characteristics of the electron-density map. The procedure can readily be applied to phase improvement based on solvent flattening and can potentially incorporate information on a wide variety of other characteristics of the electron-density map.