The method of the prior-derived F constraints (PDC) enhances the quality of reconstructions of electron densities from X-ray diffraction data by the maximum-entropy method (MEM). The method concentrates on artifacts arising due to inaccurate extrapolation of non-measured data by the MEM. While these artifacts are unavoidable, when a flat prior is used, they can be effectively suppressed, if the prior information about the structure is known in the form of a procrystal prior electron density. The missing, usually high-angle, structure factors can be effectively substituted by the structure factors derived from the procrystal prior. This approach eliminates the occurrence of spurious peaks in the difference electron densities in the vicinity of the atomic positions. The method is illustrated with a simple one-dimensional example. Its use is then demonstrated on simulated data of oxalic acid dihydrate and on experimental data of sodium nitrite.