Charge density can be accessed through accurate X-ray diffraction by crystals. It has recently become a rather routine technique. Refinement models enable a fair description of charge density changes due to chemical bonding and cohesive forces. Conversely, momentum density is observable through incoherent Compton scattering, in particular by use of high-intensity synchrotron sources. We present results concerning a first attempt at a simultaneous refinement of a model wavefunction on both diffraction and Compton data, for MgO and LiH crystals. It is shown that if the diffraction data are highly sensitive to local effects and their symmetry around atomic sites, Compton data are very dependent on the delocalization processes of electrons. Moreover, Compton measurements show a systematic deviation from self-consistent-field model calculations and this is analyzed in terms of an empirical correlation model for unions in insulators. Possible future extensions of such studies are finally discussed.