Charge density can be accessed through accurate X-ray diffraction by crysta
ls. It has recently become a rather routine technique. Refinement models en
able a fair description of charge density changes due to chemical bonding a
nd cohesive forces. Conversely, momentum density is observable through inco
herent Compton scattering, in particular by use of high-intensity synchrotr
on sources. We present results concerning a first attempt at a simultaneous
refinement of a model wavefunction on both diffraction and Compton data, f
or MgO and LiH crystals. It is shown that if the diffraction data are highl
y sensitive to local effects and their symmetry around atomic sites. Compto
n data are very dependent on the delocalization processes of electrons. Mor
eover. Compton measurements show a systematic deviation from self-consisten
t-held model calculations and this is analyzed in terms of an empirical cor
relation model for anions in insulators. Possible future extensions of such
studies are finally discussed.