Coherent x-ray scatter (also know as x-ray diffraction) has long been used to non-destructively investigate the molecular structure of materials for industrial, medical, security, and fundamental purposes. Unfortunately, molecular tomography based on coherent scatter typically requires long scan times and/or large incident fluxes, which has limited the practical applicability of such schemes. One can overcome the conventional challenges by employing compressive sensing theory to optimize the information obtained per incident photon. We accomplish this in two primary ways: we use a coded aperture to structure the incident illumination and realize massive measurement parallelization and use photon-counting, energy-sensitive detection to recover maximal information from each detected photon. We motivate and discuss here the general imaging principles, investigate different coding and sampling strategies, and provide results from theoretical studies for our structured illumination scheme. We find that this approach promises real-time molecular tomography of bulk objects without a loss in imaging performance. © 2014 SPIE-IS&T.