A baggage scanning system and method employ combined angular and energy dispersive x-ray scanning to detect the presence of a contraband substance within an interrogation volume of a baggage item. The interrogation volume is illuminated with penetrating, polychromatic x-rays in a primary fan beam from a source such as a tungsten-anode x-ray tube. An energy-dependent absorption correction is determined from measurement of the attenuation of the fan beam at a plurality of different energies. Radiation coherently scattered by substances in the interrogation volume is detected by an energy-resolved x-ray detector operated at a plurality of scattering angles to form a plurality of scattering spectra. Each scattering spectrum is corrected for energy-dependent absorption and the corrected spectra are combined to produce a scattering pattern. The experimental scattering pattern is compared with reference patterns that uniquely characterize known contraband substances. The system and method can locate and identify a wide variety of contraband substances in an accurate, reliable manner. The system provides for automated screening, with the result that vagaries of human performance are virtually eliminated. False alarms and the need for hand inspection are reduced and detection efficacy is increased.