Diffuse reflectance (DRIFT) spectra in the mid-IR region, especially of inorganic powders, often reveal inverted or derivative-like structures ("reststrahlen" bands) which make their straightforward interpretation in terms of the Kubelka-Munk theory difficult. A simulation technique based on a combination of single scattering (Mie theory) and radiative transfer (with Kubelka-Munk as a special case) is reported that allows measured DRIFT spectra to be described without use of any free "fit" parameters. The results for silica glass microspheres and silicon carbide powder show that not specular reflectance but prominent structures in the single particle scattering cross-section are responsible for the reststrahlen features which cannot be suppressed even by diluting the powder in an excess of KBr. The efficiency of a "blocker" device in DRIFTS is also discussed.