High-throughput crystallisation and characterisation platforms provide an efficient means to carry out solid-form screening during the pre-formulation phase. To determine the crystal structures of identified new solid phases, however, usually requires independent crystallisation trials to produce single crystals or bulk samples of sufficient quantity to carry out high-quality X-ray diffraction measurements. This process could be made more efficient by a robust procedure for crystal structure determination directly from high-throughput X-ray powder diffraction (XRPD) data. Quantum-chemical calculations based on dispersion-corrected density functional theory (DFT-D) have now become feasible for typical small organic molecules used as active pharmaceutical ingredients. We demonstrate how these calculations can be applied to complement high-throughput XRPD data by determining the crystal structure of piroxicam form III. These combined experimental/quantum-chemical methods can provide access to reliable structural information in the course of an intensive experimentally based solid-form screening activity or in other circumstances wherein single crystals might never be viable, for example, for polymorphs obtained only during high-energy processing such as spray drying or milling.