Mathematical models for predicting the pressure drop and grade collection efficiency for a rotary-flow cyclone are presented. The models are based on simplifying assumptions about the nature of gas flow through the cyclone, as well as the mixing of particles in the gas stream. Despite these simplifications, the predictions of the models are close to experimental measurements of pressure drop and grade collection efficiency, made on an industrial rotary-flow cyclone which is used as a precleaner for an oil mist collection system. Using these models, optimisation curves were developed which predicted the dimensions (radius and pitch) of an optimised rotary-flow cyclone that would yield the minimum cut diameter d50 for a given pressure drop. Optimisations were performed for one flow rate. Scaling equations were developed so that the results of this study can be used to design rotary-flow cyclones handling other flows.