The Ranque-Hilsch vortex tube splits a single high pressure stream of gas into cold and warm streams. Simple models for the vortex tube combined with regenerative precooling are given from which an optimization can be undertaken. Two such optimizations are needed: the first shows that at any given cut or fraction of the cold stream, the best refrigerative load, allowing for the temperature lift, is nearly half the maximum loading that would result in no lift. The second optimization shows that the optimum cut is an equal division of the vortex streams between hot and cold. Bounds are obtainable within this theory for the performance of the system for a given gas and pressure ratio. © 1999 Elsevier Science Ltd.