Abstract A theory of programmed cooling crystallization is presented based on the moment transformation of the population balance. Numerical predictions for the behaviour of a batch crystallizer agree closely with those from an alternative theory based on the discrete-supersaturation balance. A potential advantage of the present approach is shown to lie in the application of the Continuous Maximum Principle in optimal control theory to facilitate the numerical computation of optimal cooling curves. The transient behavior of a computed “size-optimal” operating policy which maximises the terminal size of the largest crystals is shown to be significantly different from either natural of linear cooling or from crontrolled cooling at a constant nucleation rate. A peak in the nucleation rate towards the end of the operation and an increased terminal crystal size is predicted for the conditions considered and this is supported by preliminary experimental work with potassium sulphate solutions in a laboratory-scale crystallizer.