Seed crystals of potassium alum were grown in batches with no secondary nucleation by a multi-stage natural cooling technique, where the temperature of the solution saturated at 40degreesC was lowered in steps from over the saturation temperature to 20degreesC. Seed crystals of 42 mum, which were introduced just at the saturation temperature of 40degreesC, were grown successfully to final sizes of 318, 563, 732, and 1070 pm, with 1-, 3-, 5-, 6-, 7-, and 9-stage coolings. The number of cooling stages and the required temperature decrease in each stage were determined a priori, using a mass balance equation, an experimental correlation of the critical seed loading ratio (over which seed loading it is guaranteed there will be no secondary nucleation) versus seed size, and solubility data. This multi-stage cooling method is a promising technique to grow seed crystals to a desired size in batch cooling crystallization.