This invention pertains to methods for achieving the commercial sterilization of foods having a pH greater than or equal to 4.5 involving concomitant treatment of the food to two or more cycles of high heat, high pressure, with a brief pause between cycles. The pressurization schedule relies on-the additional instantaneous, uniform heat from adiabatic pressurization and then instantaneous, uniform adiabatic cooling during depressurization for each cycle.