A simple, stable, time-optimal digital control program has been developed with general application to zero- or low-power nuclear reactors for power-level changes, especially power increases. The program is required to increase the power level while maintaining a minimum allowed period, and to reach the demand power with little or no overshoot. A switching criterion was derived using a discrete version of the Pontryagin Maximum Principle. The switch point was found to be dependent upon the minimum allowed period and the maximum reactivity removal rate of the controlled regulating rod. The control program developed was applied to digital simulation of three reactor models and was adapted for use on the Argonne Thermal Source Reactor (ATSR) for power-level changes. The maximum overshoot experienced was ∼1% for various minimum allowed reactor periods and reactivity removal rates.