Optimal times of changing stress-level for the simple step-stress plans under the Khamis-Higgins model (an alternative to the Weibull step-stress model) are determined for a wide range of values of the model parameters. The applicability of the "optimal time of changing stress" formula obtained by Khamis-Higgins for a known shape parameter to the case of unknown shape parameter is examined. Their formula provides a reasonable approximation to the actual optimal times of changing stress levels within a certain range of values of the stress levels and model parameters but a poor approximation outside of that range.