Summary: By running life tests at higher stress levels than normal operating conditions, accelerated life testing (ALT) quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant-stress testing, a unit is tested at a fixed stress level until failure or the termination time point of test, whereas step-stress testing allows the experimenter to gradually increase the stress levels at some prefixed time points during the test. In this work, the optimal \(k\)-level constant-stress and step-stress ALTs are compared for the exponential failure data under complete sampling and Type-I censoring. The objective is to quantify the advantage of using the step-stress testing relative to the constant-stress one. Assuming a log-linear life-stress relationship with the cumulative exposure model for the effect of changing stress in step-stress testing, the optimal design points are determined under C/D/A-optimality criteria. The efficiency of step-stress testing to constant-stress one is then discussed in terms of the ratio of optimal objective functions based on the information matrix.