This paper compares two accelerated life for Weibull distribution. One is the optimum constant stress accelerated life test which minimizes the asymptotic variance of maximum likelihood estimator of a specified quantile at design stress, and the other is corresponding simple step stress test. The models and optimum designs of constant stress and step stress tests are reviewed. Behaviors of asymptotic variances, effects of design parameters to optimum tests, and expected numbers of failures and expected test times of the two tests are investigated. The efficiency of step stress test relative to constant stress test is studied in terms of variance ratio, and robustness to preestimates of design parameters are investigated.