This paper presents a simple estimator of the shape parameter in a Weibull duration model with unobserved heterogeneity. The estimator is consistent and asymptotically normal under mild conditions, and a consistent estimator of the asymptotic variance is available. A Monte Carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution. The estimation strategy can be extended to a model with regressors and to a log-logistic model with unobserved heterogeneity. The advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived. Copyright 1990 by The Econometric Society.