Summary: Under the assumption that the exponential distribution is a reasonable model for a given population, some shrinkage estimators for the location parameter based on type I and type II censored samples have been derived. It is shown that these estimators dominate maximum likelihood estimators (MLE’s) asymptotically under the mean squared error (MSE) criterion. A Monte Carlo study shows a significant improvement of our estimators over MLE’s in terms of MSE for small samples.