This paper deals with the problem of making inferences about the mean of an exponential distribution when the sample is “time-censored”. The exact sampling distribution of the maximum likelihood estimate is obtained and used to show that the asymptotic sampling theory is inadequate unless the sample size is very large. An approximation to the distribution is proposed for use in small samples and compared with a method suggested by Bartlett (1953a). An alternative estimate is suggested which is both simple and highly efficient in certain circumstances. The methods are illustrated by examples.