A number of papers have been published on estimation of the parameter in a truncated Poisson distribution. The methods are difficult computationally and yield estimators that are optimal in one sense or the other. The present work extends a paper published by Plackett (1953) in which he presents a very straightforward estimator which is unbiased and is extremely simple to calculate. The estimate is not fully efficient, but the loss in the efficiency is offset by the gain in simplicity. In this paper we generalize the results of Plackett to the case when the distribution is truncated to the left at ‘a’ An estimate of the variance of the unbiased estimator is developed, and a table of the efficiency of the unbiased estimator for different values of a and λ is given.