In this article we revisit the problem of pretest estimation for some discrete distributions, when a prior point estimate of an unknown parameter is available A general formula for bias and mean square error of a pretest estimator is derived for a class of discrete distributions. This leads to a refinement of results reported by Kumar et al. (1992), in which the expressions for the bias and mse appear to be incorrect Efficiency of the proposed estimator is plotted for Poisson and Binomial distributions. Based on the efficiency curves, optimum level of significance for the preliminary test is suggested.