This paper considers pretest estimation of the parameters of the binomial, the Poisson and the negative binomial distributions. It is assumed that a prior point estimate of the unknown parameter is available, and this value is tested as a preliminary hypothesis by considering a suitable randomized test. Depending on the result of this test, suitable estimators of the underlying parameter are chosen. The exact results for the bias and the mean squared error of the proposed estimators are obtained, and the computations are illustrated by numerical examples.