Let \(\pi_ 1,\pi_ 2,...,\pi_ k\) be k given normal populations with unknown means and a common known variance. For the goal of finding the population with the largest mean, the authors have studied two-stage procedures with screening (elimination) at the first-stage under a decision-theoretic framework. They have derived a Bayes solution for i.i.d. normal priors under a specific loss function which includes costs of sampling, and have discussed its properties along with several approximations.