A procedure for selecting a Poisson population with smallest mean is considered using an indifference zone approach. The objective is to determine the smallest sample sizenrequired fromk≥ 2 populations in order to attain the desired probability of correct selection. Since the means procedure is not consistent with respect to the difference or ratio alone, two distance measures are used simultaneously to overcome the difficulty in obtaining the smallest probability of correct selection that is greater than some specified limit. The constants required to determinenare computed and tabulated. The asymptotic results are derived using a normal approximation. A comparison with the exact results indicates that the proposed approximation works well. Only in the extreme cases small increases innare observed. An example of industrial accident data is used to illustrate this procedure.