By using a new approach for specifying the alternative distribution, we obtain a new eliminating procedure for selecting the best one ofkexperimental categories when the measurements from each category have a one-dimensional Koopman-Darmois distribution. When thekpopulations are normal with a common known variance, a modification of this approach results in a new closed eliminating procedure for selecting the population with the greatest mean. The Monte Carlo results summarized in Tables I and II indicate the new procedures lead to a reduction in the average total sample size when compared to the other available sequential procedures. We also obtain a sequential procedure for the case when the "best" experimental category is only preferred when it is better than a specified standard.