A problem where one subpopulation is compared to several other subpopulations in terms of means with the goal of estimating the smallest difference between the means commonly arises in biology, medicine, and many other scientific fields. A generalization of Strassburger, Bretz and Hochberg (2004) approach for two comparisons is presented for cases with three and more comparisons. The method allows constructing an interval-estimator for the smallest mean difference, which is compatible with the Min test. An application to a fluency-disorder study is illustrated. Simulations confirmed adequate probability coverage for normally distributed outcomes for a number of designs.