Using Tukey–Kramer versus the ANOVA F-test as the omnibus test of the Hayter–Fisher procedure for comparing all pairs of normally distributed means, when sample sizes are unequal, is investigated. Simulation results suggest that using Tukey–Kramer leads to as much or more any-pairs power compared to using the F-test for certain patterns of mean differences, and equivalent per-pair and all-pairs power for all cases. Furthermore, using Tukey–Kramer results in a consonant test procedure, where there cannot be disagreement between the results of the omnibus test and the subsequent pairwise tests. The results suggest that when sample sizes are unequal, Tukey–Kramer may be preferred over the F-test as the omnibus test for the Hayter–Fisher procedure.