A number of multiple comparison procedures are studied whose maximum Type I error rate, experimentwise, is limited to a fixed value, the experimentwise level. Some of these procedures are slight revisions of existing methods. The procedures are compared for all-pairs power; i.e., for the probability of simultaneous significance for all pairs which are truly unequal. Results of Monte Carlo simulation show that a revision of Peritz's F method is uniformly the most powerful among all the procedures studied. The revised Peritz F method is substantially more powerful than Tukey's method with a power advantage as high as 0.50. A method due to Welsch (1972, 1977) is also quite powerful and may sometimes be recommended for greater simplicity.