Consider a two-way factorial experiment involving a “treatment” factor A with fixed effects, a “blocking” factor B with random effects, and interaction effects perhaps non-negligible. The degree of balance required for multiple comparison procedures to be applicable for the comparison of the treatment effects using ordinary least-squares estimates is investigated. For main effects to be estimated independently of MSAB, a sufficient condition is that the design consist of identical blocks, a strong condition of proportional frequencies. Surprisingly, under this condition of proportional frequencies, MSAB does not provide an appropriate variance estimate for inferences on each treatment contrast, even though the statistics F = MSA/MSAB is appropriate for testing equality of the treatment effects. In short, when factor B is random, standard methods of multiple comparisons apply using the interaction mean square MSAB as a variance estimator only when the treatment-block incidences n_n are constant. Nevertheless, for designs with identical blocks, appropriate variance estimates can be identified to allow for conservative or approximate multiple comparisons. This is illustrated for certain treatment balanced designs for comparisons with a control.