It is well known that the analysis of variance of data in crossed classifications with unequal subclass numbers that are disproportionate presents complexities not found in the case of equal or proportionate subclass frequencies. A design, model, and analysis are presented here appropriate to the estimation of treatment effects in this situation, as encumbered, however, by 2 additional features: a mixed effects model (rather than a random or fixed effects model); and finite random effect populations (rather than infinite). A numerical example is appended to illustrate the application of the theory.