In this paper several designs featuring planned unbalance are compared, using maximum likelihood (ML), for the estimation of variance components in a two-way classilicatlon model with no interaction. Asymptotic and small sample results are presented. A transformation technique is discussed for simplifying the variance-covariance matrix thereby improving the efficiency of the asymptotic computing routines and rendering the small sample simulation procedures computationally feasible. Evidence is offered in support of the viewpoint that asymptotic findings are consistent with small sample ML results for design selection if the relative asymptotic results for comparing two designs are not too close to one.