The design of experiments to estimate heritability when data are available on both parents and offspring and the offspring data have a hierarchical structure is considered. Univariate maximum likelihood (ML) estimation is discussed, and extensions to the multivariate case are outlined. The efficiency of ML estimation is evaluated in cases where simple regression estimators are available. Optimum designs for ML estimation are given when various strategies of selecting and mating are followed. The variance of the heritability estimate can be approximately halved relative to designs in which no selection of parents is done.