Methods for estimating genetic and maternal effects in crossbred populations were extended and generalized to allow estimation of optimal breed combinations. Coefficients of the effects were expressed in terms of the probabilities of obtaining genes from a given parental breed through the sire (PiS), dam (PiD) and maternal grandsire (píS). The formulas are applicable to crosses involving any number of breeds. For purposes of graphic presentation, available genetic and maternal parameters for 205-day weight derived from data involving the Angus (A), Charolais (C) and Hereford (H) breeds were used to develop response surfaces for all two-breed combinations of the A, C and H breeds. PiS, PiD and PíS ranged from 0 to 1. In crosses involving varying proportions of the A and C or the H and C breeds, an increased proportion of C genes resulted in increased 205-day weight, and the shape of the performance surface was largely determined by the breed additive effects of the C breed. Individual and maternal heterosis effects influenced the shape of the performance surface of crosses involving varying proportions of A and H. Application of results to the formation of synthetic breeds is discussed.