A method for obtaining between-breed differences in crossbreeding parameters is presented as an alternative to the conventional practice of estimating actual parameters in crossbreeding systems where a single exotic breed imported through sires or semen only is used on two or more indigenous breeds. The method involves reparameterisation of the components of the expectation of genotypic means in order to reduce the number of parameters to be estimated to a number consistent with the available genotypes. The method is essentially a linear rearrangement of the common regression model. By way of example it is shown that, for most practical situations where choice is to be made among alternative local breeds to be used in crossbreeding with an exotic breed, pairwise differences in estimates of direct and maternal effects, both additive and heterotic, are adequate. A method for estimating sampling variances of these parameters is also developed and systematically illustrated using actual data.