Using deterministic methods, rates of genetic gain (ýG) and inbreeding (ýF) were compared between pure line selection (PLS) and combined crossbred purebred selection (CCPS), for the sire line of a three-way crossbreeding scheme. Purebred performance and crossbred performance were treated as genetically correlated traits assuming the infinitesimal model. Breeding schemes were compared at a fixed total number of purebred selection candidates, i.e. including crossbred information did not affect the size of the purebred nucleus. Selection was by truncation on estimated breeding values for crossbred performance. Rates of genetic gain were predicted using a pseudo-BLUP selection index. Rates of inbreeding were predicted using recently developed methods based on long-term genetic contributions. Results showed that changing from PLS to CCPS may increase ýF by a factor of 2·14. In particular with high heritabilities and low purebred-crossbred genetic correlations, CCPS requires a larger number of parents than PLS, to avoid excessive ýF. The superiority of CCPS over PLS was judged by comparing ýG from both selection strategies at the same ýF. At the same ýF, CCPS was superior to PLS and the superiority of CCPS was only moderately reduced compared with the situation without a restriction on ýF. This paper shows that the long-term genetic contribution theory can be used to balance ýF and ýG in animal breeding schemes within very limited computing time.