Alternative selection strategies were evaluated for breeding for carcass quality, body weight, and milk traits in dairy cattle. The efficiency of different alternatives was evaluated by comparing predicted genetic responses in individual traits as well as in the aggregate genotype. Particular interest was paid to the loss of response with indices that partially or totally ignored genetic correlations between traits, reflecting selection on single-trait evaluations. Simplified indices gave almost the same total response as a full multiple-trait index, but relative responses in carcass and milk traits differed between indices. Also studied were the consequences of restricting increase in body weight of dairy cows, while selecting for carcass and milk production traits. Restriction of body weight of cows resulted in considerable loss of predicted total response.