Genetic and phenotypic parameters of productive (305-day yields of milk, MY; fat, FY and protein, PY) and reproductive (days open, DO; number of service per conception, NSC and age at first calving, AFC) traits were estimated from 1180 first lactation records on Holstein dairy cows, daughters of 93 sires and 650 dams, using multi-trait animal model. Seven selection indexes aiming to improve 305-day yields of milk, fat and protein were considered using various combinations of these three traits as sources of information. The full index (I₁), being the most accurate index, had the highest correlation with the true breeding value (r_TI = 0.629). Comparable accuracy (r_TI = 0.607) would be expected from the single trait index involving milk yield alone. At each round of selection, such a single trait index is expected to result in advantageous productive traits in terms of higher yields of milk (+727.24 kg), fat (+22.10 kg) and protein (+20.68 kg), and disadvantageous reproductive performance in terms of DO (+4.41 day), NSC (+0.01 service) and AFC (+0.15 month). To prevent deterioration in DO, NSC and AFC, separate restrictions were imposed to the full index (I_8(DO), I_9(NSC) and I_10(AFC) respectively). The optimum balance between production and fertility was obtainable via using (I_9(NSC)) instead of I₁ with slight reduction in accuracy of selection (r_TI = 0.590 vs. 0.629) and in expected gain in yields of fat (20.60 vs. 25.12 kg) and protein (19.36 vs. 23.63 kg) but with seemingly tolerable sacrifice in milk yield gain (709.13 vs. 774.07 kg).