Heritabilities, genetic and phenotypic correlations among yields of milk, fat and protein, fat percentages and protein percentages were estimated using a sire model and multivariate REML for 15357 first-lactation records of the Icelandic dairy cow. These heifers were daughters of 136 young and 55 proven Icelandic bulls. Proven sires were treated as fixed effects and did not contribute to the inter-sire variance. Heritabilities for milk, fat and protein yields and fat and protein percentages were 0.23, 0.17, 0.18, 0.18 and 0.37, respectively. Variance and covariance components were estimated for the same traits, using the first three lactations of 5705 daughters of 138 bulls. Heritabilities for milk yield in the first three lactations were 0.17, 0.12 and 0.10, for fat yield 0.17, 0.10 and 0.09 and for protein yield 0.14, 0.11 and 0.11. Genetic correlation was 0.76 between milk yield in first and second lactation and 0.66 between first and third lactation. Genetic correlations for fat and protein yields ranged from 0.51 to 0.99 and from 0.80 to 0.99 for the percentage traits. Phenotypic correlations between all traits were around 0.40. Repeatabilities were estimated as 0.40, 0.34, 0.40, 0.37 and 0.40 for milk, fat, protein, fat % and protein %, respectively.