Correlations were obtained between 18 response variables of a Jersey herd (Florida Agricultural Experiment Station, Gainesville) for 374 first lactations. Estimates were from the use of multivariate, derivative-free, restricted maximum likelihood procedures with the simplex method of partial maximization. Estimates agreed closely with those obtained previously by other methods in this and other dairy populations. All correlations between yields were high and positive; those between yields and days from parturition to first service were negative and near zero. Correlations between yields and somatic cell scores were moderate and negative; those between yields and constituent percentages in general were negative, except for the yield and percentage of the same constituent. Genetic correlations between chloride content and somatic cells and between measures of somatic cells were 1.0. Results suggest that single-trait selection for milk yield should result in correlated increases in constituent yields with slight decreases in percentage composition of constituents and somatic cell counts.