Multiple-trait BLUP evaluations of test day records require a large number of genetic parameters. This study estimated covariances with a reduced model that included covariance functions in two dimensions (stage of lactation and herd production level) and all three yield traits. Records came from all six states in Australia, were evenly distributed across the herd production levels, but decreased with increasing lactation stage from 9693 records for the 1st mo of lactation to 4199 records for the 10th mo. Using the variance component estimation package and a bivariate animal model, 1176 genetic (co)variances and 312 environmental (co)variances were estimated for 48 traits (1, 4, 7, and 10 mo of lactation; herd production levels of <20, 20 to 22, 22 to 24, >24 kg of milk/d; and milk, fat, and protein yields). The genetic (co)variances could be predicted by a multiplicative model that included 1) a term dependent on which yields (milk, fat, or protein) were involved in the covariance, 2) the covariance functions for month of lactation and herd production level, and 3) a covariance function for the interaction between these. This model required only 27 parameters instead of the 1176 (co)variances. For the environmental (co)variances, a model was fitted that contained several additional covariance functions. This model reduced the number of parameters from 312 to 71. For the same trait at the same production level, genetic correlations between test days ranged from 0.59 to 1, and environmental correlations ranged from 0.17 to 0.48. Genetic correlations between milk and fat, milk and protein, and fat and protein were 0.38, 0.83, 0.59, respectively, and correlations between the herd production levels ranged from 0.79 to 0.97. Failure to consider herd production level in a test day model evaluation might result, for instance, in overweighting of early lactation information from high production herds compared with information coming from bulls tested across all production levels.