Legendre polynomials were used to describe the (co)variance matrix within a random regression test day model. The goodness of fit depended on the polynomial order of fit, i.e., number of parameters to be estimated per animal but is limited by computing capacity. Two aspects: incomplete lactation records and heterogeneous variances were investigated to reduce the order of fit needed. Analysis of the original data set, which contained 50% incomplete lactation records, required a fifth-order of fit and showed too high variances at the end of the lactation. Variance component estimates from only complete lactation records improved the goodness of fit. Correlations estimated were more alike those observed and substantially lower variances at the end of lactation were obtained, such that a fourth-order seemed sufficient. Correction for heterogeneous variances across classes of days in milk improved the estimated correlation structure further and the mean square errors of prediction were better, resulting in a third-order of fit being sufficient. Overall, use of only complete lactation records for parameter estimation and correction for heterogeneous variances allowed a reduction of two parameters that need to be estimated per animal.