peer reviewed ; Random regression test-day models using Legendre polynomials are commonly used for the estimation of genetic parameters and genetic evaluation for test-day milk production traits. However, some researchers have reported that these models present some undesirable properties such as the overestimation of variances at the edges of lactation. Describing genetic variation of saturated fatty acids expressed in milk fat might require the testing of different models. Therefore, 3 different functions were used and compared to take into account the lactation curve: (1) Legendre polynomials with the same order as currently applied for genetic model for production traits; 2) linear splines with 10 knots; and 3) linear splines with the same 10 knots reduced to 3 parameters. The criteria used were Akaike’s information and Bayesian information criteria, percentage square biases, and log-likelihood function. These criteria indentified Legendre polynomials and linear splines with 10 knots reduced to 3 parameters models as the most useful. Reducing more complex models using eigenvalues seemed appealing because the resulting models are less time demanding and can reduce convergence difficulties, because convergence properties also seemed to be improved. Finally, the results showed that the reduced spline model was very similar to the Legendre polynomials model.