Several functions were used to model the fixed part of the lactation curve and genetic parameters of milk test-day records to estimate using French Holstein data. Parametric curves (Legendre polynomials, Ali-Schaeffer curve, Wilmink curve), fixed classes curves (5-d classes), and regression splines were tested. The latter were appealing because they adjusted the data well, were relatively insensitive to outliers, were flexible, and resulted in smooth curves without requiring the estimation of a large number of parameters. Genetic parameters were estimated with an Average Information REML algorithm where the average information matrix and the first derivatives of the likelihood functions were pooled over 10 samples. This approach made it possible to handle larger data sets. The residual variance was modeled as a quadratic function of days in milk. Quartic Legendre polynomials were used to estimate (co)variances of random effects. The estimates were within the range of most other studies. The greatest genetic variance was in the middle of the lactation while residual and permanent environmental variances mostly decreased during the lactation. The resulting heritability ranged from 0.15 to 0.40. The genetic correlation between the extreme parts of the lactation was 0.35 but genetic correlations were higher than 0.90 for a large part of the lactation. The use of the pooling approach resulted in smaller standard errors for the genetic parameters when compared to those obtained with a single sample.