Lactation curve shape can affect an animal's health, feed requirements, and milk production throughout the year. We implemented a random regression model for the genetic evaluation of lactation curve shapes of dairy traits in French Alpine goats for their first 3 parities. Milk, fat, and protein yields, fat and protein contents, somatic cell score, and fat/protein ratio were considered. The data consisted of test-day records from 49,849 first lactation Alpine goats during their first 3 lactations. The reference model used a Legendre polynomial of order 2 for each parity to describe the genetic and permanent environmental effects, and was compared with a model that combined the second and third parities. A rank reduction of the variance-covariance matrix was also performed using an eigenvalue decomposition for each parity from the 2 models. Genetic parameters were consistent between the models tested. With a reduction to rank 2 and combining the second and third parities, the first 2 principal components correctly summarized the genetic variability of milk yield level and persistency, with a near-nil correlation between the 2, and with a much shorter computation time than the reference model. A favorable correlation of +0.43 between milk yield persistency and fat/protein ratio persistency at the beginning of the lactation was found from buck estimated breeding values.