Nine mathematical models were compared for their ability to predict daily milk yields (n = 294,986) in standard 305-d and extended lactations of dairy cows of Costa Rica. Lactations were classified by parity (first and later), lactation length (9 to 10, 11 to 12, 13 to 14, 15 to 16, and 16 to 17 mo), and calving to conception interval (1 to 2, 3 to 4, 5 to 6, 7 to 8, and 9 to 10 mo). Of the nine models, the diphasic model and lactation persistency model resulted in the best goodness of fit as measured by adjusted coefficient of determination, residual standard deviation, and Durbin-Watson coefficient. All other models showed less accuracy and positively correlated residuals. In extended lactations, models were also fitted using only test-day records before 305 d, which resulted in a different ranking. The diphasic model showed the best prediction of milk yield in standard and extended lactations. We concluded that the diphasic model provided accurate estimates of milk yield for standard and extended lactations. Interpretation of parameters deserves further attention because of the large variation observed. As expected, the calving to conception interval was found to have a negative effect on milk yield for cows with a standard lactation length. In extended lactations, these negative effects of pregnancy on milk yield were not observed.