A total of 71,518 days open (DO) and number of services per conception (NSC) records of 28,523 Iranian Holstein cows were analysed by random regression model. Akaike’s information criterion and likelihood ratio test suggested that a model with quadratic Legendre polynomials for additive genetic and permanent environmental was best. Heritability in different parities ranged from 0.103 to 0.045 in first parity and 0.054 to 0.030 in sixth parity for DO and NSC, respectively. Estimated genetic correlations between parities decreased continuously with increasing distance between parities for both DO and NSC. The first eigenfunction explained 89.99% and 97.22 % of the total genetic variance of DO and NSC, while the second eigenfunction accounted 6.24% and 3.18%, respectively. Different selection indices were constructed for DO and NSC. Genetic response to improve overall fertility was greater when the index included the first eigenvector than the response obtained from indices excluding it. Similar genetic gains were obtained from the first eigenvector, which had a nearly flat associated eigenfunction along lactations and from selection by the intercept of the random regression. The first eigenvector indices were responsible of changes in the level of DO and NSC in a similar manner for all parities, without altering the shape of the response curve across parities. The second and third eigenvector indices modified the shape of this curve but the improvement in genetic gains by including them in the selection index were small (DO) or negligible (NSC) due to the small amount of variability associated with these components.