Random regression models with Legendre polynomials of the 2nd, 3rd and 4th degree (RR2, RR3 and RR4) were compared with regard to the estimation of breeding values for the average daily gain of Czech Pied bulls. A multi-trait model (MTM) could be used asreference model. In general, models RR3 and RR4 returned higher rank correlations with MTM in comparison to model RR2. Additionally, the number of common animals in the 1% and 10% top-lists showed that models RR3 and RR4 are to be preferred over RR2 when it comes to the estimation of breeding values.