Random regression models (RRM) allows considering heterogeneous residual variances to describe the growth for each age. However, this feature increases the number of parameters to be estimated in the maximization likelihood function process. Searching for more parsimonious RRM, several approaches have been suggested. One of them is the use of different structures of residual variances modelled through step function in different classes with similar variance or through variance functions. A total of 7,369 records of body weight of partridges, measured from birth to 210 days of partridges born from 2000 to 2004 were used in this research. The random regression models applied to the data set considered different structures of residual variances and were performed by the restricted maximum likelihood method. The residual variances were modeled using classes of 210 (R210) and 30 (R30) ages and variance functions with orders ranging from quadratic (VF2) to nine (VF9). The R30 considered birds weighted in the same week. The random effects included were the genetic additive direct and the permanent environment effects of the animal. It was not possible to include the maternal effects in the models. All random effects were modelled by sixth order regression on Legendre polynomials. The models were compared by the likelihood ratio test, the Akaike's information criterion and the Schwarz's Bayesian information criterion. Best results were showed by the models R210 and VF5. In conclusion, the most parsimonious model was VF5 and should be applied to fit growth records of partridges.