Data from a divergent experiment for birthweight (BrW) environmental variability were used to estimate genetic parameters for BrW trait and its environmental variability by fitting both homoscedastic (HO) and heteroscedastic (HE) models. A total of 5 475 records of BrW from animals born from inbred dams, and 7 140 pedigree records were used. The heritability of BrW using the model HO was 0.27, with the litter effect much more important, 0.43. The model HE provided a genetic correlation between the trait and its environmental variability that was very high and negative, -0.97, and a high value for the additive genetic variance for environmental variability, suggesting an artefact in the model. The residual skewness was found to be essentially null. A model considering the genetic correlation null was also fitted, and used to obtain the breeding values for the selection process. Moreover, the trait was considered as maternal resulting in similar estimates under the model HO, but more reasonable for the genetic correlation between the trait and its environmental variability of 0.48 with a value of 0.25 for the additive genetic variance regarding environmental variability under the model HE. This led to the conclusion that environmental variability of BrW in mice must be selected via dams. Estimated parameters in a reduced dataset without inbred animals did not substantially change this conclusion.