Data from an experimental mice population selected from 18 generations to increase weight gain were used to estimate the genetic parameters associated with environmental variability. The analysis involved three traits: weight at 21 days, weight at 42 days and weight gain between 21 and 42 days. A dataset of 5273 records for males was studied. Data were analysed using Bayesian procedures by comparing the Deviance Information Criterion (DIC) value of two different models: one assuming homogeneous environmental variances and another assuming them as heterogeneous. The model assuming heterogeneity was better in all cases and also showed higher additive genetic variances and lower common environmental variances. The heterogeneity of residual variance was associated with systematic and additive genetic effects thus making reduction by selection possible. Genetic correlations between the additive genetic effects on mean and environmental variance of the traits analysed were always negative, ranging from -0.19 to -0.38. An increase in the heritability of the traits was found when considering the genetic determination of the environmental variability. A suggested correlated canalised response was found in terms of coefficient of variation but it could be insufficient to compensate for the scale effect associated with an increase of the mean.