Selection for an optimum value and decreasing variability is of technical and economical interest in several animal production. An heteroscedastic model is proposed. It involves a genotypic value for the mean and a genotypic value for the log variance, associated with a single phenotypic value which can be either continuous or categorical. Several selection are mentioned and analysis of sheep data evidences the existence of a genetic effect contributing to the environmental variance of litter size. Simulations are performed to determine the response on mean and variability of a selection aimed to canalise the number of twins in sheep.