Phenotypic plasticity and canalization are important topics in quantitative genetics and evolution. Both concepts are related to environinental sensitivity. The latter can be. modeled using a model with genetically Structured environmental variance. This work reports the result.,: of a genetic analysis of adult weight in the snail Helix aspersa. Several models of heterogeneous variance are fitted using a Bayesian, MCMC approach. Exploratory analyses using posterior predictive model checking and model comparisons based on the deviance information criterion favor a model postulating a genetically structured heterogeneous environmental variance. Our analysis provides a strong indication of a positive genetic correlation between additive genetic values affecting the Mean and those affecting environmental variation of adult body weight. The possibility of manipulating environmental variance by selection is illustrated numerically using estimates of parameters derived from the snail data set.