The structure of environmentally induced phenotypic covariation can influence the effective strength and magnitude of natural selection. Yet our understanding of the factors that contribute to and influence the evolutionary lability of such covariation is poor. Most studies have either examined environmental variation without accounting for covariation, or examined phenotypic and genetic covariation without distinguishing the environmental component. In this study we examined the effect of mutational perturbations on different properties of environmental covariation, as well as mean shape. We use strains of Drosophila melanogaster bearing well-characterized mutations known to influence wing shape, as well as naturally-derived strains, all reared under carefully-controlled conditions and with the same genetic background. We find that mean shape changes more freely than the covariance structure, and that different properties of the covariance matrix change independently from each other. The perturbations affect matrix orientation more than they affect matrix eccentricity or total variance. Yet, mutational effects on matrix orientation do not cluster according to the developmental pathway that they target. These results suggest that it might be useful to consider a more general concept of 'decanalization', involving all aspects of variation and covariation.