Genetic variation for individual traits is typically abundant, but for some multivariate combinations it is very low, suggesting that evolutionary limits might be generated by the geometric distribution of genetic variance. To test this prediction, we artificially selected along all eight genetic eigenvectors of a set of eight quantitative traits in Drosophila serrata. After six generations of 50% truncation selection, at least one replicate population of all treatments responded to selection, allowing us to reject a null genetic subspace as a cause of evolutionary constraint in this system. However, while all three replicate populations of the first five selection treatments displayed a significant response, the remaining three, characterized by low genetic variance in their selection indexes in the base population, displayed inconsistent responses to selection. The observation that only four of the nine replicate populations evolved in response to the direct selection applied to them in these low genetic variance treatments, led us to conclude that a nearly null subspace did limit evolution. Dimensions associated with low genetic variance are often found in multivariate analyses of standing genetic variance in morphological traits, suggesting that the nearly null genetic subspace may be a common mechanism of evolutionary constraint in nature.