Populations are subjected to diverse environmental conditions that affect fitness and induce evolutionary or plastic responses, resulting in phenotypic divergence among populations. Some authors contend such divergence is concentrated along a single major axis of trait covariance, even if that axis does not lead populations directly toward fitness optimum. Other authors argue that divergence can occur readily along many phenotype axes at the same time. We use populations of threespine stickleback (Gasterosteus aculeatus) from 14 lakes with contrasting ecological conditions to find some resolution along the continuum between these two extremes. Unlike many previous studies, we included several functional suites of traits (defensive, swimming, trophic) potentially subject to different sources of selection. We find that populations exhibit dimensionality of divergence that is high enough to preclude a history of constraint along a single axis – both for divergence in multivariate mean trait values and for the structure of trait covariances. Dimensionality varied among trait suites and were strongly influenced by the inclusion of specific traits, and integration of trait suites varied between populations. We leverage this variation into new insights about the process of divergence and suggest that similar analyses could increase understanding of other adaptive radiations.