Inter-module physiological integration of colonial organisms can facilitate colony-wide coordinated responses to stimuli that strengthen colony fitness and stress resistance. In scleractinian corals, whose colonial integration ranges from isolated polyps to a seamless continuum of polyp structures and functions, this coordination improves responses to injury, predation, disease, and stress and may be one of the indications of an evolutionary origin of Symbiodinium symbiosis. However, observations of species-specific coral bleaching patterns suggest that highly integrated coral colonies may be more susceptible to thermal stress, and support the hypothesis that communication pathways between highly integrated polyps facilitate the dissemination of toxic byproducts created during the bleaching response. Here we reassess this hypothesis by parameterizing an integration index using 7 skeletal features that have been historically employed to infer physiological integration. We examine the relationship between this index and bleaching response across a phylogeny of 88 diverse coral species. Correcting for phylogenetic relationships among species in the analyses reveals significant patterns among species characters that could otherwise be obscured in simple cross-species comparisons using standard statistics, whose assumptions of independence are violated by the shared evolutionary history among species. Similar to the observed benefits of increased coloniality for other types of stressors, the results indicate a significantly reduced bleaching response among coral species with highly integrated colonies.