Distantly related species entering similar biological niches often adapt by evolving similar morphological and physiological characters. The extent to which genomic molecular convergence, and the extent to which coding mutations underlie this convergent phenotypic evolution remain unknown. Using a novel test, we ask which group of functionally coherent genes is most affected by convergent amino acid substitutions between phenotypically convergent lineages. This most affected sets reveals 75 novel coding convergences in important genes that pattern a highly adapted organ: the cochlea, skin and lung in echolocating, aquatic and high-altitude mammals, respectively. Our test explicitly requires the enriched converged term to not be simultaneously enriched for divergent mutations, and correctly dismisses relaxation-based signals, such as those produced by vision genes in subterranean mammals. This novel test can be readily applied to birds, fish, flies, worms etc., to discover more of the fascinating contribution of protein coding convergence to phenotype convergence.