There are many compelling examples of molecular convergence at individual genes. However, the prevalence and the relative importance of adaptive genome-wide convergence remain largely unknown. Many recent works have reported striking examples of excess genome-wide convergence, but some of these studies have been called into question because of the use of inappropriate null models. Here, we sequenced and compared the genomes of 12 species of anole lizards that have independently converged on suites of adaptive behavioral and morphological traits. Despite extensive searches for a genome-wide signature of molecular convergence, we found no evidence supporting molecular convergence at specific amino acids either at individual genes or at genome-wide comparisons; we also uncovered no evidence supporting an excess of adaptive convergence in the rates of amino acid substitutions within genes. Our findings indicate that comprehensive phenotypic convergence is not mirrored at genome-wide protein-coding levels in anoles, and therefore, that adaptive phenotypic convergence is likely not constrained by the evolution of many specific protein sequences or structures.