Abstract Phenotypic convergence is an exciting outcome of adaptive evolution, occurring when species find similar solutions to the same problem. Unraveling the molecular basis of convergence provides a way to link genotype to adaptive phenotypes, but can also shed light on the extent to which evolution is repeatable and predictable. Many recent genome-wide studies have uncovered a striking pattern of diminishing convergence over time, ascribing this pattern to the presence of intramolecular epistatic interactions. Here, we consider gene tree discordance as an alternative driver of convergence levels over time. We demonstrate that gene tree discordance can produce patterns of diminishing convergence by itself, and that controlling for discordance as a cause of apparent convergence makes the pattern disappear. We also show that synonymous substitutions, where neither selection nor epistasis should be prevalent, have the same diminishing pattern of molecular convergence among closely related primate species. Finally, we demonstrate that even in situations where biological discordance is not possible, errors in species tree inference can drive these same patterns. Though intramolecular epistasis is undoubtedly affecting many proteins, our results suggest an additional explanation for this widespread pattern. These results contribute to a growing appreciation not just of the presence of gene tree discordance, but of the unpredictable effects this discordance can have on analyses of molecular evolution.