1. Few studies have examined how the anatomy of an animal signal contributes to, or limits, the evolution of signal differentiation among closely related species. 2. In Anolis lizards, adult males extend a large, conspicuous dewlap as part of a territorial advertisement display. Males of species from the island of Jamaica rely on the rapid extension of the dewlap to facilitate display detection by territorial neighbours and conspecific females. Males of other species on the island of Puerto Rico extend the dewlap at considerably slower speeds and instead rely on other strategies to maintain an effective display. What initially prompted this divergence in display between the islands is unknown, but evidence suggests that it may have something to do with the way the dewlap is extended during display. 3. Our goal was to determine whether an innovation in the dewlap lever in Jamaican lineages, but absent in Puerto Rican lineages, accounted for the evolution of the high-speed dewlap on Jamaica. We began by modelling the performance of the Anolis dewlap as a first order lever system. We then simulated changes to this system relating to its morphology, articulation and input force in biologically realistic ways to predict how such changes impact dewlap speed. Finally, we compared these predictions to data on the morphology of the dewlap lever system from museum specimens and actual dewlap speed recorded for lizards in the field. 4. This investigation revealed that changes to the dewlap lever have affected the performance of the dewlap display in at least two ways. Within islands, structural changes to the hyoid morphology seem to have led to differences in dewlap speed among species. Between islands, however, differences in dewlap speed were most likely the result of a major increase in muscle contraction velocity that powers the dewlap extension in Jamaican species, but has not originated in species on Puerto Rico. 5. Our study shows how the biomechanics of a social signal can have important implications for understanding why closely related species might differ in signal behaviour, despite apparent similarities in the selection pressures that act on the signal.