Despite longstanding interest in convergent evolution, factors that result in deviations from fully convergent phenotypes remain poorly understood. In birds, the evolution of flightless wing-propelled diving has emerged as a classic example of convergence, having arisen in disparate lineages including penguins (Sphenisciformes) and auks (Pan-Alcidae, Charadriiformes). Nevertheless, little is known about the functional anatomy of the wings of flightless auks because all such taxa are extinct, and their morphology is almost exclusively represented by skeletal remains. Here, in order to re-evaluate the extent of evolutionary convergence among flightless wing-propelled divers, wing muscles and ligaments were reconstructed in two extinct flightless auks, representing independent transitions to flightlessness: Pinguinus impennis (a crown-group alcid), and Mancalla (a stem-group alcid). Extensive anatomical data were gathered from dissections of 12 species of extant charadriiforms and 4 aequornithine waterbirds including a penguin. The results suggest that the wings of both flightless auk taxa were characterized by an increased mechanical advantage of wing elevator/retractor muscles, and decreased mobility of distal wing joints, both of which are likely advantageous for wing-propelled diving and parallel similar functional specializations in penguins. However, the conformations of individual muscles and ligaments underlying these specializations differ markedly between penguins and flightless auks, instead resembling those in each respective group’s close relatives. Thus, the wings of these flightless wing-propelled divers can be described as convergent as overall functional units, but are incompletely convergent at lower levels of anatomical organization—a result of retaining differing conditions from each group’s respective volant ancestors. Detailed investigations such as this one may indicate that, even in the face of similar functional demands, courses of phenotypic evolution are dictated to an important degree by ancestral starting points.