Putatively vesicular structures on graptolites, for example scopulae, tend to attract interest and debate. For most of the nineteenth century scopulae were considered to be reproductive organs, similar to those of modern hydrozoans, and termed graptogonophores. Despite the increasing acceptance of a hemichordate affinity for graptolites in the twentieth century, the proposed reproductive function remained largely unchallenged, and latterly overlooked. Similarly, disarticulated sclerites from the problematic fossil Dawsonia have been regarded as scopulae broken from graptolites.This work reassesses these structures: morphometric analysis demonstrates that the similarity between scopulae and Dawsonia is superficial. Moreover, comparison with isolated graptolites and vesicular graptolitic tissues shows that scopulae are best considered to be two-dimensional paddle-like appendages. Their two-dimensional nature indicates their function is more likely hydrodynamic than reproductive, leaving the term graptogonophore obsolete. Scopulae are only known in biserial graptolites but have arisen independently on several occasions, though in each instance their fossil occurrence is extremely rare. This may be consistent with modification to inhabit an infrequent and probably marginal habitat.