Recent seafloor mapping around volcanic islands shows that submarine landslide deposits are common and widespread. Such landslides may cause devastating tsunamis, but accurate assessment of tsunami hazard relies on understanding failure processes and sources. Here we use high-resolution geophysical data offshore from Montserrat, in the Lesser Antilles, to show that landslides around volcanic islands may involve two fundamentally different sources of sediment (island-flank and larger seafloor-sediment failures), and can occur in multiple stages. A combination of these processes produces elongate deposits, with a blocky centre (associated with island-flank collapse), surrounded by a smoother-surfaced deposit that is dominated by failed seafloor sediment. The failure of seafloor sediment is associated with little marginal accumulation, and involves only limited downslope motion. Submarine landslide deposits with similar blocky and smooth-surfaced associations are observed in several locations worldwide, but the complex emplacement processes implied by this morphological relationship can only be revealed by high-resolution geophysical data. Such complexity shows that the volume of landslide deposits offshore of volcanic islands cannot simply be used in tsunami models to reflect a single-stage collapse of primary volcanic material. By applying predictive equations for tsunami amplitude to investigate general scenarios of volcanic island landslide generation, we show that the tsunami hazard associated with volcanic island collapse remains highly significant. Volcanic flank failures, even if relatively small, may generate large local tsunamis, but associated seafloor sediment failures, even if they have a much greater volume, have a substantially lower potential for tsunami generation. © 2011 Elsevier B.V.