Studies of subduction zone seismogenesis and tsunami potential, particularly of large subduction zones, have recently seen a resurgence after the great 2004 earthquake and tsunami offshore of Sumatra, yet these global studies have generally neglected the tsunami potential of small subduction zones such as the Puysegur subduction zone, south of New Zealand. Here, we study one such relatively small subduction zone by analysing the historical seismicity over the entire plate boundary region south of New Zealand, using these data to determine the seismic moment deficit of the subduction zone over the past ~100 yr. Our calculations indicate unreleased moment equivalent to a magnitude Mw 8.3 earthquake, suggesting this subduction zone has the potential to host a great, tsunamigenic event. We model this tsunami hazard and find that a tsunami caused by a great earthquake on the Puysegur subduction zone would pose threats to the coasts of southern and western South Island, New Zealand, Tasmania and southeastern Australia, nearly 2000 km distant. No claim to original US government works Geophysical Journal International ?? 2010 RAS.