Tsunami earthquakes generate large tsunamis but only moderate ground shaking. The discrepancy between the magnitude of the surface wave and the resulting tsunami height makes them a serious threat to coastal communities and a problem for tsunami early warning. Although at least 13 tsunami earthquakes took place since 1896, there is little consent on what controls their genesis. It remains unclear if they are tied to distinct subduction-zone structures or geometries or if they can occur along all active margins. To help shed light on the genesis of these unusual earthquakes, I combine marine acoustic data from subduction-zone segments that experienced tsunami earthquakes in order to search for structural similarities in the nature of the subducting oceanic plate. The structural comparison indicates that tsunami earthquakes preferentially occur in regions where the subducting plate is characterized by excess topography which is not blanketed by trench sediment. While subducted, the topographic obstacles likely cause fracturing along their track. This contributes to the development of a thick, structurally and lithological complex, and fragmented plate-boundary shear-zone, which may be prone to fail at a low velocity during a tsunami earthquake. The results suggest that when assessing the risk of a tsunami earthquake, special focus should be placed on the combination of lower-plate topography and trench sediment thickness.