We have developed a new method for inverting tsunami waveforms that reveals considerable detail in megathrust slip during subduction zone earthquakes. Previous methods have ensured compliance with the shallow-water theory used to compute tsunami waveforms by using large subfaults that generate only long-wavelength seafloor deformation. We show that a better approach is to use small subfaults coupled with a smoothing criterion that ensures compliance with the shallow-water approximation. In an application of the method to historical earthquakes in the Nankai Trough, southwestern Japan, we find that the areas with slip > 1 m for the earthquakes of 1944 and 1946, which ruptured adjacent segments of the subduction zone, are separated by a sharp, non-overlapping boundary. This establishes that interseismic accumulation of strain energy extends very close to the boundary between rupture zones, and strongly suggests that this boundary is associated with a physical barrier to rupture.