The thinned continental crust of the Australian plate is being obliquely subducted beneath the South Island on the Pacific plate along the Fiordland margin of New Zealand. Morphostructural analysis reveals that the continental slope of Fiordland is cut by faults that appear to splay southwestward from the onland transpressive dextral Alpine fault system. Active strike-slip movement occurs close to the shoreline where upper canyon courses are dextrally offset relative to the fiords. The canyons, however, postdate strike-slip movement on the fault splays on the slope, indicating that the splays are no longer active. These now-inactive strike-slip faults have imparted a saw-tooth backstop geometry to the margin that controls the locus of sediment accretion in the trench. Accretion occurs as two discrete lobes, each at a left step in the backstop. The morphology and internal structure of the accretionary lobes indicate that there is partial strain partitioning between the Alpine fault and the base of the continental slope. Oblique convergence in association with a stepped backstop produces strongly curved fold axes and thrusts that abut almost orthogonally against the toe of the margin. Thus Fiordland provides a tectonic model for oblique convergence at a previously structured margin.