The Miocene in Southern New Zealand was dominated by strike-slip tectonics. Stratigraphic evidence from this time attests to two zones of subsidence in the south: (a) a middle Cenozoic pull-apart basin and (b) a regionally extensive subsiding lake complex, which developed east and distal to the developing plate boundary structure. The lake overlay a block of crust with a significantly weak mid-crustal section and we pose the question: can rheological transitions at an angle to a plate boundary produce distal subsidence and/or uplift? We use stratigraphic, structural and geophysical observations from Southern New Zealand to constrain three-dimensional numerical models for a variety of boundary conditions and rheological scenarios. We show that coincident subsidence and uplift can result from purely strike-slip boundary conditions interacting with a transition from strong to weak to strong mid-crustal rheology. The resulting pattern of vertical displacement is a function of the symmetry or asymmetry of the boundary conditions and the extent and orientation of the rheological transitions. For the Southern New Zealand case study, subsidence rates of ~0.1 mm/yr are predicted for a relative plate motion of 25 mm/yr, leading to ~500 m of subsidence over a 5 Ma time period, comparable to the thickness of preserved lacustrine sediments.