Ice-shelf basal melting is tightly coupled to ice-shelf morphology. Ice shelves, in turn, are coupled to grounded ice via their influence on compressive stress at the grounding line (‘ice-shelf buttressing’). Here, we examine this interaction using a local parameterization that relates the basal melt rate to the ice-shelf thickness gradient. This formulation permits a closed-form solution for a steady-state ice tongue. Time-dependent numerical simulations reveal the spatial and temporal evolution of ice-shelf/ice-stream systems in response to changes in ocean temperature, and the influence of morphology-dependent melting on grounding-line retreat. We find that a rapid (<1 year) re-equilibration in upstream regions of ice shelves establishes a spatial pattern of basal melt rates (relative to the grounding line) that persists over centuries. Coupling melting to ice-shelf shape generally, but not always, increases grounding-line retreat rates relative to a uniform distribution with the same area- average melt rate. Because upstream ice-shelf thickness gradients and retreat rates increase nonlinearly with thermal forcing, morphology-dependent melting is more important to the response of weakly buttressed, strongly forced ice streams grounded on beds that slope upwards towards the ocean (e.g. those in the Amundsen Sea)