Glaciers often erode, transport and deposit sediment much more rapidly than nonglacial environments, with implications for the evolution of glaciated mountain belts and their associated sedimentary basins. But modelling such glacial processes is difficult, partly because stabilizing feedbacks similar to those operating in rivers have not been identified for glacial landscapes. Here we combine new and existing data of glacier morphology and the processes governing glacier evolution from diverse settings to reveal such stabilizing feedbacks. We find that the long profiles of beds of highly erosive glaciers tend towards steady-state angles opposed to and slightly more than 50 per cent steeper than the overlying ice-air surface slopes, and that additional subglacial deepening must be enabled by non-glacial processes. Climatic or glaciological perturbations of the ice-air surface slope can have large transient effects on glaciofluvial sediment flux and apparent glacial erosion rate.