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The impact of late Cenozoic climate on the East Antarctic Ice Sheet is uncertain. Poorly constrained patterns of relative ice thinning and thickening impair the reconstruction of past ice-sheet dynamics and global sea-level budgets. Here we quantify long-term ice cover of mountains protruding the ice-sheet surface in western Dronning Maud Land, using cosmogenic Chlorine-36, Aluminium-26, Beryllium-10, and Neon-21 from bedrock in an inverse modeling approach. We find that near-coastal sites experienced ice burial up to 75–97% of time since 1 Ma, while interior sites only experienced brief periods of ice burial, generally <20% of time since 1 Ma. Based on these results, we suggest that the escarpment in Dronning Maud Land acts as a hinge-zone, where ice-dynamic changes driven by grounding-line migration are attenuated inland from the coastal portions of the East Antarctic Ice Sheet, and where precipitation-controlled ice-thickness variations on the polar plateau taper off towards the coast.