Side-scan sonar and sub-bottom acoustic profiler data and sediment cores reveal the processes that controlled sediment transport and deposition on the continental shelf of the Antarctic Peninsula Pacific margin off Anvers Island, during deglaciation over the last 11,000 years or more. Glacial flutes and striations mark the flow of low-profile ice streams draining the interior, across the middle and outer shelf. Most probably, ice sheets were grounded to the continental shelf edge along this margin during the last glacial maximum. Iceberg furrows overwrite the ice sheet record in areas between 500 and 350 m water depth, and reflect calving from a retreating ice shelf front. Cores show open marine sedimentation replacing diamicton deposition close to the grounding line during this retreat, which rapidly cleared the outer and middle shelf shortly before 11,000 years BP (from AMS14C dates on organic carbon). The shallower, scoured and largely sediment-free inner shelf cleared later, probably before 6000 years BP. Open marine sediments on the middle and outer shelf include a pelagic biogenic component and suspended sediment from modern glacier tongues, supplemented by resuspension of older sediment in shallow shelf regions (by currents and by grounded icebergs). Sedimentation is too slow to be able to fill in the concave-up profile of the continental shelf during a full interglacial, confirming the intense glacial-interglacial cyclicity of sedimentation on the continental slope inferred from seismic reflection profiles. The observed rapid deglaciation of the middle and outer shelf supports published numerical model results that the Antarctic Peninsula’s narrow interior and broad continental shelf make the ice sheet sensitive to imposed eustatic sea-level change. A low-profile marine-based ice sheet over the continental shelf during glacial maximum would have made a major contribution to that sensitivity, in the early stages of deglaciation. It follows that the Antarctic Peninsula ice sheet, and probably most others, are not so sensitive today.