Current understanding of Pleistocene ice-sheet history is based on collective inferences from three separate avenues of study: (1) the geologic and paleoceanographic records, (2) the isostatic record, and (3) the behaviour of contemporary glaciers and ice sheets. The geologic record provides good constraint on the areal extent of former ice sheets, while isostatic deflection patterns provide important information about late-glacial ice-sheet thickness. The picture emerging from geologic and isostatic deductions is suggestive of a thin and mobile Laurentide Ice Sheet relative to present-day Greenland and Antarctica. We model Laurentide Ice Sheet evolution through a glacial cycle to explore the glaciological mechanisms that are required to replicate the geologic and isostatic evidence. A number of glaciological processes important to the ice-sheet evolution are not fully understood, including marine-based ice dynamics, iceberg calving, rheologic properties of ice, and basal flow dynamics. We present a spectrum of glacial cycle simulations with different treatments of poorly constrained physical processes. We conclude that glaciological model reconstructions can only be reconciled with the late-glacial geologic record of a thin, low-sloping Laurentide Ice Sheet by invoking (1) extremely deformable ice, (2) widespread basal flow, or (3) paleoclimate–ice-sheet fluctuations which give last glacial maximum ice sheets that are far from equilibrium.