The record of sea-level change at Barbados derived from the dating of fossil corals1,2,3 has been used to argue that globally averaged, or eustatic, sea level during the Last Glacial Maximum was approximately 120 m below present3. This estimate is roughly 10 m lower than inferences based on sea-level data from other far-field sites4 and, if correct, would suggest that the Barbados record is a largely uncontaminated measure of eustasy3. However, these previous analyses1,2,3,4 were based on numerical corrections for glacial isostatic adjustment that adopted one-dimensional viscoelastic Earth models. Here we assess the impact of three-dimensional mantle viscoelastic structure on predictions of post-glacial sea-level change at Barbados. Our simulations indicate that the predictions are strongly perturbed by the presence of a high-viscosity slab associated with subduction of the South American Plate beneath the Caribbean Plate. The slab suppresses local deformation and reduces the sea-level rise predicted during the deglaciation phase. To accommodate this reduction while maintaining a fit to the Barbados sea-level record requires an excess ice volume at the Last Glacial Maximum equivalent to about 130 m of eustatic sea-level rise. Given a downward revision in estimates of the Antarctic ice sheet contribution5 to this excess ice volume, we conclude that a significant amount of Northern Hemisphere ice at the Last Glacial Maximum remains unaccounted for in sea-level-based ice sheetreconstructions.