We present gravitationally self-consistent predictions of sea level change that would follow the disappearance of either the West Antarctic Ice Sheet (WAIS) or marine sectors of the East Antarctic Ice Sheet (EAIS). Our predictions are based on a state-of-the-art pseudo-spectral sea level algorithm that incorporates deformational, gravitational and rotational effects on sea level, as well as the migration of shorelines due to both local sea-level variations and changes in the extent of marine-based ice cover. If we define the effective eustatic value (EEV) as the geographically uniform rise in sea level once all marine-based sectors have been filled with water, then we find that some locations can experience a sea level rise that is ∼40 per cent higher than the EEV. This enhancement is due to the migration of water away from the zone of melting in response to the loss of gravitational attraction towards the ice sheet (load self-attraction), the expulsion of water from marine areas as these regions rebound due to the unloading, and the feedback into sea level of a contemporaneous perturbation in Earth rotation. In the WAIS case, this peak enhancement is twice the value predicted in a previous projection that did not include expulsion of water from exposed marine-sectors of the West Antarctic or rotational feedback. The peak enhancements occur over the coasts of the United States and in the Indian Ocean in the WAIS melt scenario, and over the south Atlantic and northwest Pacific in the EAIS scenario. We conclude that accurate projections of the sea level hazard associated with ongoing global warming should be based on a theory that includes the complete suite of physical processes described above.