Predictions are presented of secular changes in the geoid arising from glacial-isostatic adjustment (GIA) following the Last Glacial Maximum and from present-day mass changes in the Greenland Ice Sheet (GIS). Geoid displacement from ongoing GIA is dominated by ice-load changes outside of Greenland at lower spherical-harmonic degrees (2000 m). Spatial variability is noted when the present-day GIS response is expanded to degree and order 32. This is detectable by GRACE when assuming an optimistic accuracy, but is too small by a factor of ca. 3 for an alternate accuracy estimate. Present-day GIS geoid displacement rates are generally less than the equivalent response from ice-mass changes in Antarctica, Patagonia and Alaska.