In global space geodetic solutions, radial site motions are usually estimated relative to the geocenter (the center of figure of the solid Earth). Most geodesists estimate the motion of the geocenter assuming both that sites do not move radially and that sites move laterally as predicted by plate motion model NUVEL-1A <DeMets et al., 1990, 1994>. Here we estimate the motion of the geocenter assuming that the plate interiors deform radially and laterally as predicted by the postglacial rebound model of Peltier <1994> or that of Peltier <1996> without assuming a priori knowledge about relative plate motion. Radial site motions estimated relative to this rebound-adjusted geocenter are in the same reference frame as the rebound model predictions, whereas site motions estimated without adjusting for rebound are not. We further constrain the motion of the rebound-adjusted geocenter using satellite laser ranging's sensitivity to the center of mass (of the solid Earth, the oceans, and the atmosphere) by assuming that the mean velocity between the rebound-adjusted geocenter and the center of mass is negligible over the time period of geodetic measurement. Twenty years of observation with satellite laser ranging and very long baseline interferometry record the isostatic response of the solid Earth to the unloading of the late Pleistocene ice sheets. The misfits of the postglacial rebound model of Peltier <1994> and that of Peltier <1996> are 34% and 16% less, respectively, than the misfit of the rigid plate model. Sites at Onsala (Sweden) and Algonquin Park (Ontario) are observed to be rising at 3 mm/yr and 2 mm/yr, respectively, reflecting unloading of the Fennoscandian and Laurentide ice sheets. Sites along the east coast of the United States are subsiding at <2 mm/yr, indicating that the forebulge produced by the Laurentide ice sheet is currently collapsing very slowly. Sites beneath the margins of the ice sheets during the last glacial maximum are currently moving laterally away from the ice sheet centers at <1.5 mm/yr, in disagreement with the moderately fast outward motion predicted by the model of Peltier <1996>. ¿ 1999 American Geophysical Union