Ice-age paleotopography and mantle viscosity can both be inferred from observations of Earth’s response to the most recent deglaciation event of the current ice age, This procedure requires iterative application of a theoretical model of the global process of glacial isostatic adjustment. Results demonstrate that the iterative inversion procedure converges to a paleotopography that is extremely close to that from the ICE-4G model. The accompanying mantle viscosity profile is furthermore shown to reconcile the requirements of aspherical geoid anomalies related to the mantle convection process, thus resolving a fundamental issue concerning mantle rheology. The combined model also explains postglacial sea level histories for the east coast of the United States.