A formal inverse procedure is used to infer radial mantle viscosity profiles from several observations related to the glacial isostatic adjustment process. The data sets consist of Late Pleistocene and Holocene sea level data from Scandinavia, the Barents Sea, Central Europe, Canada, and the far field, as well as observations of changes in the Earth's rotation and gravitational field, and present-day uplift and gravity changes in Scandinavia. Inferences of mantle viscosity are robust against assumptions such as the a priori viscosity model and model discretization. However, the quality of ice sheet reconstruction remains crucial for the inverse inference. The importance to discuss regional mantle viscosity models in view of the lateral variability in mantle properties has been evident. Our inference suggests a two order of magnitude increase of mantle viscosity with depth, and volume-averaged upper and lower mantle viscosities around 7 ¿ 1020 and 2 ¿ 1022 Pa s, respectively. Mantle viscosity does not need to increase sharply across the 660-km seismic discontinuity. The viscosity profiles suggested are also able to reconcile the large-scale geoid anomaly related to mantle convection.