The last deglaciation event of the current ice age, which began approximately 18,00 years ago and ended about 7000 years ago, continues to exert a profound influence on the vertical motion of the solid earth in and surrounding the regions which were once ice covered. Observations of such vertical motions may be employed to constrain the radial viscoelastic structure of the planet and therefore to contribute in an important way to the understanding of geodynamic processes in general. In this paper both present-day rates of vertical motion as recorded on the tide gauges and long time scale records of vertical motion as recorded in 14C-controlled relative sea level histories are employed to refine previously constructed models of the radial viscoelastic structure. An interesting sidelight to this analysis is the demonstration that the lower mantle viscosity inferred from the vertical motion data could represent a transient rather than the steady state value, a fact which would help considerably to reconcile the small viscosity stratification required by the glacial rebound data with the large stratification which seems to be required by some recent analyses of the geoid height anomalies associated with internal density heterogeneity of the mantle which has been revealed by application of seismic tomographic techniques. A further product of these new analyses is obtained by the application of the glacial isostatic adjustment model to filter this signal from the secular trends to relative sea level observed on tide gauges from both the east and west coasts of the North American continent. These results may be important in the context of recently proposed scenarios of climatic change.