We outline a new parameterization which, when applied to RSL curves for sites within previously glaciated regions, yields a data set which is insensitive to details of the ice loading history over the region. The parameterization recognizes the exponential-like form of the RSL histories in such regions, and it provides a set of estimates for the characteristic decay time of that form. These estimates permit robust inferences of mantle viscosity below previously glaciated regions which are relatively unbiased by assumptions regarding the details off the surface ice cover. We apply the new parameterization to a small set of oft-studied RSL curves in N.E. Hudson Bay. Using forward and inverse analyse of the decay time estimates we derive constraints on the radial profile of mantle viscosity below the region, and assess a set of previously proposed models for the viscosity profile below the area.