At the centres of previously glaciated regions such as Hudson Bay in Canada and the Gulf of Bothnia in Fennoscandia, it has been observed that the sea level history follows an exponential formand that the associated decay time is relatively insensitive to uncertainty in the ice loading history. We revisit the issue of decay time sensitivity by computing relative sea level histories for Richmond Gulf and James Bay in Hudson Bay and Angerman River in Sweden for a suite of reconstructions of the North American and Fennoscandian Ice Sheets and Earth viscosity profiles. We find that while some Earth viscosity models do indeed show insensitivity in computed decay times to the ice history, this is not true in all cases. Moreover, we find that the location of the study site relative to the geometry of the ice sheet is an important factor in determining ice sensitivity, and based on our set of ice sheet reconstructions, conclude that the location of James Bay is not well-suited to a decay time analysis. We describe novel corrections to the RSL data to remove the effects associated with the spatial distribution of sea level indicators as well as for other signals unrelated to regional ice loading (ocean loading, rotation and global mean sea level changes) and demonstrate that they can significantly affect the inference of viscosity structure. We performed a forward modelling analysis based on a commonly adopted 2-layer, sublithosphere viscosity structure to determine how the solution space of viscosity models changes with the input ice history at the three study sites. While the solution spaces depend on ice history, for both Richmond Gulf and Angerman River there are regions of parameter space where solutions are common across all or most ice histories, indicating low ice load sensitivity for these mantle viscosity parameters. For example, in Richmond Gulf, upper mantle viscosity values of (0.3-0.5)x10(21) Pa s and lower mantle viscosity values of (5-50)x10(21) Pa s tend to satisfy the data constraint consistently for most ice histories considered in this study. Similarly, the Angerman River solution spaces contain a solution with an upper mantle viscosity of 0.3 x 10(21) Pa s and lower mantle viscosity values of (5-50)x10(21) Pa s common to 9 of the 10 ice histories considered there. However, the dependence of the viscosity solution space on ice history suggests that joint estimation of ice and Earth parameters is the optimal approach.