A number of previous analyses have suggested that the relative sea level record in Hudson Bay constrains the viscosity of the lower mantle to be near 1021 Pa s. These conclusions have been based on a limited number of forward calculations which have assumed an isoviscous lower mantle region. We compute Frechet kernels for the RSL data in Hudson Bay to determine the detailed depth-dependent sensitivity of the data to variations in a viscosity profile which is consistent with the past inferences. We find that the RSL data provide a robust constraint on the average viscosity in the top half of the lower mantle only (the average must be near 1021 Pa s). The data are less sensitive to variations in the viscosity below approximately 1800 km depth and in the upper mantle. Forward analyses included herein show that the data admit models whose average viscosity in the deep mantle (below 1800 km depth) and in the upper mantle can differ significantly from the value (near 1021Pa s) estimated for the top half of the lower mantle. The total variation in the viscosity from the surface to the CMB can exceed an order of magnitude or more and still satisfy the constraint provided by the Hudson Bay RSL data set. The necessity of invoking an isoviscous mantle model in previous studies is thus seen to be a consequence of the limited class of viscosity model solutions employed in those studies. ¿ American Geophysical Union 1992