We discuss the isostatic adjustment of the earth in response to Pleistocene deglaciation, and derive constraints on the earth's viscosity profile. We model the earth as viscoelastic, self-gravitating, realistically stratified and spherically symmetric. It is shown that the earth's relaxation eigenspectrum, besides possessing a small set of well-known discrete modes, also includes infinitely dense sets of modes (a continuous spectrum) which separate into classes that depend on the principal restoring force of the mode. Methods for estimating the continuous spectrum are discussed, and the effects on the predicted uplift are assessed. We find that the effects of the continuous spectrum are far less important than those of the discrete modes, though the presence of the continuous spectrum can make the discrete modes more difficult to identify. The continuous spectrum does become important when computing the rebound due to more recent loading, such as might be associated with present-day changes in polar ice. We use our model to refine predictions of the earth's response to Pleistocene glacial loading, with particular emphasis on implications for mantle viscosity. We have used time histories that are consistent with the recently recalibrated 14C time-scale. A special effort is made to match the geologic records of sea-level at sites in the vicinity of Hudson Bay. We find, consistent with the results of other authors, that the curvatures of the records are sensitive indicators of lower-mantle viscosity, but that there are inconsistencies between the records at different sites. However, we find we are also able to change the predicted curvatures by modifying the temporal and spatial distribution of the ice loads. If we assume a factor of 50 increase in viscosity between the upper and lower mantles, and if we assume that the ice on the eastern side of Hudson Bay melted a few thousand years later than the ice on the western side (a result consistent with recent geologic evidence), we are able to match the observed sea-level data about as well as we are able to, if we use, instead, a uniform mantle viscosity profile. A model with a factor of 50 jump in viscosity predicts a large free-air gravity anomaly over northern Canada that is reasonably consistent with what is observed, whereas a uniform viscosity model does not (though some authors have argued that the observed North American gravity anomaly may be mostly a consequence of mantle convection, and largely unrelated to postglacial rebound). Our objective here is not to present a preferred ice model or viscosity profile. Rather, we conclude only that the interpretation of the data is ambiguous, and that the mantle viscosity profile can not yet be uniquely inferred from them.