The recently observed acceleration in the node of the orbit of the LAGEOS satellite has previously been shown to provide a good constraint on the viscosity of the earth's mantle beneath the 670-km seismic discontinuity. This paper explores then extent to which the previously inferred lower mantle viscosity may be traded off against variations of other properties of the radial viscoelastic structure. We show explicitly that the nontidal acceleration of rotation inferred from the LAGEOS data, and predicted as a consequence of the earth's response to the last deglaciation event of the current ice age, is relatively insensitive both to variations of lithospheric thickness and to the presence or absence of plausible chemical heterogeneity across the 670-km interface. It therefore provides a high-quality constraint on the viscosity of the deep mantle. With the upper mantle viscosity fixed at the nominal value of 1021 Pa s, the bounds on lower mantle viscosity &ngr;LM are such that 2¿1021 Pa s≤&ngr;LM≤~6¿1021 Pa s even when allowance is made for the presence of a viscous boundary layer at the base of the upper mantle such as would exist if the mantle convective circulation were layered.