The present-day velocity of true polar wander (TPW) and the displacement of the axis of rotation of the Earth in response to ice ages, resulting from stratified, viscoelastic Earth models, are sensitive to the nonadiabatic density gradient in the mantle. Previous studies, based on a fully nonadiabatic, or chemically stratified mantle, overestimated the present-day TPW for lower mantle viscosities in the range 1021--1022 Pa s. For a density profile in agreement with the reference seismological model, where nonadiabaticity is confined to the transition zone between 420 and 670 km, the predicted present-day TPW for viscosities on the order of 1021 Pa s is 0.65--0.9 deg/Myr, substantially lower than the 3.0 deg/Myr obtained for the chemical mantle. This decrease is due to the lack of an isostatic restoring force in the adiabatic case or to a global reduction of the buoyancy, which favors the attainment of rotational equilibrium. The correctness of this physical interpretation is demonstrated by the behavior of a fully adiabatic phase change that can be satisfactorily modeled by deleting the buoyancy restoring modes due to chemical density contrasts. This finding provides quantitative support to the procedure used in previous studies to simulate the rotational behavior of an adiabatic transition zone by simply deleting the buoyancy modes triggered by the (chemical) density contrasts at 670 km, as done by Mitrovica and Milne <1998> for present-day TPW and by Ricard and Sabadini <1990> for long-term TPW driven by mantle density anomalies. The reduction of present-day TPW induced by the Pleistocenic deglaciation, for an adiabatic mantle with nonadiabatic density gradients due to phase changes localized in the transition zone, impacts the inversion of the lower mantle viscosity. Predictions based on such a model are characterized by two best fit values in proximity of 1021 and 1022 Pa s, resembling the behavior of the time derivative of the second-degree component of the gravity field. The reduction of predicted present-day TPW due to Pleistocene deglaciation suggests that other mechanisms, such as present-day ice mass instability in Antarctica and Greenland, are presently contributing to the drift of 0.9 deg/Myr of the axis of rotation toward Newfoundland. The secular drift of the adiabatic mantle model during the continuous occurrence of ice ages is increased by 50% with respect to the chemically stratified one, showing a longer decay time after termination of the ice cycles. This mantle model confirms that ice cycles cannot be the major source of TPW for timescales of 106--107 years.