We have constructed a thermomechanical model for upper mantle convection such that the thickness and structure of the lithosphere are determined self-consistently by the heat transported by convection. In this study of the interaction between the lithosphere and upper mantle, strongly temperature- and pressure-dependent rheologies for both Newtonian and non-Newtonian creep mechanisms are employed. For a strictly temperature-dependent rheology an insignificant amount of heat, less than 12.5 mW/m2, can be transported convectively for an interior viscosity, 0(1021 Pas), compatible with postglacial rebound. On the other hand, for similar values of the viscosity steady heat fluxes between 20 and 40 mW/m2 are produced by introducing pressure dependence into the rheology. For the temperature-and pressure-depenent flow law the horizontally averaged interior temperature displays very little variation with the amount of heat evacuated, once all of the rheological parameters are fixed. This finding may have important ramifications for parameterized convection. We employ both the single-mode, mean field approximation and the complete two-dimensional equations, using finite elements, to obtain solutions for the various types of rheologies. From evaluating the geophysically relevant observables, such as topography, free air gravity anomalies surface heat flow, and stress fields in the lithosphere, we find that the lateral variations of these quantitites predicted by a non-Newtonian rheology are much smaller than those derived from a linear rheology. These results suggest that surface variations of geophysical observables are more compatible with a non-Newtonian rheology in the upper mantle.