Equation-of-state (EOS) modeling, whereby the seismic properties of a specified thermochemical structure are constructed from mineral physics constraints, and compared with global seismic data, provides a potentially powerful tool for distinguishing between plausible mantle structures. However, previous such studies at lower mantle depths have been hampered by insufficient evaluation of mineral physics uncertainties, overestimation of seismic uncertainties, or biases in the type of seismic and/or mineral physics data used. This has led to a wide, often conflicting, variety of models being proposed for the average lower mantle structure. In this study, we perform a thorough reassessment of mineral physics and seismic data uncertainties. Uncertainties in both the type of EOS, and mineral elastic parameters, used are taken into account. From this analysis, it is evident that the seismic variability due to these uncertainties is predominantly controlled by only a small subset of the mineral parameters. Furthermore, although adiabatic pyrolite cannot be ruled out completely, it is problematic to explain seismic velocities and gradients at all depth intervals with such a structure, especially in the interval 1660–2000 km. We therefore consider a range of alternative thermal and chemical structures, and map out the sensitivity of average seismic velocities and gradients to deviations in temperature and composition. Compositional sensitivity is tested both in terms of plausible end-member compositions (e.g., MORB, chondrite), and via changes in each of the five major mantle oxides, SiO₂, MgO, FeO, CaO, and Al₂O₃. Fe enrichment reduces both P and S velocities significantly, while Si enrichment (and Mg depletion) increases P and S velocities, with a larger increase in P than in S. Using purely thermal deviations from adiabatic pyrolite, it remains difficult to explain simultaneously all seismic observations. A superadiabatic temperature gradient does improve the seismic fit in the lowermost mantle, but should be accompanied by concurrent bulk chemistry changes. Our results suggest that the most plausible way to alter bulk chemistry in the lowermost mantle, simultaneously fitting density, bulk velocity and shear velocity constraints, is an increasing contribution of a hot, basalt-enriched component with depth.