Recent first-principles calculations have shown that a simple DOS scattering model, wherein the electronic scattering rates are assumed to be proportional to the density-of-states, better approximates the true scattering properties than the commonly used constant relaxation-time and constant mean-free-path approximations. This work investigates how the thermoelectric properties predicted with the DOS model compare to the other two scattering models, using three analytical electron dispersions (parabolic band in 3D/2D/1D, Kane band in 3D/2D/1D, and ring-shaped quartic band in 2D). Our findings show that the scattering models can lead to significant differences, and can disagree about whether certain band structures can provide benefits. A constant relaxation-time is found to always be optimistic compared to a constant mean-free-path, while the DOS scattering model shows no such clear trend. Notably, the 1D parabolic band and 2D quartic band exhibit the highest power factors with the DOS model, resulting from a rapid decrease in density-of-states, and thus scattering -suggesting a possible strategy for improved thermoelectrics based on engineering band structures with sharp/discontinuous drops in density-of-states. This work highlights the importance of simple and accurate scattering models when rigorous ab-initio scattering calculations are not feasible. arXiv:1911.06414v1 [cond-mat.mtrl-sci]