We have calculated the thermopower of the Bi2Sr2CuO6 and Bi2Sr2CaCu2O8 superconductors using an ARPES-derived dispersion, with a model pseudogap, and a marginal-Fermi liquid scattering rate that has a minimum with respect to energy at the van Hove singularity (vHs). Good fits with data are achieved across the entire phase diagram, thus confirming the dispersions, the locations of the vHs and the dominance of the diffusion thermopower over the phonon drag contribution.