Organohalide-perovskite solar cells have emerged as a leading next-generation photovoltaic technology. However, despite surging efficiencies, many questions remain unanswered regarding the mechanisms of operation. Here we report a detailed study of the electro-optics of efficient CH3NH3PbI3-perovskite-only planar devices. We report the dielectric constants over a large frequency range. Importantly, we found the real part of the static dielectric constant to be ∼70, from which we estimate the exciton-binding energy to be of order 2 meV, which strongly indicates a non-excitonic mechanism. Also, Jonscher's Law behaviour was consistent with the perovskite having ionic character. Accurate knowledge of the cell's optical constants allowed improved modelling and design, and using this information we fabricated an optimized device with an efficiency of 16.5%. The optimized devices have ∼100% spectrally flat internal quantum efficiencies and minimal bimolecular recombination. These findings establish systematic design rules to achieve silicon-like efficiencies in simple perovskite solar cells.