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The balance of photogeneration and recombination gives rise to an optimum bandgap for any solar cell. The radiative limit represents the lowest permissible level of recombination in a solar cell and, therefore, places an upper limit on the voltage that can be attained. Introducing additional nonradiative recombination results in a loss in voltage that can only be compensated for by moving to higher bandgaps. Consequently, the optimal bandgap for solar energy conversion will rise with increasing nonradiative recombination rate. This balance was recognized by Shockley and Queisser for single-junction solar cells and is here extended to multijunction solar cells. A rise in optimal bandgaps has been observed in simulated single-, double-, and triple-junction devices as nonradiative recombination increases. Optimal bandgaps between excellent and poor diode quality devices are shown to differ by 100s of meV under 1-sun illumination with both terrestrial and extraterrestrial spectra but exhibit no significant change at high concentration due to the dominance of the radiative component in the recombination dynamics.