Transient optoelectronic measurements were used to evaluate the factors determining the open-circuit voltage of a series of planar photovoltaic devices based on hybrid perovskite layers with varying iodine/bromine ratios. Employing differential charging and transient photovoltage measurements, we used a simple device model based on the charge-carrier-density dependence of nongeminate recombination to re-create correctly not only the measured device open-circuit voltage (VOC) as a function of light intensity but also its dependence on bromine substitution. The 173 (±7) mV increase in device voltage observed with 20% bromine substitution is shown to result from a 227 (±8) mV increase in effective electronic band gap, which was offset in part by a 56 (±5) mV voltage loss due to faster carrier recombination. The faster recombination following 20% bromine substitution can be avoided by indene–C60 bisadduct (ICBA) substitution into the [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) electron-collection layer, resulting in a further 73 (±7) mV increase in device VOC. These results are consistent with surface recombination losses at the perovskite/fullerene interface being the primary limitation on the VOC output of bromine-substituted devices. This study thus presents, and experimentally validates, a simple model for the device physics underlying voltage generation in such perovskite-based solar cells and demonstrates that this approach can provide key insights into factors limiting this voltage output as a function of material energetics.