Bismuth-based solar absorbers have recently garnered attention due to their promise as cheap, nontoxic, and efficient photovoltaics. To date, however, most show poor efficiencies far below those seen in commercial technologies. In this work, we investigate two such promising materials, BiSI and BiSeI, using relativistic first-principles methods with the aim of identifying their suitability for photovoltaic applications. Both compounds show excellent optoelectronic properties with ideal band gaps and strong optical absorption, leading to high predicted device performance. Using defect analysis, we reveal the electronic and structural effects that can lead to the presence of deep trap states, which may help explain the prior poor performance of these materials. Crucially, detailed mapping of the range of experimentally accessible synthesis conditions allows us to provide strategies to avoid the formation of killer defects in the future.