All-inorganic perovskites (such as CsPbI₃) are emerging as new candidates for photovoltaic applications. Unfortunately, this class of materials present two important weaknesses in their way to commercialization: poor stability and toxicity. This paper explores the possibility of lessening both stability and toxicity related problems, as well as obtaining improved photovoltaic efficiencies through the propitious fine-tuning of the chemical composition. Therefore, a systematic ab initio study of the family of all-inorganic perovskites with the general formula Rb_aCs_1−aSn_bPb_1−bI₂Br (a = 0–0.125 and b = 0–1) is here presented. Our results provide a complete description on the connections between the chemical composition, crystal structure, intrinsic stability, electronic properties, and absorption features, pointing out that all-inorganic Rb_aCs_1−aSn_bPb_1−bI₂Br (a = 0.125 and 1 > b > 0.5) perovskites would be adequate candidates for photovoltaic applications with improved stability and reduced Pb concentration.