New bromide compounds A2BIBIIIBr6 with a double perovskite structure provide variety and flexibility of optoelectronic properties, and some of them are of poor toxicity in comparison with such popular lead halides. The promising compound with a double perovskite structure was proposed recently for the ternary system of CsBr-CuBr-InBr3. Analysis of phase equilibria in the CsBr-CuBr-InBr3 ternary system showed stability of the quasi-binary section of CsCu2Br3–Cs3In2Br9. Formation of the estimated phase Cs2CuInBr6 by melt crystallization or solid-state sintering was not observed, most likely, as a result of higher thermodynamic stability of binary bromides CsCu2Br3 and Cs3In2Br9. The existence of three quasi-binary sections was observed, while no ternary bromide compounds were found.