The formation of non-stoichiometric cubic perovskite solid solutions based on BaZn1/3Nb2/3O3 (BZN) was examined along 10 different directions in the BaO-ZnO-Nb2O5 ternary system. Limited ranges of non-stoichiometry were observed along several pseudo-binaries and the BZN structure can accommodate a variety of different types of defects. Although the deviations from stoichiometry are quite small, typically similar to 1 mole%, they induce large changes in the extent and stability of the 1:2 B-site ordering, the sintering and microstructure, and the dielectric loss properties. The highest Q x fs (similar to 110 000 at 8 GHz) in the system, which coincide with the highest degree of order, were located in two regions along the BZN-Ba5Nb4O15 and BZN-BaNb2O6 lines. The results of this study provide an explanation for the large variations in crystal structure and Q x fs previously reported for BZN and other related systems (e.g., Ba(Zn1/3Ta2/3)O-3), and demonstrate that non-stoichiometric starting compositions provide a route to the highest Q values.