The effect of different muffling environments on the structure and dielectric losses of Ba(Zn1/3Nb2/3)O-3 (BZN) microwave ceramics was investigated. The microwave dielectric losses of stoichiometric BZN pellets heated in ZnO-rich environments were severely degraded (e.g. Q x f similar to 15 000 in ZnO powder) compared with samples muffled in their own powder (Q x f similar to 80 000). Structure analyses and gravimetric measurements confirmed that the ceramics muffled in ZnO powder or vapor absorb excess ZnO to form non-stoichiometric solid solutions with reduced cation order and Q. By using starting compositions in the (1-x) BZN-(x) BaNb4/5O3 binary (x = 0.04), the stoichiometry can be tailored to ensure that after the uptake of ZnO, the ceramics remain well ordered and are located in a high Q region of the system. For example, ZnO-vapor-protected (0.96)BZN-(0.04)BaNb4/5O3 reached a very high Q x f (similar to 105 000) after sintering at 1400 degrees C for 5 h.