In this paper, we present new methods of designing Bragg reflector structures using simple non-Maxwellian models for both cylindrical and spherical structures. This allows us to obtain an unloaded Q-factor of a few hundred thousand with a one-layer Bragg reflector resonator at room temperature and at microwave frequencies using low loss crystals. Design equations are verified using rigorous techniques such as Finite Element analysis, Method of Lines and Method of Moments.