Compensation of thermally induced birefringence directed toward compensation of depolarization and bifocusing in laser rods is treated with simple beam transfer matrices. When we apply a 90-deg polarization-rotating element to a resonator, the radial and the tangential eigensolutions of the resonator change significantly. The effect of this alteration on the resonator's stability is investigated in detail. The outcome is used to design a single- and double-rod resonator resulting in 53 W with an M2 approximately 1.5 and 182 W of output power with an M2 approximately 1.2, respectively.