A lasing method including the steps of providing a laser resonator; utilizing birefringence compensation in said resonator whereby said resonator is induced to operate in a Laguerre-Gaussian higher order mode; and utilizing polarized outcoupling of lasing energy at said higher order mode from said resonator. In the illustrative application, the laser resonator is a high-power, solid-state laser resonator. In the specific embodiment, the inventive method further includes the step of changing an outcoupling preference for a non-degenerate high-order Laguerre-Gaussian mode. In one embodiment, the step of changing outcoupling preference includes the step of changing an outcoupling polarization. In another embodiment, the step of changing outcoupling preference includes the step of changing an orientation of a roof edge of a prism in the laser resonator. Lower order Laguerre modes are discouraged from appearing in an output of the resonator by adding loss at the center of the rod aperture of the resonator or detuning the orientation of a first or a second quarter-wave plate. In the illustrative embodiment, the gain lifetime of the resonator is longer than an interpulse period thereof.