The diffractive effects of a single laser rod in an unstable super-Gaussian coupled cavity are modeled for a range of cavity configurations, with an intracavity, zero-thickness aperture. After fundamental mode propagation through a maximally flat output coupler, beam quality (M2) and far-field power loss values are related. Beam quality is most sensitive to cavity magnification and aperture Fresnel number, both correlated to the aperture-equivalent Fresnel number. In contrast, variation of M2 with aperture position is sufficiently conservative to predict the intensity profile of a solid-state laser with a typical gain length, in good agreement with experimental data.