This work presents a study of a fully nonastigmatic design of a single-longitudinal-mode, wavelength-tunable, unidirectional alexandrite ring laser cavity and assessment of its performance compared to more complex laser design requiring astigmatism compensation. A “displaced mode” nonastigmatic laser cavity design eliminating astigmatic cavity elements is developed around an alexandrite crystal end-pumped by a low-brightness, high-power red diode laser pump system. Single-longitudinal-mode, continuous-wave operation is demonstrated with output power of 700 mW with an excellent TEM00 mode (M2<1.1) across a wide pump power range. Wavelength tuning from 748–773 nm is produced using a birefringent filter plate. The nonastigmatic alexandrite laser design achieves better spatial quality and resilience to maintain TEM00 operation across wide variation in pump-induced lensing compared to the astigmatic design. To the best of our knowledge, this is the first wavelength-tunable, single-longitudinal-mode operation of a unidirectional alexandrite ring system in a fully nonastigmatic cavity regime.