We report for the first time to our knowledge an experimental demonstration of wavelength self-tuning in a K5Nd(MoO4)4 broadband-emitting laser crystal (KNM), as well as a theoretical treatment of the system based on its birefringence properties. The self-frequency-tuning of the laser along the full spectral range of the KNM crystal was obtained by rotating a birefringent gain plate in its own plane. The gain plate was placed inside a resonator at Brewster's angle. The tuning characteristics of the spectral filter were obtained by use of the Jones vector formalism. The calculated wavelength-selective tuning precisely matches the experimental observations.