A 10 kHz, broadly tunable (305-334 nm) Ce3+:LiLuF4 laser is found to flip polarization when tuning about the long wavelength peak at 327 nm. We now present investigations into this behavior which show that at 327 nm the sigma-polarized small signal gain is higher than pi polarized small signal gain thus accounting for the polarization flipping. However it was also found that when the laser cavity forced sigma-polarized laser oscillation the laser output was smaller than that obtained when pi-polarized laser oscillation was forced, indicating the presence of a polarization specific loss. Absorption studies of Ce:LiLuF suggest that there is a large ESA cross-section for sigma-polarization. The presence of this polarization-specific ESA would account for the reduction in power extraction efficiency for sigma-polarized lasing resulting in the relatively low output powers obtained when the laser flips to sigma-polarization. (C) 2000 Optical Society of America.