We present a comprehensive characterization of a laser, based on a high-quality heavily doped Yb:YLF crystal. The analysis includes the comparison of the laser efficiency in respect of the absorbed pump for both pi and sigma-polarization. In particular, for the tunable laser, we report an enhancement of the tuning range obtained by adapting the output coupler transmission in respect of the lasing wavelength. The experimental results obtained for various output coupling have also been compared with a numerical model in order to give information for a further enlargement of the tuning range.