We report highly efficient cw performance of a Co:MgF//2 laser operating over the wavelength range 1. 5 mu m to 2. 0 mu m. This is an inherently low-gain laser but it is nevertheless an important candidate as a useful source for 1. 55 mu m. We have been successful in growing high quality crystals of MgF//2 with a relatively high Co**2** plus concentration (approximately 4%) which has enabled us to obtain up to 31% energy conversion from a cw Nd:YAG pump laser operating TEM//0//0 at 1. 3 mu m. We obtain 330 mW at 1. 55 mu m using 1. 4% output coupling, and 1 W at 1. 86 mu m using 3. 6% output coupling.