We report high-resolution infrared laser spectra of the Ne, Ar, Kr-HF binary complexes solvated in liquid helium droplets. The present experiments show that the vibrational relaxation rates become progressively faster in the series Ne, Ar, and Kr-HF. Ar-HF is an intermediate case, with vibrational relaxation occurring on the time scale of the flight time of the droplets through the apparatus (0.5 ms). In this case, the data show that the relaxation rate is also dependent upon the size of the helium droplet in which the complex is solvated.