A simple, unitary distorted-wave method is used to investigate vibrationally inelastic collisions in He-CO and HE-HF. This approach is reasonably accurate yet significantly faster than close coupling. Because the approach is fully analytic, no computational difficulties occur near threshold energies as is commonly the case with close-coupling schemes. Moreover, unlike simple perturbative approaches, the present method conserves probability and treats the coupling to infinite order in the potential strength so that multiquanta transitions are provided. Inelastic cross sections for energies up to 10 eV and relaxation rate constants for temperatures up to 3800 K are computed and compared to close-coupling and experimental results. Qualitative features such as Landau-Teller rate behavior are correctly reproduced, and, in the high temperature limit where the present approach is applicable, reasonable quantitative agreement is found between computed and measured rates for He-CO. Computed He-HF rates are smaller than predicted by experiment but exhibit the correct temperature dependence (slope) on Landau-Teller plots. Because of its large energy spacing, H-F is significantly more quantum-like in nature than CO and may therefore require special computational consideration. In particular, vibrational-rotational coupling effects ignored in this treatment may be significant for He-HF.