A new generation of near-infrared instruments, such as the Greenhouse Gases Observing Satellite (GOSAT) and the ill-fated Orbiting Carbon Observatory (OCO), aims to measure concentrations of trace gases through the high-resolution measurements of spectra of reflected sunlight. Accurate retrievals of trace gas amounts from these data present a computational challenge for the underlying radiative transfer algorithms because these algorithms must simulate the angle-dependent radiances at high spectral resolution within near-infrared gas absorption bands in scattering atmospheres. Such calculations can be prohibitively expensive for certain applications. Building upon previous work by others, we describe a simple yet accurate technique to accelerate the radiative transfer of many monochromatic wavelengths in the visible and near infrared. It is tested over a large variety of profile types, including cases with high solar zenith angle, large amounts of atmospheric scattering, highly polarizing, non-Lambertian surfaces, and bands with overlapping gases. Speed gains of 1–2 orders of magnitude are demonstrated, with typical errors less than 0.1% for most atmospheres and less than 0.5% for even the most challenging cases.