The accuracy and speed of three well-known computational techniques (DISORT, the δ–four-stream approximation, and the two-stream approximation), and the matrix inversion method, which is less well known, have been investigated. Results are presented for both broadband actinic and net fluxes over a range of parameters including solar zenith cosine, relative humidity, and altitude for two different surface/aerosol systems: terrestrial and oceanic. The matrix inversion method can only calculate actinic fluxes; therefore, this is the main focus of this paper. Investigations into the comparative accuracy of the four techniques for the oceanic model with and without a cloud layer included are also presented.(DISORT is taken as the benchmark for this research.)