We develop two algorithms for determining two inherent optical properties (IOPs) from radiometric measurements in vertically homogeneous waters. The first algorithm is for estimation of the ratio of the backscattering to absorption coefficients from measurements of only the vertically upward radiance and the downward planar irradiance at depths where the light field is in the asymptotic regime. The second algorithm enables estimation of the absorption coefficient from measurement of the diffuse attenuation coefficient in the asymptotic regime after use of the first algorithm. Multiplication of the two estimates leads to an estimate for the backscattering coefficient. The algorithms, based upon the use of a simplified phase function and the asymptotic eigenmode, are shown to potentially provide good starting conditions for iteratively determining the absorption and backscattering coefficients of a wide variety of waters. The uncertainty in the estimates defines a subspace for IOPs that may reduce ambiguity in such iterative solutions. Because of the ease of estimating the backscattering to absorption ratio from in-water measurements, this IOP deserves further investigation as a proxy for biogeochemical quantities in the open ocean.