Accurate solutions to the scalar equation of transfer in a homogeneous layer with optical thickness 2.5 «= r* «= ~ are obtained numerically for phase functions with large forward and backward peaks The Neumann series solution and the doubling method of van de Huist are employed. The results are presented graphically and are compared with intensities computed by the small-angle method of Roma- nova and with fluxes computed by Eddington's approximation, the Schuster-Schwarzschild approximation and with a modified two-stream approximation. Romanova's method appears quite accurate, but the last three approximations must be used with care for single-scattering albedos less than unity