Our iterative inversion algorithm for retrieving absorption a(z) and backscattering b(b)(z) from profiles of upwelling and downwelling irradiance, on the basis of assuming a depth-independent phase function for the medium, was found to have unsatisfactory accuracy for b(b)(z) in clear waters. We modified the algorithm here by assuming a depth-independent phase function for the particles and then performing an additional iteration over the fraction of total scattering that is due to the water itself. The modified algorithm's accuracy is considerably improved over the original in clear waters and reduces to the original in waters for which the particle contribution to b(b)(z) is dominant.