Three methods for estimating the vertical distribution of ozone below 10 mb, by inverting the equation of radiative transfer, are presented. The methods are discussed in terms of spectral measurements of back-scattered ultraviolet radiation and allow for all orders of scattering, as well as polarization of the diffusely reflected sunlight. These methods are compared with a statistical method for both 0% and 5% random measurement errors. There were no significant improvements using methods based on the inversion of the radiative transfer equation compared with the statistical method.