We describe a new inversion algorithm for retrieving ozone densities and aerosol extinctions from SAGE II measurements.  The primary differences between the new algorithm and the current operational SAGE II inversion are the order of the species and altitude inversions, and the methods used to calculate aerosol  extinction and remove saturated signals.  Ozone densities retrieved at altitudes from 15 to 30 km using the new algorithm are compared to those from the operational SAGE II inversion, as well as to ozone densities from coincident balloon ozonesonde measurements at four different locations in the northern hemisphere between 1984 and 1991.  The results of the comparison show that the ozone densities resulting from the operational and new algorithms agree to within 1% above 22 km.  Below 22 km, the new results are lower than the operational results by up to 30%, depending on altitude and location.  At all four stations the new results agree better with the sondes, decreasing the SAGE II/sonde differences by a factor of two or more.