Stratospheric ozone can be measured with good global coverage and good vertical resolution by continuous scanning of the limb of the sunlit atmosphere. In the near future there will be several satellite instruments exploiting this limb-scanning method using the UV-visible region of the spectrum, e.g., the Optical Spectrograph and Infrared Imaging System (OSIRIS) launched on the Odin satellite in February 2001, and the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography launched on Envisat in March 2002. Envisat also carries the Global Ozone Monitoring by Occultation of Stars instrument, which will measure limb-scattered sunlight under bright limb occultation conditions. In this paper we present an inversion method to retrieve vertical ozone profiles from limb scatter measurements. The method uses a modified onion-peeling approach. Multiple scattering is taken into account by a precalculated total to single-scattering radiance ratios tabulated as a function of wavelength, tangent altitude, and several other relevant parameters. The sensitivity of the retrieval method is studied using the OSIRIS instrument as an example. Constituent retrieval errors are estimated by applying the method to simulated OSIRIS measurements.