The Optical Spectrograph and InfraRed Imaging System (OSIRIS) instrument on board the Odin spacecraft has been measuring limb-scattered radiance since 2001. The vertical radiance profiles measured as the instrument nods are inverted, with the aid of the SASKTRAN radiative transfer model, to obtain vertical profiles of trace atmospheric constituents. Here we describe two newly developed modes of the SASKTRAN radiative transfer model: a high-spatial-resolution mode and a Monte Carlo mode. The high-spatial-resolution mode is a successive-orders model capable of modelling the multiply scattered radiance when the atmosphere is not spherically symmetric; the Monte Carlo mode is intended for use as a highly accurate reference model. It is shown that the two models agree in a wide variety of solar conditions to within 0.2 %. As an example case for both models, Odin-OSIRIS scans were simulated with the Monte Carlo model and retrieved using the high-resolution model. A systematic bias of up to 4 % in retrieved ozone number density between scans where the instrument is scanning up or scanning down was identified. The bias is largest when the sun is near the horizon and the solar scattering angle is far from 90°. It was found that calculating the multiply scattered diffuse field at five discrete solar zenith angles is sufficient to eliminate the bias for typical Odin-OSIRIS geometries.