An onion-peeling iterative, least-squares relaxation method to retrieve mixing ratio profiles from limb thermal emission spectra is presented. The method has been tested on synthetic data, containing various amounts of added random noise for O(3), HNO(3), and N(2)O. The retrieval method is used to obtain O(3) and HNO(3) mixing ratio profiles from high-resolution thermal emission spectra. Results of the retrievals compare favorably with those obtained by others.