Abstract. Motivated by the initial selection of a high-resolution solar occultation Fourier transform spectrometer (FTS) to fly to Mars on the ExoMars Trace Gas Orbiter, we have been developing algorithms for retrieving volume mixing ratio vertical profiles of trace gases, the primary component of which is a new algorithm and software for retrieving vertical profiles of temperature and pressure from the spectra. In contrast to Earth-observing instruments, which can rely on accurate meteorological models, a priori information, and spacecraft position, Mars retrievals require a method with minimal reliance on such data. The temperature and pressure retrieval algorithms developed for this work were evaluated using Earth-observing spectra from the Atmospheric Chemistry Experiment (ACE) FTS, a solar occultation instrument in orbit since 2003, and the basis for the instrument selected for a Mars mission. ACE-FTS makes multiple measurements during an occultation, separated in altitude by 1.5–5 km, and we analyse 10 CO₂ vibration–rotation bands at each altitude, each with a different usable altitude range. We describe the algorithms and present results of their application and their comparison to the ACE-FTS data products. The Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) provides vertical profiles of temperature up to 40 km with high vertical resolution. Using six satellites and GPS radio occultation, COSMIC's data product has excellent temporal and spatial coverage, allowing us to find coincident measurements with ACE with very tight criteria: less than 1.5 h and 150 km. We present an intercomparison of temperature profiles retrieved from ACE-FTS using our algorithm, that of the ACE Science Team (v3.5), and from COSMIC. When our retrievals are compared to ACE-FTS v3.5, we find mean differences between −5 and +2 K and that our retrieved profiles have no seasonal or zonal biases but do have a warm bias in the stratosphere and a cold bias in the mesosphere. When compared to COSMIC, we do not observe a warm/cool bias and mean differences are between −4 and +1 K. COSMIC comparisons are restricted to below 40 km, where our retrievals have the best agreement with ACE-FTS v3.5. When comparing ACE-FTS v3.5 to COSMIC we observe a cold bias in COSMIC of 0.5 K, and mean differences are between −0.9 and +0.6 K.