We present a new parameter retrieval algorithm for Mars Global Surveyor Thermal Emission Spectrometer data. The algorithm uses Newtonian first-order sensitivity functions of the infrared spectrum in response to variations in physical parameters to fit a model spectrum to the data at 499, 1099, and 1301 cm(-1). The algorithm iteratively fits the model spectrum to data to simultaneously retrieve dust extinction optical depth, effective radius, and surface temperature. There are several sources of uncertainty in the results. The assumed dust vertical distribution can introduce errors in retrieved optical depth of a few tens of percent. The assumed dust optical constants can introduce errors in both optical depth and effective radius, although the systematic nature of these errors will not affect retrieval of trends in these parameters. The algorithm does not include the spectral signature of water ice, and hence data needs to be filtered against this parameter before the algorithm is applied. The algorithm also needs sufficient dust spectral signature, and hence surface-to-atmosphere temperature contrast, to successfully retrieve the parameters. After the application of data filters the algorithm is both relatively accurate and very fast, successfully retrieving parameters, as well as meaningful parameter variability and trends from tens of thousands of individual spectra on a global scale (Elteto, A., Toon, O.B. [2010]. Icarus, this issue). Our results for optical depth compare well with TES archive values when corrected by the single scattering albedo. Our results are on average 1-4 K higher in surface temperatures from the TES archive values, with greater differences at higher optical depths. Our retrieval of dust effective radii compare well with the retrievals of Wolff and Clancy (Wolff, M.J., Clancy, R.T. [2003]. J. Geophys. Res. 108 (E9), 5097) for the corresponding data selections from the same orbits. (C) 2010 Elsevier Inc. All rights reserved.