The methodology of spectroscopic remote sensing with high-resolution Fourier-transform spectra obtained from low Earth orbit by the Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment is discussed. During the course of the Atmospheric Laboratory for Applications and Science (ATLAS) shuttle missions (1992-1994) a flexible, yet reproducible, retrieval strategy was developed that culminated in the near-real-time processing of telemetry data into vertical profiles of atmospheric composition during the ATLAS-3 mission. The development, evolution, robustness, and validation of the measurements are presented and assessed with a summary comparison of trace-gas observations within the Antarctic polar vortex in November 1994.