This paper presents a study of the spectroscopy of ({ }^{12} \mathrm{CF}{3}{ }^{79} \mathrm{Br}) using the Doppler-free saturated absorption technique. Many lines in the (\nu{1}) fundamental and (\nu_{1}+\nu_{6} \leftarrow \nu_{6}) hot band of this molecule have been recorded using the (9-\mu \mathrm{m}) band of a carbon dioxide laser. The absolute frequencies of the linecenters of these absorptions have been measured to an accuracy of (\pm 25 \mathrm{kHz}), using frequencies calibrated against a (4.3-\mu \mathrm{m}) fluorescence lock. Hyperfine structure due to the (\mathrm{Br}) nucleus has been resolved, the splittings between individual quadrupole components being measured to a precision of about (\pm 5 \mathrm{kHz}). Determination of these splittings provided the means for assignment of many of the lines when reference was made to a concurrent infrared-radiofrequency double resonance experiment. The saturation data were fitted to a vibration-rotation Hamiltonian including centrifugal terms up to sextic, to which was added a hyperfine Hamiltonian based on the one derived by Aliev and Hougen. c) 1993 Academic Press. Inc.