A primary difficulty in obtaining radiofrequency spectra is that the size of the quantum is usually much smaller than kT, so that upper and lower states of a transition have practically equal populations and any resulting absorption must be weak; absorption and stimulated emission rates will be very similar. This difficulty is circumvented by using a laser to depopulate one of the states, while a further gain is obtained by detecting a laser quantum (
v
≫kT/h) following absorption of a radiofrequency quantum (
v
≪kT/h). A carbon dioxide laser is used to saturate vibration-rotation transitions in the 10 μm region and, by using an expanded laser beam of diameter 35 mm and an interaction length of some 10 m, radiofrequency spectra are obtained at linewidths below 20 kHz. This approaches the limit implied by the transit time for a molecule traversing the laser beam, and contrasts strongly with earlier work using a radiofrequency cell within the laser cavity. A rate-equation model of the experiment is explored. The new resolution and precision available are applied to hyperfine transitions in the ground and
v
6
= 1 states of CH
3
I. It is shown that, although current hamiltonians represent most of the hyperfine structure well, a new term to represent vibration-nuclear magnetic coupling must be introduced. Finally, a new interpretation is put on the hyperfine spectrum of CH
3
CI.
