We present a simple theory of the gas-phase far-infrared collision-induced absorption spectra of two molecules with tetrahedral symmetry, methane (CH4) and tetrafluoromethane (CF4). We assume that in these molecules CIA arises through octopolar and hexadecapolar induction. By neglecting the small anisotropies in the intermolecular CH4-CH4and CF4-CF4potentials, we can express the spectral profiles as convolutions of single-molecule free rotation spectra with intermolecular translational components. Information theory is used to estimate the ‘least biased’ form for the latter, based on our knowledge of their spectral moments (the calculation of the zeroth through sixth moments is described in an appendix). In this way we avoid the need to make questionable assumptions about the system dynamics. The computed lineshapes are in excellent agreement with the available experimental data.