The low-temperature rotational relaxation of CO in self-collisions and in collisions with the rare-gas atoms Ne and He has been investigated in supersonic expansions with a combination of resonance-enhanced multiphoton ionization (REMPI) spectroscopy and time-of-flight techniques. For the REMPI detection of CO, a novel 2 + 1' scheme has been employed through the A(1)Pi state of CO. From the measured data, average cross sections for rotational relaxation have been derived as a function of temperature in the range 5-100 K. For CO-Ne and CO-He, the relaxation cross sections grow, respectively, from values of similar to 20 and 7 angstrom(2) at 100 K to values of similar to 65-70 and -20 angstrom(2) in the 5-20 K temperature range. The cross section for the relaxation of CO-CO grows from a value close to 40 angstrom(2) at 100 K to a maximum of 60 angstrom(2) at 20 K and then decreases again to 40 angstrom(2) at 5 K. These results are qualitatively similar to those obtained previously with the same technique for N-2-N-2, N-2-Ne, and N-2-He collisions, although in the low-temperature range (T < 20 K) the CO relaxation cross sections are significantly larger than those for N-2. Some discrepancies have been found between the present relaxation cross sections for CO-CO and CO-He and the values derived from electron-induced fluorescence experiments.