A dispersed shock wave may be defined as one in which finite changes occur over distances large compared to the mean free path in the gas. In contrast a shock wave in air extends over only a few mean free paths. When internal motions in a molecule are excited rather slowly by collisions, as is the case for molecular vibration, the shock wave may be partly dispersed; then, the sharp shock front is followed by a diffuse tail leading to complete thermal equilibrium. Alternatively, it may be fully dispersed, so that adjustments in the energy in all the degrees of freedom proceed slowly and in parallel. The purpose of this note is to point out that within a narrow speed range, from a shock Mach number of 1 to 1.042, shocks in carbon dioxide are fully-dispersed in the above sense. Such waves have been observed experimentally using a shock tube and interferometer. The possible existence of such waves was first pointed out by Bethe & Teller (1941) purely as a matter of academic interest. This note treats the problem in the same spirit.