Leighton and Murray have argued that there is a polar reservoir of solid CO: on Mars that lasts throughout the year and whose vapor pressure determines the mean partial pressure of CO: in the atmosphere. This model is discussed in the light of recent data, and several difficulties emerge. First, such a system might be unstable, owing to the tendency of poleward heat transport to increase with atmospheric pressure. Second, the annual retreat of the CO: frost cover would be slower according to the model than that observed. Moreover, the observations seem to indicate that the residual polar cap that lasts throughout the year is composed of water ice rather than CO:. Finally, observations of water vapor in the atmosphere appear to be inconsistent with a permanent CO: cold trap in continuous existence for many years. These difficulties hold also for a CO: reservoir buried by water ice and for a hydrated CO: