Data from the Mars Orbiter Camera experiment on Mars Global Surveyor show that the 2001 spring regression of the Mountains of Mitchel, a bright region in the south polar cap of Mars, was faster than in 1999. Those two years differed in that a large spring dust storm occurred in 2001, while 1999 was relatively dust free. We have modeled the effects of atmospheric dust on the CO2 sublimation rate, using a Monte Carlo radiative transfer model. We explicitly accounted for the two major effects of atmospheric dust: 1) reduction of the direct solar heating and 2) the opposing increase in the absorption of IR thermal dust emission by the surface. Our modeling supports the hypothesis that this year's faster regression of the Mountains of Mitchel was related to the early spring global dust storm.