This work describes transport and thermodynamic processes that control water vapor near the tropopause during the SAGE III-Ozone Loss and Validation Experiment (SOLVE), held during the Arctic 1999/2000 winter season. Aircraft-based water vapor, carbon monoxide, and ozone measurements are analyzed so as to establish how deeply tropospheric air mixes into the Arctic lowermost stratosphere and what the implications are for cloud formation and water vapor removal in this region of the atmosphere. There are three major findings. First, troposphere-to-stratosphere exchange extends into the Arctic stratosphere to about 13 km. Penetration is to similar levels throughout the winter; however, because ozone increases with altitude most rapidly in the early spring, tropospheric air mixes with the highest values of ozone in that season. The effect of this upward mixing is to elevate water vapor mixing ratios significantly above their prevailing stratospheric values of about 5 ppmv. Second, the potential for cloud formation in the stratosphere is highest during early spring, with about 20% of the parcels which have ozone values of 300--350 ppbv experiencing ice saturation in a given 10 day period. Third, during early spring, temperatures at the tropopause are cold enough so that 5--10% of parcels experience relative humidities above 100%, even if the water content is as low as 5 ppmv. The implication is that during this period, dynamical processes near the Arctic tropopause can dehydrate air and keep the Arctic tropopause region very dry during early spring.