We develop a series of models of transport in the upper tropical troposphere in order to explain the observed abundance and isotopic composition of stratospheric water vapor. We start with the Rayleigh fractionation process and add the effects of mixing and recirculation of stratospheric air through the upper troposphere. We compare our measurements with model calculations for a range of input parameters and find that the observations are best explained by a model that mixes vapor from roughly 11 km (carried aloft either as condensate or through radiative heating and uplift) with air that has been dehydrated (in a large convective system) to a mixing ratio substantially below the saturation mixing ratio of the mean tropical tropopause. The result is that while most of the moisture comes from convective outflow near 11 km, most of the air in the upper troposphere consists of dehydrated air from convective systems with cloud top temperatures below that of the mean tropical tropopause. We also find that the water vapor mixing ratio in the stratosphere is determined not only by the temperature of the tropical tropopause but also by the relative importance of radiative heating, recirculation of stratospheric air, and deep convection in supplying air to the upper troposphere. Our results show that water vapor isotope ratios are a powerful diagnostic tool for testing the results of general circulation models.