An analytic model of transport and microphysics in the tropical tropopause layer (TTL) is extended to include stable isotopes of water. The model, running along trajectories, is tested against in situ and satellite observations of HDO and H218O in the Upper Troposphere and Lower Stratosphere (UT/LS). The model is able to reproduce the range of isotopic depletions observed in the data, and reproduce individual episodes that mirror or depart from Rayleigh fractionation processes. The results indicate that water substance in the upper troposphere does not follow a Rayleigh distillation model due to the presence of condensed phase water. Stratospheric abundances of stable isotopes of water can be understood based on known isotopic physics, convective transport of ice, and gradual dehydration.