We use a Lagrangian, one-dimensional cloud model to simulate ice cloud formation and dehydration along trajectories in the tropical tropopause layer (TTL). Time-height curtains of temperature along the trajectory paths are extracted from meteorological analyses. The temperatures are adjusted near the tropopause such that the spatial average cold point temperature matches tropical radiosonde measurements. Temperature perturbations due to Kelvin waves, Rossby gravity waves, and high-frequency gravity waves are superimposed. The cloud model tracks the growth and sedimentation of individual ice crystals. Ice number densities in the cloud simulations without waves range from 1 cm-3) and smaller crystals (1--10 ¿m radius), resulting in less sedimentation but still effective dehydration overall. Inclusion of wave-driven temperature oscillations decreases the final TTL H2O mixing ratio somewhat primarily because the wave perturbations decrease the tropical average cold point tropopause temperature by ~0.75 K. Ultimately, air rising through the TTL is effectively dehydrated with or without wave perturbations. In general, the model results suggest that the final water vapor mixing ratios are primarily controlled by the minimum temperatures encountered by parcels and that they are relatively insensitive to factors such as the wave-driven temperature variability, the supersaturation threshold for ice nucleation, and the rate of ascent through the tropopause layer. However, the frequency and geographical distribution of cloud formation is very sensitive to these parameters. On average, the clouds dehydrate the air along trajectories down to mixing ratios ~10--40% higher than the temperature minimum saturation mixing ratio. The simulations predict efficient freeze-drying of air by cloud formation within the TTL: For the December--January 1995/1996 period simulated the average final H2O mixing ratios at the tropopause (370--380 K potential temperature) range from 2.5 to 3.2 ppmv. These values are somewhat lower than the estimates of the stratospheric water vapor entry value from satellite and in situ measurements; hence an additional source of water (such as injection by deep convection) may be required to explain the observed tropical tropopause humidity.