Recent measurements made near the tropical tropopause during the NASA Cirrus Regional Study of Tropical Anvils and Cirrus Layers - Florida Area Cirrus Experiment (CRYSTAL-FACE) indicate persistent ice saturation ratios (si) of about 1.2--1.3 in cold ice clouds (T < 200 K) even when the ice surface area is substantial <Gao et al., 2004>. These observations challenge the conventional thinking that any water vapor in excess of ice saturation should be depleted by crystal growth given sufficient time. Here we use model simulations to evaluate the impact of this steady-state ice supersaturation on cirrus formed in situ within the tropical tropopause layer and water vapor fluxes across the tropical tropopause. We show that cirrus occurrence frequencies are unexpectedly increased, and we estimate an increase of about 0.5--1 ppmv in the water vapor concentration in air entering the stratosphere. Inclusion of the enhanced in-cloud supersaturation in our simulations improves agreement with satellite measurements of water vapor.