The stratosphere has been cooling by about 2K/decade at 30--60 km over the past several decades and by lesser amounts toward the tropopause. Climate model calculations suggest that stratospheric water vapor is an important contributor to the observed stratospheric cooling, but there are large differences among recent GCM simulations for prescribed changes in stratospheric water vapor, which point to problems with the current GCM treatment of the absorption and emission by stratospheric water vapor. We show that the correlated k-distribution treatment with sufficient resolution is capable of simulating accurately cooling by stratospheric water vapor. We obtain equilibrium cooling of about 0.3 K that extends from 20 km to the top of the atmosphere, and adjusted radiative forcing of 0.12 Wm-2, for a stratospheric water vapor increase of 0.7 ppmv which has been estimated for the period 1979--1997. ¿ 2001 American Geophysical Union