A three-dimensional cloud-resolving model is used to investigate the relative contributions of cumulus clouds and slow, large-scale nonconvective ascent to the transport of mass and moisture into the tropical stratosphere. When run to equilibrium, the simulation reproduces key features of the thermal and cloud structure in the tropical tropopause region, including a sharp cold point with a thin cirrus layer above the level of cumulus outflow. The simulated nonconvective mass flux into the stratosphere is 2 orders of magnitude greater than the cumulus mass flux, and the nonconvective water flux is several times greater than the cumulus water flux. The water content of air entering the stratosphere is controlled by the coldest temperature experienced by the air during its slow nonconvective ascent. Temperature fluctuations associated with convectively generated gravity waves reduce this coldest temperature slightly below that of the large-scale temperature minimum.