A new version of the Model of Atmospheric Transport and Chemistry (MATCH) is developed, which uses a coordinate that is terrain-following near the surface and becomes isentropic in the upper troposphere. Starting from a simulation of age of air and water vapor in a standard version of National Center for Atmospheric Research's Middle Atmospheric Community Climate Model (MACCM), we use the meteorological fields to drive two versions of the off-line MATCH model: the standard hybrid-pressure coordinate (MATCH) and the new hybrid-isentropic coordinate (IMATCH). An analysis of the age of air estimates from MACCM, MATCH, and IMATCH and observations shows that the hybrid-isentropic model, IMATCH, is better able to capture the observed ages than either the original online MACCM or the hybrid-pressure MATCH model. Comparisons of water vapor distributions in the tropical lower stratosphere in the three different model versions and observations suggest that IMATCH produces a better propagation of the seasonal cycle than the other models. Analysis of the model results and vertical velocities suggests that the improvements in the age of air and the water vapor simulations are largely due to the reduced numerical vertical diffusion in IMATCH in the lower tropical stratosphere region. In this region, diabatic vertical motions are much smaller than reversible adiabatic motions, making simulations less susceptible to numerical errors if the transport is calculated on isentropic surfaces. Because the lower tropical stratosphere acts as the source region for transport into the stratosphere, correct simulation of the transport in the lower tropical stratosphere is crucial for improving model simulations of the stratosphere.