The use of the linear wave treatment to describe the eddy motions in a zonal mean model leads to the identification of the irreversible transient waves as the process responsible for the diffusive transport of tracers in the stratosphere. Recent estimates based on an idealized general circulation model (GCM) calculation and the observed transient wave statistics between 20¿N and 80¿N suggest that, in the stratosphere, the horizontal diffusion coefficient should be ≲3¿109 cm2 s-1, a value about 1 order of magnitude smaller than values previously used in most two-dimensional models. A simple model of zonally averaged transport of stratospheric trace gases in isentropic coordinates is developed to test this hypothesis of small eddy diffusion. In this model, the eddy transport arising from the irreversible transient waves is assumed to act along the isentropic surfaces and is represented by a single horizontal diffusion coefficient, kyy. The advective transport in the model is effected by the zonal mean diabatic circulation calculated diagnostically from a given zonal mean diabatic heating rate, of which no post hoc adjustment has been attempted. We show that the observed stratospheric distribution of N2O and HNO3 may be adequately simulated in the model with small values of Kyy that are consistent with physical estimates mentioned above. The result that the observed concentrations of the stratospheric trace gases can be simulated using small values of eddy diffusion coefficient is expected to be equally applicable for models in pressure coordinates using the residual mean circulations.