Results are presented for experiments which examine the ability of the University of Wisconsin (UW) hybrid isentropic‐sigma (θ‐σ) and sigma (σ) coordinate models and the NCAR Community Climate Model 2 (CCM2) to transport and conserve the joint distributions of potential temperature (θ) or equivalent potential temperature (θe) and a source‐free inert trace constituent identical to the respective initial distribution (tθ or tθe). Under the idealized isentropic conditions of these experiments, the governing equations for the atmospheric continuum require that the joint distributions (θ, tθ or θe, tθe) be conserved throughout the integration. Deviation in the paired values is an objective measure of a model's skill to conserve the joint distributions. Results show that conservation remains higher in the UW θ‐σ model than in the other models, even near the interface between isentropic and sigma model domains.