AbstractPotential advances are investigated in the area of generalized anelastic approximations. Consistent control‐volume integrals are designed and compared for the established Lipps–Hemler form (of anelastic approximation) and Durran's pseudo‐incompressible form. The Durran system provides a unique theoretical tool—useful for research of geophysical and stellar flows—within the existing set of reduced, Boussinesq‐type fluid models. It represents thermal aspects of compressibility free of sound waves, yet the momentum equation is unapproximated. The latter admits unabbreviated baroclinic production of vorticity, thus facilitating separation of compressibility and baroclinicity effects per se. Compared with other reduced fluid models, there is little cumulative experience with integrating the Durran system. Perhaps the first conservative integrations of Durran's equations are presented, using flux‐form transport methods and exact projection for the associated elliptic problem. Because the resulting code is built from a preexisting anelastic model, the consistency of the numerics is assured thus minimizing uncertainties associated with ad hoc code comparisons. While broader physical implications are addressed, theoretical considerations are illustrated with examples of atmospheric flows. Copyright © 2007 John Wiley & Sons, Ltd.