The freshness of fruits and vegetables can be prolonged by storage in an optimum atmosphere of oxygen and carbon dioxide that slows the respiratory process. The technology known as modified atmosphere packaging (MAP) seeks to create such an environment passively during shipping, storage, and marketing of produce. It is shown here that the combination of a high flux membrane (selective permeation of gases) patch with perforations (or holes that provide non-selective permeation of gases) in the package film offer a versatile route to create whatever oxygen and carbon dioxide environment may be needed for a given product. Detailed mathematical models are developed here for describing and designing such systems. Particular attention is devoted to the steady-state analysis where produce respiration is balanced by transport into and out of the package. The perforations serve the dual function of allowing convective flow of gases to prevent package volume shrinkage and non-selective permeation of gases to adjust the ratio of CO2/O-2 transport. Detailed predictive models for both functions are developed.