We present a computationally efficient new method for simulating the interactions of large-scale atmospheric circulations with deep convection in a 3D cloud-resolving model. This is accomplished by reducing the scale difference between the large-scale and convective circulations. Our method, Diabatic Acceleration and REscaling (DARE), consists of accelerating all diabatic processes, reducing the planetary radius and increasing its rotation rate. A second useful interpretation of this rescaling, Reduced Acceleration in the VErtical (RAVE) is also presented briefly. The DARE/RAVE approach is expected to be useful for a wide range of problems involving interactions between large-scale circulation, deep convection, and associated cloud and radiation processes, whose investigation has long been plagued by deficiencies in cumulus/cloud parameterizations. Initial results from a near-global scale equatorial β-plane simulation using the DARE approach are briefly presented.