A formulation based on the anelastic approximation yields time-dependent simulations of convective updrafts, downdrafts and other aspects of convection-such as stratiform layers-under reasonably flexible geometry assumptions. Termed anelastic convective entities (ACEs), such realizations can aid understanding of convective processes, and potentially provide time-dependent building blocks for parameterization at a complexity between steady-plume models and cloud-resolving simulations. Even for cases deliberately formulated to provide a comparison to a traditional convective plume, ACE behavior differs substantially because dynamic entrainment, detrainment and nonhydrostatic perturbation pressure are consistently included. Entrainment varies with the evolution of the entity but behavior akin to deep-inflow effects noted in observations emerges naturally. The magnitude of mass flux with nonlocal pressure effects consistently included is smaller than for a corresponding traditional steady-plume model. ACE solutions do not necessarily approach a steady state even with fixed environment but can exhibit chains of rising thermals, and even episodic deep convection. The inclusion of nonlocal dynamics allows a developing updraft to tunnel through layers with substantial convective inhibition (CIN). For cases of nighttime continental convection using GoAmazon soundings, this is found to greatly reduce the effect of surface-inversion CIN. The observed convective cold top is seen as an inherent property of the solution, both in a transient, rising phase and as a persistent feature in mature deep convection. An embedded ACE configuration allows stratiform cloud formation by time-dependent detrainment modified by dynamic feedbacks during the grid-scale adjustment process. SIGNIFICANCE STATEMENT: Convective storms cause hazardous events such as flooding, often with economic losses. Forecasting such events and how they change in a warming climate for mitigation planning is hard. In modern numerical weather and climate models, one issue standing out is that model cannot satisfactorily simulate nighttime storms over land commonly observed over, for instance, the North American Great Plains or the Amazon basin. Here, we propose a new model-named anelastic convective entity (ACE)-with two purposes in mind: (i) to be useful for improving numerical models; and (ii) to help understand convective processes in general. Preliminary results covered here are promising, especially for the nighttime convection problem.