Low and high clouds of shallow extent, especially stratocumulus and even more so for high-level cirrus clouds that reside where vertical resolution is particularly coarse, are poorly represented in large-scale models such as global climate models and weather forecasting models. This adversely affects, among others, estimation of cloud feedbacks for climate prediction and weather forecasts. Here we address vertical resolution as a reason for the failure of these models to adequately represent shallow clouds. We introduce a new methodology, the Framework for Improvement by Vertical Enhancement (FIVE). FIVE computes selected processes on a one-dimensional vertical grid with local high resolution in the boundary layer and near the tropopause. In addition to the host model, variables on the locally high-resolution grid are predicted in parallel so that high-resolution information is retained. By exchanging tendencies with one another, the host model and high-resolution field are always synchronized. The methodology is demonstrated for drizzling stratocumulus capped by a sharp inversion. First, FIVE is applied to a single-column model to identify the cause of biases associated with computing an assigned process at low resolution. Second, a two-dimensional regional model coupled with FIVE is shown to produce results comparable to those performed with high vertical resolution. FIVE is thus expected to represent low clouds more realistically and hence reduce the low-cloud bias in large-scale models. Finally, we propose a number of methods that will be developed and tested to further optimize FIVE.