Observations and cloud-resolving simulations suggest that a convective updraft structure drawing mass from a deep lower-tropospheric layer occurs over a wide range of conditions. This occurs for both mesoscale convective systems (MCSs) and less-organized convection, raising the question: Is there a simple, universal characteristic governing the deep inflow? Here we argue that nonlocal dynamics of the response to buoyancy are key. For precipitating deep-convective features including horizontal scales comparable to a substantial fraction of the troposphere depth, the response to buoyancy tends to yield deep inflow into the updraft mass flux. Precipitation features in this range of scales are found to dominate contributions to observed convective precipitation for both MCS and less-organized convection. The importance of such nonlocal dynamics implies thinking beyond parcel models with small-scale turbulence for representation of convection in climate models. Solutions here lend support to investment in parameterizations at a complexity between conventional and superparameterization.