Large-eddy simulations of shear-free stratocumulus-topped layers tend strongly toward a two-layer structure as the negative area in the buoyancy flux profile that would be necessary to maintain a mixed layer increases to more than 10% of the positive area. In addition to identifying a threshold for what amounts to a convective transition, the simulations provide further evidence that a commonly used entrainment closure is ill-founded. Lastly the simulations demonstrate that attempts to formulate a similarity theory for convective layers must account for the geometry of the buoyancy-flux profile, and not simply its integral. ¿ 2000 American Geophysical Union