The problem of intense, truncation-scale storms that form in high resolution versions of the Community Atmosphere Model Version 4 (CAM4) is studied. These storms are characterized by extreme vertical motion and heavy precipitation. The problem arises when some individual parameterizations do not produce an atmospheric-like state because they are restrained by the time scales assumed in their formulation. Other unconstrained parameterizations which follow then work in unintended ways.The behavior of the moist parameterization components is examined in CAM4 for one typical, strong cell.At T340 spectral truncation with a 5 minute time step, the deep and shallow convection parameterizations do not remove instabilities and supersaturation because they have time scales of 1 hour and 30 minutes, respectively. Then, the prognostic cloud water scheme, which is not constrained by a time scale, does remove supersaturation.That local release of latent heat drives very strong vertical motion and horizontal convergence which transports even more water vapor into the column, exacerbating the problem.Two simple model problems are introduced that illustrate the ramifications of the time scale and time step mismatch.When either the time scales are shortened or the time step is lengthened the convection parameterizations are more active and the strong storms do not form.