Two recent activities offer an opportunity to test general circulation model (GCM) convection and its interaction with large-scale dynamics for observed Madden–Julian oscillation (MJO) events. This study evaluates the sensitivity of the Goddard Institute for Space Studies (GISS) GCM to entrainment, rain evaporation, downdrafts, and cold pools. Single Column Model versions that restrict weakly entraining convection produce the most realistic dependence of convection depth on column water vapor (CWV) during the Atmospheric Radiation Measurement MJO Investigation Experiment at Gan Island. Differences among models are primarily at intermediate CWV where the transition from shallow to deeper convection occurs. GCM 20-day hindcasts during the Year of Tropical Convection that best capture the shallow–deep transition also produce strong MJOs, with significant predictability compared to Tropical Rainfall Measuring Mission data. The dry anomaly east of the disturbance on hindcast day 1 is a good predictor of MJO onset and evolution. Initial CWV there is near the shallow–deep transition point, implicating premature onset of deep convection as a predictor of a poor MJO simulation. Convection weakly moistens the dry region in good MJO simulations in the first week; weakening of large-scale subsidence over this time may also affect MJO onset. Longwave radiation anomalies are weakest in the worst model version, consistent with previous analyses of cloud/moisture greenhouse enhancement as the primary MJO energy source. The authors’ results suggest that both cloud-/moisture-radiative interactions and convection–moisture sensitivity are required to produce a successful MJO simulation.