Robust and nonrobust aspects of Atlantic meridional overturning circulation (AMOC) variability and mechanisms are analyzed in several 600-yr simulations with the Community Earth System Model. The simulations consist of a set of cases where a few loosely constrained ocean model parameter values are changed, a pair of cases where round-off level perturbations are applied to the initial atmospheric temperature field, and a millennium-scale integration. The time scales of variability differ among the cases with the dominant periods ranging from decadal to centennial. These dominant periods are not stationary in time, indicating that a robust characterization of AMOC temporal variability requires long, multimillennium-scale simulations. A robust aspect is that positive anomalies of the Labrador Sea (LS) upper-ocean density and boundary layer depth and the positive phase of the North Atlantic Oscillation lead AMOC strengthening by 2–3 years. Respective contributions of temperature and salinity to these density anomalies vary across the simulations, but in a majority of the cases temperature contributions dominate. Following an AMOC intensification, all cases show that advection of warm and salty waters into the LS region results in near-neutral density anomalies. Analysis of the LS heat budget indicates that temperature acts to increase density in all cases prior to an AMOC intensification, primarily due to losses by sensible and latent heat fluxes. The accompanying salt budget analysis reveals that the salt contribution to density anomalies varies across the cases, taking both positive and negative values.