Phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) both grossly underestimate the magnitude of low-frequency Sahel rainfall variability; but unlike CMIP5, CMIP6 mean historical precipitation does not even correlate with observed multi-decadal variability. We demarcate realms of simulated physical processes that may induce differences between these ensembles and prevent both from explaining observations. We partition all influences on simulated Sahelian precipitation variability into five components: (1) teleconnections from sea surface temperature (SST); (2) atmospheric and (3) oceanic variability internal to the climate system; (4) the SST response to external radiative forcing; and (5) the “fast” (not mediated by SST) precipitation response to forcing. In a vast improvement from previous ensembles, the mean spectral power of Sahel rainfall in CMIP6 atmosphere-only simulations is consistent with observed low-frequency variance. The mean low-frequency variability is dominated by teleconnections from observed global SST, and the fast response only hurts its performance. We estimate that the strength of simulated teleconnections is consistent with observations using the previously-established North Atlantic Relative Index (NARI) to approximate the role of global SST, and apply this relationship to the coupled CMIP ensembles to infer that both fail to explain low-frequency historical Sahel rainfall variability mostly because they cannot explain the observed combination of forced and internal SST variability. Yet differences between CMIP5 and CMIP6 in mean Sahel precipitation and its correlation with observations do not derive from differences in NARI, but from the fast response to forcing or the role of other SST patterns.