We examine and contrast the simulation of Sahel rainfall in phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6). On average, both ensembles grossly underestimate the magnitude of low-frequency variability in Sahel rainfall. But while CMIP5 partially matches the timing and pattern of observed multi-decadal rainfall swings in its historical simulations, CMIP6 does not. To classify model deficiency, we use the previously-established link between changes in Sahelian precipitation and the North Atlantic Relative Index (NARI) for sea surface temperature (SST) to partition all influences on Sahelian precipitation into five components: (1) teleconnections to SST variations; the effects of (2) atmospheric and (3) SST variability internal to the climate system; (4) the SST response to external radiative forcing; and (5) the “fast” response to forcing, which is not mediated by SST. CMIP6 atmosphere-only simulations indicate that the fast response to forcing plays only a small role relative to the predominant effect of observed SST variability on low-frequency Sahel precipitation variability, and that the strength of the NARI teleconnection is consistent with observations. Applying the lessons of atmosphere-only models to coupled settings, we imply that the failure of coupled models in simulating 20th century Sahel rainfall derives from their failure to simulate the observed combination of forced and internal variability in SST. Yet differences between CMIP5 and CMIP6 Sahel precipitation do not mainly derive from differences in NARI, but from either their fast response to forcing or the role of other SST patterns.