The offline linearized ocean-atmosphere model (LOAM), which was developed to quantify the impact of the climatological mean state on the variability of the El Niño-Southern Oscillation (ENSO), is used to illuminate why ENSO changed between the modern-day and early/mid-Holocene simulations in two climate modeling studies using the NCAR Climate System Model (CSM) and the Hadley Centre Coupled Model, version 3 (HadCM3). LOAM reproduces the spatiotemporal variability simulated by the climate models and shows both the reduction in the variance of ENSO and the changes in the spatial structure of the variance during the early/mid-Holocene. The mean state changes that are important in each model are different and, in both cases, are also different from those hypothesized to be important in the original papers describing these simulations. In the CSM simulations, the ENSO mode is stabilized by the mean cooling of the SST. This reduces atmospheric heating anomalies that in turn give smaller wind stress anomalies, thus weakening the Bjerknes feedback. Within the ocean, a change in the thermocline structure alters the spatial pattern of the variance, shifting the peak variance farther east, but does not reduce the overall amount of ENSO variance. In HadCM3, the ENSO mode is stabilized by a combination of a weaker thermocline and weakened horizontal surface currents. Both of these reduce the Bjerknes feedback by reducing the ocean's SST response to wind stress forcing. This study demonstrates the importance of considering the combined effect of a mean state change on the coupled ocean-atmosphere system: conflicting and erroneous results are obtained for both models if only one model component is considered in isolation.