Changes in the mean circulation of the equatorial Pacific Ocean partly control the strong decadal modulation of El Nino-Southern Oscillation (ENSO). This relationship is considered from the linear stability of a conceptual recharge/discharge model with parameters tuned from the observed mean state. Whereas decadal changes in the mean thermocline depth alone are usually considered in conceptual ENSO models, here focus is given to decadal changes in the mean stratification of the entire upper ocean (e.g., the mean thermocline depth, intensity, and thickness). Those stratification changes modify the projection of wind stress forcing momentum onto the gravest ocean baroclinic modes. Their influence on the simulated frequency and growth rate is comparable in intensity to the one of usual thermodynamic and atmospheric feedbacks, while they have here a secondary effect on the spatial structure and propagation of SST anomalies. This sensitivity is evidenced in particular for the climate shift of the 1970s in the Simple Ocean Data Assimilation (SODA) dataset, as well as in a preindustrial simulation of the Geophysical Fluid Dynamics Laboratory (GFDL) model showing stratification changes similar to the ones after 2000. Despite limitations of the linear stability approach, conclusions on the sensitivity to stratification may be extended to interpret the modulation and diversity of ENSO in observations and in general circulation models.