The sensitivity of the variability of an eddy-driven jet to the upper- and lower-level baroclinicity of the mean state is analyzed using a three-level quasi-geostrophic model on the sphere. The model is forced by a relaxation in temperature to a steady, zonally symmetric profile with varying latitude and intensity of the maximum baroclinicity. The leading EOF of the zonally- and vertically-averaged zonal wind is characterized by a meridional shift of the eddy-driven jet. While changes in the upper-level baroclinicity have no significant impact on the persistence of this leading EOF, an increase in lower-level baroclinicity leads to a reduced persistence. For small lower-level baroclinicity, the leading EOF follows a classical zonal index regime, for which the meridional excursions of the zonal wind anomalies are maintained by a strong positive eddy feedback. For strong lower-level baroclinicity, the jet enters a poleward propagation regime, for which the eddy forcing continuously acts to push the jet poleward and prevents its maintenance at a fixed latitude. The enhanced poleward propagation when the lower-level baroclinicity increases is interpreted as resulting from the broader and weaker potential vorticity gradient which enables the waves to propagate equatorward and facilitates the poleward migration of the critical latitude. Finally, the decrease in EOF1 persistence as the lower-level baroclinicity increases is shown not to result from the impact of changes in the mean climatological jet latitude.