We revisit Galí’s (2014 ) analysis by extending his model to incorporate persistent bubble shocks. We find that, under adaptive learning, a stable bubbly steady state and the associated sunspot solutions under optimal monetary policy are not E-stable. When deriving the unique forward-looking minimum stable variable (MSV ) solution around an unstable bubbly steady state, we obtain results that are consistent with the conventional views: leaning against the wind policy reduces bubble volatility and is optimal. Such a steady state and the associated MSV solution are E-stable.