I examine the impact of alternative monetary policy rules on a rational asset price bubble, through the lens of an OLG model with nominal rigidities. A systematic increase in interest rates in response to a growing bubble is shown to enhance the fluctuations in the latter, through its positive effect on bubble growth. The optimal monetary policy seeks to strike a balance between stabilization of the bubble and stabilization of aggregate demand. The paper's main findings call into question the theoretical foundations of the case for "leaning against the wind" monetary policies.