This paper shows how the tradeoff between the traditional objective of monetary policy—stabilization of output and inflation—is affected by augmenting the central bank’s mandate with responsibility for stabilizing a financial variable: a policy of ‘leaning against the wind’. To quantify the extent of the tradeoff we estimate a version of the Gertler and Karadi (J. Monetary Econ., 2011) model on United Kingdom data over the period 1993-2015, and compute optimal monetary policy under commitment for a range of central bank objectives. Our main finding is that increased regard for financial variables (including the debt-to-GDP ratio, lending spreads and bank leverage): (a) makes inflation stabilization increasingly costly in terms of output stabilization; (b) raises the marginal cost in terms of output and inflation volatility of reducing financial volatility; (c) has effects that depend crucially on the nature of the underlying disturbance, and on the precise variable that policy aims to stabilize. Our results provide a menu of options from which policymakers who choose to lean against the wind can select.