Abstract We extend the Monacelli [Monacelli, T. (2005). Monetary policy in a low pass-through environment. Journal of Money, Credit and Banking, 37(6), 1047–1066] model to allow for a central bank that penalizes nominal interest rate paths that are too close to the zero lower bound. We analytically derive the optimal interest-rate policy rule in each equilibrium under four policy regimes: (i) benchmark commitment to an ex-ante optimal monetary-policy plan; (ii) benchmark discretionary policy; (iii) optimal delegation to a discretionary policy maker with similar preferences to society; and (iv) optimal delegation to a discretionary policy maker with an additional taste for interest-rate smoothing. Under the commitment benchmark, the optimal interest-rate rule is proved to be intrinsically inertial, whereas this property is non-existent under discretionary policy. In the absence of commitment, there are gains to delegating policy to an interest-rate smoothing central banker. We show that while the endogenous law of one price gap in the model exacerbates the optimal policy trade-off that arises under discretionary policy, the latter feature of interest-rate smoothing acts to weaken it, by mimicking intrinsic inertia under the commitment policy.