Monetary policy is modeled as governed by a known rule, except for a time-varying target rate of inflation. The variable target is taken as representing either discretionary deviations from the rule, or as the outcome of a policymaking committee that is unable to arrive at a consensus. Stochastic simulations of FRB/US, the Board of Governors' large, rational-expectations model of the U.S. economy, are used to examine the benefits of reducing the variability in the target rate of inflation. We find that putting credible boundaries on target variability introduces an important non-linearity in expectations. This improves policy performance by focusing agents' expectations on policy objectives. But improvements are limited; it does not generally pay to reduce target variability to zero. The non-linearity in expectations can be used to conduct a policy with greater attention to output stabilization than otherwise. The results provide insights as to why inflation-targeting countries use bands and why the bands are narrower than studies suggest they should be. Also, a numerical technique that approximates to arbitrary precision a non-linear process with a linear method is also demonstrated. This greatly speeds the simulations and makes them more robust.