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Monetary policy is sometimes formulated in terms of a target level of inflation, a fixed time horizon and a constant interest rate that is anticipated to achieve the target at the specified horizon. These requirements lead to constant interest rate (CIR)instrument rules. Using the standard New Keynesian model, it is shown that some forms of CIR policy lead to both indeterminacy of equilibria and instability under adaptive learning. However, some other forms of CIR policy perform better. We also examine the properties of the different policy rules in the presence of inertial demand and price behaviour.