In this paper we solve for the optimal (Stackelberg) policy in a model of credibility and monetary policy developed by Cuckierman and Meltzer(1486) . Unlike the (Nash) solution provided by Cuckierman and Meltzer the dynamic optimisation problem facing the monetary authority in this case isnot of a linear quadratic form and certainty equivalence does not apply. The learning behaviour of the private sector (regarding the policy maker's preferences ) becomes intimately linked with the choice of the optimal policy and cannot be separated as in the certainty equivalent case. Once the dual effect of the optimal Stackelberg policy is recognised the monetary authority has an additional channel of influence to consider beyond that taken into account by sub—optimal certainty equivalent , Nash, policy rules. Unlike Nash behaviour the Stackelberg solution implies no inflationary bias but it lacks credibility. The learning behaviour of the private sector does not sufficiently inhibit the incentive of the monetary authority to cheat in this model despite the fact that this learning is explicitly recognised in the Stackelberg solution.