Common wisdom holds that the central banker has to be independent from the government under the hypothesis of rational expectations. However, the assummption of learning puts into question the optimal combinations of conservatism and independence the government should choose. We show in this paper using a New Keynesian model that the central banker should be hawkish as learning, instrument- and goal-independence increase. For a substantial level of instrument independence, an increase in learning and goal-independence reduce the inflation bias and the stabilization bias, however, the welfare loss simultaneously increases.