A discretionary monetary policy gives rise to a constant average inflation bias, a state-contingent inflation bias, and a stabilization bias when output is persistent. The paper considers institutional arrangements ("contracts") for central banks that remove these policy imperfections. The average and state-contingent inflation biases can be removed by directing the central bank to target the growth of nominal income and appoint a central banker with a specific relative weight attached to output stabilization. An alternative to this institutional solution is to direct central banks to aim for a feasible output target. Although this would remove the inflationary biases, the government must appoint a "liberal" (as opposed to "conservative") central banker in order to implement optimal stabilization.