A literature has grown up around papers by Kydland and Prescott (1977) and Barro and Gordon (1983) which shows how governments have an incentive to inflate the economy (to generate extra output) then the private sector will anticipate this and the economy will stick at a high inflation equilibrium. Walsh (1995) proposed a way round this - for the government to delegate monetary policy to an independent central bank working under a contract defined in terms of inflation. Walsh argued that the inflation bias in policy could be eliminated without interfering with the government's ability to stabilise output when it needed to. This paper criticises Walsh's result showing that if there are political pressures on the real interest rates then the inflation bias might vary from period to period. The paper argues that it is not practical to write contracts for every period, so good contracts will interfere with stabilisation policy. Such a contract may be no better than other means of preserving credibility, like, for example, the ERM. The paper discusses how close Walsh's contract is to the practice of inflation targeting; arguing that there is some, but by no means a complete, read-across from one to the other. This paper also suggests that Walsh's solution to the credibility problem is not a solution at all. There is no obvious way that government can be made to enforce the contract, other than that they may be concerned about their reputations. In this respect, regimes like the ERM are more effective, since it is possible for those who stay in - at least in principle - to penalise those who renege by withdrawing associated benefits of membership.