Different authors have argued the importance of central banker's secrecy over alternative targets of monetary policy. One of the argument is based on the welfare results in a well known signalling game of monetary policy by Vickers (1986). This work aims to show how this argument crucially depends on the cost of separation and the specification of the prior beliefs held by private agents about the preferences of central banker. This is performed by solving a model similar to that solved by Vickers (1986) under a different assumption (a continuum of types) about the support of the distribution of prior beliefs. Welfare analysis shows that the result underlying the argument by Persson and Tabellini (1990) about the convenience of Central Banker's secrecy is upturned when the priors are skewed towards high inflation and alternative devices like credible pegging of a nominal variable, delegation and (negotiated) wage controls may be welfare enhancing. Furthermore, we show that if an appointed central banker has to incurr signalling costs a Rogoff (1985) type result can not be obtained and secrecy may be a bad substitute for commitment.