How much information should a Central Bank (CB) have about (i) policy objectives and (ii) operational shocks to the effect of monetary policy? We consider a version of the Barro-Gordon credibility problem in which monetary policy signals an inflation-biased CB's private information on both these dimensions. We find that greater CB competence---more private information---about policy objectives is desirable while greater competence about operational shocks need not be. When the CB has less private information about operational shocks, the public infers that monetary policy depends more on the CB's information about objectives. Inflation expectations become more responsive to monetary policy, which mitigates the CB's temptation to produce surprise inflation.