The present paper extends the literature on central bank transparency that relies on information heterogeneity among private agents in four directions. First, it adds the interest rate to the list of signals that the central bank can reveal. Second, it allows for more than one economic fundamental. Third, it extends the range of uncertainties that matter. So far the literature has focused on uncertainty about the economic fundamentals, assumed to be estimated with known precision; we also allow for uncertainty about precision. Fourth, it derives results that are general in the sense that they do not depend on any particular social welfare criterion. Each extension sheds new light on the role of central bank transparency. While uncertainty about the fundamentals results in the now familiar common knowledge effect, uncertainty about information precision creates a fog effect, which reduces the quality of decision taken by the central bank and the private sector. In the absence of the fog effect, full transparency is generally not desirable, because it deprives the central bank from the ability to optimally manipulate private sector expectations. When the central bank fog is large, full transparency is usually the best communication strategy, even when the private sector fog is large. We also find that it is usually desirable for the central bank to divulge some information, even if it is erroneous.