Using a New Keynesian framework, this paper shows that, under optimal discretion and optimal pre-commitment in a timeless perspective, imperfect transparency about the relative weight that the central bank assigns to output-gap stabilization generally reduces the average reaction of inflation to inflation shocks and the volatility of inflation, but increases these of the output gap in static and dynamic terms, and more so when inflation shocks are highly persistent. On balance, when inflation shocks are not excessively persistent, opacity could improve social welfare, more likely under pre-commitment than under discretion, if the weight assigned to output-gap stabilization is low.