Chalmer’s version of two-dimensional semantics offers interesting and original solutions to traditional problems of neo-Fregean and neo-Russellian theories of meaning. However, I will argue that his theory is not completely successful because it does not solve some important forms of Frege’s puzzle (Mates’ puzzle, and the informativness of identity statements with demonstratives). First I will show that the solution to Mates’ puzzle offered by Chalmers is metalinguistic, and therefore inappropriate since it avoids the problem which is to be solved. Next I will show that the solution makes Chalmers break the compositionality principle, which he says he accepts, and on which some of the main notions of his theory are based. Finally I will point out that Chalmers’ theory cannot account for the informativness of identity statements with demonstratives, no matter whether they are interpreted de dicto or de re.