How successful are Fregean theories compared with guise-theoretic Millian theories in dealing with a range of problematic propositional attitude ascriptions? The range considered is roughly that of Paderewski puzzles and their relatives. I argue that these fall into two categories: in one category, the Fregean theory looks to be under pressure from guise-theoretic rivals, though I argue that Fregeans can, to advantage, borrow some guise-theoretic machinery. Concerning the other category, which includes Kripke's two Paderewski puzzles, I argue that these puzzles are neutral between Fregean and Millian approaches; more generally, they have no direct bearing on semantics. Their solution requires correct views about rationality, self-knowledge and transparency.