This paper explores a puzzling contrast: "even" can be used in denials of presuppositions, but only when it appears below negation. I present a solution to this puzzle that makes crucial use of the additive presupposition of "even". This presupposition is controversial; I argue that the evidence used to challenge its presence does not show what it is claimed to show. I show that the puzzle is not unique to English and sketch crosslinguistic implications of the proposed analysis.