In response to an article by Odintsov and Wansing which defines a formal notion of hyperintensionality and claims that, according to this notion, Leitgeb’s logic HYPE cannot be hyperintensional, I put forward three notions of hyperintensionality. I show that HYPE satisfies only the weakest of these three notions, and claim that HYPE can be understood as a sort of middle ground between an intensional logic and a hyperintensional logic.