This paper investigates adverb extraction out of traditional adjective phrases (TAPs) like “extremely expensive”, in a number of Slavic, Romance, and Germanic languages, and establishes two novel generalizations regarding such extraction out of predicative and attributive TAPs, also showing what the (un)availability of such extraction reveals about the structure of TAPs cross-linguistically and in different constructions in a single language. I argue that attributive TAPs are never bare APs in languages that use only one adjectival form attributively. Languages that use two adjectival forms in the attributive position allow adverb extraction out of predicative and attributive TAPs, which indicates that adverb extraction is possible only if a bare AP is used in this position. More generally, I argue that extended projections of different lexical categories tend to be uniform within a language with respect to how much structure they project.