This study presents a corpus-based analysis of adjective phrases consisting of a grading element (‘grader’), a deadjectival adverb and an adjectival head. The interest of this pattern derives from the fact that these three constituents can occur in three different orders, as exemplified by more cognitively complex, cognitively more complex and more complex cognitively. The analysis builds primarily on the distinction between domain and non-domain adverbs. ADJPs with domain adverbs have different patterns from ADJPs with other adverbs. Whereas the adverb–grader–adjective order predominates in ADJPs with domain adverbs, the grader–adverb–adjective order is the most frequent type in ADJPs with non-domain adverbs. Within the set of non-domain adverbs, a secondary distinction is made between lexical and more grammatical types. Lexical adverbs are found to preferentially associate with the grader–adverb–adjective order while the more grammatical adverbs gravitate towards the adverb–grader–adjective order. The following five factors account for the empirical results: branching direction, the frequent-unit-first hypothesis, proximity, analogy/uniformity and modifier–head order. Structural representations are argued to draw on lexical information which is not coded by terminal nodes.