This paper examines the internal structure of achievement predicates, in particular that of Degree Achievement (DA) predicates. It is argued, based on evidence from again-ambiguities, that the internal structure of a DA predicate (e.g., widen) differs from that of a Result State (RS) predicate (e.g., open). Traditionally, again-ambiguities have been used to argue that certain predicates are decomposable into BECOME and a small-clause; by examining the entailments (or lack thereof) between readings of ambiguous sentences containing DA and RS predicates, it is shown that a BECOME-again analysis is possible only for sentences containing RS predicates. A different type of scopal account is then proposed for DA predicates, in which the amibiguity is explained by the scopal possibilities of again with respect to a complex degree phrase.