In this study, I argue that appositives in the traditional sense and afterthoughts should be treated as a single construction. Afterthoughts share the attested properties of appositives, differing only in linear position. Therefore, I refer to appositives that appear adjacent to the anchor as anchor-adjacent appositives and those that appear non-adjacent to the anchor as afterthought appositives. Within the framework of Constructionbased HPSG, I show that the parenthetical properties of anchor-adjacent and afterthought appositives can be accounted for without having to assume a noncanonical structure. Syntactically, appositives are integrated into the host clause as NP-adjuncts. Specifically, I propose a new subtype of the headmodifier- cx(construction): head-parenthetical-modifier -cx. In terms of semantics, I propose a new semantic dimension to deal with parenthetical elements, inspired by Potts’ (2005) work.