The classification of that is, or (in other words), and or rather as reformulation markers would seem to suggest that the utterances they introduce achieve relevance in the same way. However, the examination of a range of discrepancies between reformulations introduced by or, on the one hand, and reformulations introduced by that is, on the other, suggests that any account of the pragmatics of reformulation must be a non-unitary one. In this paper, I build on Burton-Roberts' (1993) suggestion that the reformulations introduced by or are meta-linguistic in character, and show how these can be distinguished from the reformulations introduced by that is, which must be analysed at the level of conceptual representation. I also show how this distinction corresponds to a distinction between the different ways in which a parenthetical construction may be pragmatically integrated with its host. As Potts (2005) would predict, parenthetical that is-reformulations are not themselves part of the truth-conditional content of their hosts. However, in contrast with or-reformulations, they communicate information about the propositional content of their hosts, and in this way can contribute to the identification of their truth-conditional content at the level of pragmatic interpretation.