In this paper we hypothesise that Denial of Expectation (DofE) across turns in dialogue signalled by “but” can involve a range of different expectations, i.e., not just causal expectations, as  argued in the literature. We will argue for this hypothesis and outline a methodology to distinguish the relations these denied expectations convey. Finally we will demonstrate the practical utility of this hypothesis by showing how it can improve generation of appropriate responses to DofE and decrease the likelihood of misunderstandings based on incorrectly interpreting these underlying cross-speaker relations.