This paper addresses the distinction between plan-based and expectation-based “but”, focusing on dialogue-specific cross-turn “but” which relates material across speakers. We focus here on cases in which it signals denial of expectation (DofE) and concession following work by Lagerwerf (1998) and Knott (1999a). We will unify prior treatments (Thomas, 2003a; Thomas, 2003b) of plan-based and expectation-based DofE “but” and present a single algorithm that models both phenomena in the PTT (Poesio and Traum, 1998) Information State (IS, Matheson et al., 2000) model of dialogue. We also propose a novel treatment of concession in Task-Oriented Dialogue (TOD). We motivate this work by showing how it predicts speakers’ expectations and can be implemented in the IS model of dialogue to facilitate discourse understanding and natural language generation (NLG).