This paper develops an account of additive concessive conditionals, ACCs, such as the German Wir gehen wandern, auch wenn es regnet ‘We will go walking even (lit. also) if it is raining’. Concessivity is here understood as an essentially modal notion: the actual world does not conform to contextual assumptions, expectations or priorities (Muller 2016). I adopt a modal analysis of conditionals which interprets them relative to an ordering source (Kratzer 1986). With ACCs, the concessive interpretation arises from the contradiction between the asserted conditional “if p then q” and the conditional perfection (CP) “if p then not q” of the conditional presupposed by the additive “if not p then q” (Pasch 1995). This contradiction triggers the inference that the actual world does not conform to the ordering constraints that restrict the CP of the additive presupposition. This account predicts that additive conditionals should not receive a concessive interpretation in contexts that do not support conditional perfection. This prediction is borne out. The ACC data for this paper will be drawn from German and Cuzco Quechua.