Typically, the semantics of concessive conjunctions such as obwohl in German or although in English has been described by taking recourse to conditionality. König (1991b), for example, claims that obwohl has two meaning parts: (i) It has the truth-conditional meaning of the logical conjunction ∧ and (ii) it expresses the concessive presupposition p → ¬q. In this paper, we argue that the underlying conditional semantics of obwohl has to be analyzed as a tripartite quantified structure with an implicit modal in the sense of Kratzer (1978, 1991, 2012). This analysis has the advantage that the two meaning components of obwohl do not enter in a logical contradiction as in the traditional analysis. Furthermore, the specific semantic and pragmatic properties of German spoken variants of concessive clauses (i.e. obwohl-clauses with V2-order and disintegrated obwohl-clauses with verb-final order) can be derived without further assumptions within the quantificational analysis proposed in this paper.