It is widely assumed that Mandarin lexically distinguishes between the disjunctions used in alternative questions (háishì) and disjunctive propositions (huòzhě). This paper challenges this standard view by presenting a decompositional analysis of háishì. Specifically, we argue that the hái and shì in háishì are both semantically active, with hái conveying additivity and shì exhaustivity. The nesting of these two particles gives rise to the mutual exclusivity presupposition, a presupposition observed cross-linguistically in alternative questions. As a result, háishì should not be regarded as an interrogative disjunctor but rather as an adverb taking scope over a full CP. This analysis offers several empirical and theoretical advantages: (i) it resolves the distributional contrast between háishì and huòzhě without resorting to ad hoc assumptions; (ii) it provides a unified syntactic strategy for constructing Mandarin alternative questions; and (iii) it extends to the two additional non-disjunctive uses of háishì.