A longstanding puzzle in the semantics/pragmatics of questions has been the subtle differences between positive (e.g. Is it …?), low negative (Is it not …?), and high negative polar questions (Isn’t it …?). While they are intuitively ways of asking “the same question”, each has distinct felicity conditions and gives rise to different inferences about the speaker’s attitude towards this issue and expectations about the state of the discourse. In contrast to their non-interchangeability, the vacuity of double negation means that most theories predict all three to be semantically identical. In this chapter, we build on the non-vacuity of double negation found in inquisitive semantics (e.g. Groenendijk & Roelofsen (2009), AnderBois (2012), Ciardelli et al. (2013)) to break this symmetry. Specifically, we propose a finer-grained version of inquisitive semantics – what we dub ‘two-tiered’ inquisitive semantics – which distinguishes the ‘main’ yes/no issue from secondary ‘projected’ issues. While the main issue is the same across positive and negative counterparts, we propose an account deriving their distinctive properties from these projected issues together with pragmatic reasoning about the speaker’s choice of projected issue.