 The theories discussed above all construe question meanings as sets of propositions, and are therefore referred to as proposition set theories. It has been argued that question meanings as construed by proposition set theories are all too coarse-grained to account for certain linguistic phenomena. In order to address this issue, several theories have been developed that adopt more fine-grained, structured notions of question meanings. Such theories have been couched in different semantic frameworks, which are all more fine-grained than the standard possible world framework. For instance, the proposal of Krifka (2001) is couched in a structured meanings framework, that of Ginzburg and Sag (2000) in situation semantics, that of Ginzburg (2005), Cooper and Ginzburg (2012) in type theory with records, that of Aloni et al. (2007a) in dynamic semantics, and that of Blutner (2012) in ortho-algebraic semantics. We will illustrate the general approach here by focusing on the proposal of Krifka (2001), which in turn has its roots in earlier work of Hull (1975), Tichy (1978), Hausser (1978), von Stechow and Zimmermann (1984), von Stechow (1991), and Ginzburg (1992).