This paper argues for a new approach to the semantics of degree questions. According to the standard analysis (see, among others, Rullmann 1995 and Beck & Rullmann 1997), a degree question's LF contains a variable that ranges over individual degrees and is bound by the degree-question operator how. In contrast with this, the authors claim that the variable which is bound by the degree-question operator how does not range over individual degrees but over intervals of degrees, by analogy with Schwarzschild & Wilkinson's (2002) proposal regarding the semantics of comparative clauses. Not only do the interval-based semantics predict the existence of certain readings that are not predicted under the standard view, they are also able (and this is the authors' main focus), together with other natural assumptions, to account for the sensitivity of degree questions to negative-islands, as well as for the fact, uncovered by Fox & Hackl (2007), that negative islands can be obviated by some properly placed modals.