Asking and answering questions is a staple of human communication. To answer a question effectively, a hearer must interpret the speaker's intention given the specific question asked. ‘Wh’-questions like ‘Where can I get coffee?’ are underspecified for (non-)exhaustivity, i.e., how many answers must be provided to resolve the speaker's goal. Intuitions from the semantics literature report that questions are generally exhaustive, and non-exhaustive only in the context of specific linguistic factors (e.g., the modal ‘can’, certain ‘wh’-words). To test these assumptions, we collected question paraphrase ratings for naturally occurring root questions in variable linguistic contexts. In contrast to previous claims, we find that questions are not biased for exhaustivity. However, other prior observations are supported by the data. We argue that a full account of the observed distribution of meanings must integrate discourse factors like the hearer's estimate of the speaker's goal, alongside (or subsuming the effect of) linguistic cues.