The verb 'imagine' admits of perspectival modification: we can imagine things from above, from a distant point of view, or from the point of view of a Russian. But in such cases, there need be no person, either real or imagined, who is above or distant from what is imagined, or who has the point of view of a Russian. We call this the puzzle of perspectival displacement. This paper sets out the puzzle, shows how it does not just concern language, but also states of imagining themselves, and then presents a solution. The solution draws on the idea that many reports of imagining conceal a distinctive kind of question, and such concealed questions have an extra argument place for (what we will call) an experiencer from whose perspective things are imagined. This solution has a range of advantages over other proposals in the literature, and helps to advance two debates concerning perspectival engagement with fiction.