Data from a range of different experimental paradigms -- in particular (but not only) the dot perspective task -- have been interpreted as evidence that humans automatically track the perspective of other individuals. Results from other studies, however, have cast doubt on this interpretation, and some researchers have suggested that phenomena that seem like perspective-taking might instead be the products of simpler behavioural rules. The issue remains unsettled in significant part because different schools of thought, with different theoretical perspectives, implement the experimental tasks in subtly different ways, making direct comparisons difficult. Here, we explore the possibility that subtle differences in experimental method explain otherwise irreconcilable findings in the literature. Across five experiments we show that the classic result in the dot perspective task is not automatic (it is not purely stimulus-driven), but nor is it exclusively the product of simple behavioural rules that do not involve mentalizing. Instead, participants do compute the perspectives of other individuals rapidly, unconsciously and involuntarily, but only when attentional systems prompt them to do so (just as, for instance, the visual system puts external objects into focus only as and when required). This finding prompts us to clearly distinguish spontaneity from automaticity. Spontaneous perspective-taking may be a computationally efficient means of navigating the social world.