Previous studies have suggested that pupil size increases with covert shifts of attention to the peripheral as compared to the (para)foveal visual field, i.e., with increasing attentional breadth. This finding is crucial because it matches the theoretical prediction that (para)foveal vision benefits more from the visual acuity provided by small pupils than peripheral vision does. However, no study has investigated this question while controlling for all possible confounds (e.g., task difficulty). Throughout three experiments (N=100) we tested whether pupil size increases with increasing attentional breadth, and if this effect depends on the shape of attention, that is, whether attention is broadly (Annulus Attention) or narrowly (Spotlight Attention) distributed. We found that pupil size increases with covert shifts of attention to the peripheral visual field, i.e., increasing attentional breadth, with no clear difference between the two shapes of attention. We further found a correlation with performance, suggesting a functional benefit of the link between attentional breadth and pupil size. Finally, we propose that cognitively driven pupil dilation is not merely a convenient marker of activity in brain areas such as the Locus Coeruleus, but rather is an adaptive response that reflects an emphasis on peripheral vision over foveal vision.