How small a packet of photons can be made?

In contradistinction not only to the seventy-year-old notion of poor localizability of a photon but also to a recent result of principal revisions of the notion, we demonstrate that N-photon pulsed wave functions of a specific type exhibit faster than an exponential falloff of energy and photodetection rate with distance from the pulse center. The wave functions are cylindrical and exhibit an exceptionally strong localization in two dimensions out of three. Our approach involves a “technology transfer” in the sense that, in order to tackle the problem belonging to quantum optics, we make use of results obtained recently in the study of the so-called nondiffracting localized solutions to the classical wave equation.