The atomizer is a cap-shaped shroud that contains a stack of flat stamped metal inserts. When assembled onto the nozzle of a fuel injector, the atomizer causes the inserts to be axially sandwiched between the shroud's end wall and the exterior end of the nozzle. In the zone of sandwiching, the inserts have circumferential discontinuities that in cooperation with the nozzle end and the shroud's end wall define air assist openings for the assist air to flow radially inwardly toward the injected fuel that has just been injected from the nozzle. An air assist opening in one insert is thereby both circumferentially and axially offset from an air assist opening in another insert.