We propose and discuss a kinematic mechanism underlying the recently discovered 'near-zero energy structure' in the photoionization of atoms in strong mid-infrared laser fields, based on trajectories which revisit the ion at low velocities exactly analogous to the series responsible for low-energy structures. The different scaling of the new series, as $E\sim {I}_{p}^{2}/{U}_{p}$, suggests that the near-zero energy structure can be lifted to higher energies, where it can be better resolved and studied, using harder targets with higher ionization potential.