  Predictions for processes involving soft photons, up to next-to-leading power
(NLP) in the photon energy, can be obtained using the Low-Burnett-Kroll (LBK)
theorem. The consistency of the theorem has been a recent topic of
investigation since it is traditionally formulated in terms of a non-radiative
amplitude, which is evaluated with unphysical momenta. We address such
questions and propose a formulation of the LBK theorem which relies on the
evaluation of the non-radiative amplitude with on-shell, physical momenta. We
use this form to numerically study the impact of NLP contributions to
cross-sections for $pp$ and $e^-e^+$ processes involving soft-photon emission.
