  The study of next-to-leading-power (NLP) corrections in soft emissions
continues to attract interest both in QCD and in QED. Soft-photon spectra in
particular provide a clean case-study for the experimental verification of the
Low-Burnett-Kroll (LBK) theorem. In this paper we study the consistency of the
LBK theorem in the context of an ambiguity arising from momentum-conservation
constraints in the computation of non-radiative amplitudes. We clarify that
this ambiguity leads to various possible formulations of the LBK theorem, which
are all equivalent up to power-suppressed effects (i.e. beyond the formal
accuracy of the LBK theorem). We also propose a new formulation of the LBK
theorem with a modified shifted kinematics which facilitates the numerical
computation of non-radiative amplitudes with publicly available tools.
Furthermore, we present numerical results for soft-photon spectra in the
associated production of a muon pair with a photon, both in $e^+e^-$
annihilation and proton-proton collisions.
