  The search for new physics in single- and multi-photon final states with
large missing energy at LEP and future e^+ e^- colliders requires precise
predictions for the Standard Model irreducible background. While at LEP1 the
theoretical situation is under control, going to LEP2 (and beyond) some
improvements are necessary. To approach the aimed $O(1%)$ theoretical accuracy,
the tree-level matrix elements for the processes $e^+ e^- \to \nu \bar\nu
n\gamma$, with n=1,2,3, are exactly computed in the Standard Model, including
the possibility of anomalous couplings for single-photon production. Due to the
presence of observed photons in the final state, particular attention is paid
to the treatment of higher-order QED corrections. Comparisons with existing
calculations are shown and commented. An improved version of the event
generator NUNUGPV is presented.
