  In a five-dimensional model with one Universal Extra Dimension (UED), signals
for a pair of n = 1 Kaluza-Klein excitations could be easily observed at a
future e+ e- collider if the process in question is kinematically allowed.
However, these signals would prove difficult to distinguish from those
predicted in other models, such as those with an extended gauge symmetry or
supersymmetry. A much better power of discrimination is provided by the fact
that the same machine could also produce the n=2 gauge bosons \gamma_2 and Z_2
as resonances in fermion pair-production without any upgrade in the collision
energy \sqrt{s}. Assuming a fixed \sqrt{s}, as is expected at upcoming e+e-
machines, we investigate the role of beam radiation in helping to excite such
resonances through radiative returns. We then show how these resonances can
yield unambiguous signals for UED, if taken in conjunction with the production
of Z_1 pairs, identified by their decays to leptons and missing transverse
energy.
