  In this paper we present a numerical implementation of the one-loop QED
corrections to the hard-bremsstrahlung process e- e+ \to e- e+ gamma. These
corrections can be included in the Monte Carlo event generators employed for
simulating Bhabha scattering events at low-energy high-luminosity
electron-positron colliders. The calculation is performed by employing the
reduction method developed by Ossola, Papadopoulos and Pittau. Our results are
implemented in a modular code for the numerical evaluation of the scattering
amplitudes for any given phase-space point. In a similar way, we also evaluate
the one-loop QED corrections to e- e+ \to mu- mu+ gamma, which represents an
interesting application of the method in the presence of two different mass
scales in the loops.
