  We evaluate the O(alpha) QED corrections to the recoil electron energy
spectrum in the process nu_l + e --> nu_l + e (+gamma), where (+gamma)
indicates the possible emission of a photon and l=e, mu or tau. The soft and
hard bremsstrahlung differential cross sections are computed for an arbitrary
value of the photon energy threshold. We also study the O(alpha) QED
corrections to the differential cross section with respect to the total
combined energy of the recoil electron and a possible accompanying photon.
Their difference from the corrections to the electron spectrum is investigated.
We discuss the relevance and applicability of both radiative corrections,
emphasizing their role in the analysis of precise solar neutrino electron
scattering experiments.
