  In this paper we extend the calculation of the QED corrections to deep
inelastic lepton-proton scattering with a tagged photon, taking into account
the full corrections on the lepton side. Comparing to previous results that
were obtained by considering only large logarithmic terms at leading and
next-to-leading accuray, we find that the difference is in general quite small,
however, it may be significant in the region of large $y$ and small $x$.
