  We present the exact O(alpha) correction to the process e+ e- -> e+ e- +
gamma in the low angle luminosity regime at SLC/LEP energies. We give explicit
formulas for the completely differential cross section. As an important
application, we illustrate the size of the respective corrections of O(alpha^2)
to the SLC/LEP luminosity cross section. We show explicitly that our results
have the correct infrared limit, as a cross-check. Some comments are made about
the implementation of our results in the framework of a Monte Carlo event
generator. This latter implementation will appear elsewhere.
