  We consider the error budget for the calculation of the LEP/SLC luminosity in
the Monte Carlo event generator BHLUMI4.04 from the standpoint of new
calculations of the exact result for the O(alpha) correction to the process e+
e- -> e+ e- + gamma in the low angle luminosity regime at SLC/LEP energies, for
the double bremsstrahlung effect e+ e- -> e+ e- + gamma gamma in this regime,
and for the size of the two-loop virtual correction to e+ e- -> e+ e- in this
regime in context of Yennie-Frautschi-Suura exponentiation. We find that the
error on the O(alpha**2) photonic correction can be reduced from the currently
published value 0.1% to the value 0.027%. This leads to an over-all precision
tag for the currently available program BHLUMI4.04 of 0.061%. This reduction of
the precision of the calculation is important for the final LEP1 EW precision Z
physics tests of the Standard Model.
