For the small-angle Bhabha-scattering process, we consider the error budget for the calculation of the LEP/SLC luminosity in the Monte Carlo event generator BHLUMI 4.04, from the standpoint of new calculations of exact results for the respective O(alpha**2) photonic corrections in the context of the Yennie-Frautchi-Suura exponentiation. We find that an over-all precision tag for the currently available program BHLUMI 4.04 can be reduced from 0.11% to 0.061% at LEP1 and from 0.25% to 0.122% at LEP2. For the large-angle Bhabha process, we present the Monte Carlo program BHWIDE and compare its predictions with predictions of other Monte Carlo programs as well as semi-analytical calculations.
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