  We investigate \emph{bi-valued} auctions in the digital good setting and
construct an explicit polynomial time deterministic auction. We prove an
unconditional tight lower bound which holds even for random superpolynomial
auctions. The analysis of the construction uses the adoption of the finer lens
of \emph{general competitiveness} which considers additive losses on top of
multiplicative ones. The result implies that general competitiveness is the
right notion to use in this setting, as this optimal auction is uncompetitive
with respect to competitive measures which do not consider additive losses.
