  We propose to address the fine tuning problem of inflection point inflation
by the addition of extra vacuum energy that is present during inflation but
disappears afterwards. We show that in such a case, the required amount of fine
tuning is greatly reduced. We suggest that the extra vacuum energy can be
associated with an earlier phase transition and provide a simple model, based
on extending the SM gauge group to SU(3)_C \times SU(2)_L\times U(1)_Y\times
U(1)_{B-L}, where the Higgs field of U(1)_{B-L} is in a false vacuum during
inflation. In this case, there is virtually no fine tuning of the soft SUSY
breaking parameters of the flat direction which serves as the inflaton.
However, the absence of radiative corrections which would spoil the flatness of
the inflaton potential requires that the U(1)_{B-L} gauge coupling should be
small with g_{B-L}\leq 10^{-4}.
