  We consider observational constraints and fine-tuning issues in a
renormalizable model of inflection point inflation, with two independent
parameters. We derive constraints on the parameter space of this model arising
from the WMAP 7-year power spectrum. It has previously been shown that it is
possible to successfully embed this potential in the MSSM. Unfortunately, to do
this requires severe fine-tuning. We address this issue by introducing a hybrid
field to dynamically uplift the potential with a subsequent smooth phase
transition to end inflation at the necessary point. Large parameter regions
exist where this drastically reduces the fine-tuning required without ruining
the viability of the model. A side effect of this mechanism is that it
increases the width of the slow-roll region of the potential, thus also
alleviating the problem of the fine-tuning of initial conditions. The MSSM
embedding we study has been previously shown to be able to explain the
smallness of the neutrino masses. The hybrid transition does not spoil this
feature as there exist parameter regions where the fine-tuning parameter is as
large as $10^{-1}$ and the neutrino masses remain small.
