  Recently it has been argued that some of the fine-tuning problems of the MSSM
inflation associated with the existence of a saddle point along a flat
direction may be solved naturally in a class of supergravity models. Here we
extend the analysis and show that the constraints on the Kahler potentials in
these models are considerably relaxed when the location of the saddle point is
treated as a free variable. We also examine the effect of supergravity
corrections on inflationary predictions and find that they can slightly alter
the value of the spectral index. As an example, for flat direction field values
$|\bar{\phi}_0|=1\times10^{-4}M_P$ we find $n\sim0.92 ... 0.94$ while the
prediction of the MSSM inflation without any corrections is $n\sim0.92$.
