  In this paper, we consider logarithmic radiative corrections and higher order
terms to the supersymmetric hilltop F- and D-term hybrid inflation models.
Conventional F- and D-term hybrid inflation only predicts $n_s \gae 0.98$. We
show that via a positive quadratic and a negative quartic correction the
spectral index can be reduced to $n_s=0.96$ suggested from latest WMAP result
and also cosmic string problem appeared in SUSY hybrid inflation can be solved
with mild tuning of the parameters if $\kappa \lae 0.01$ for F-term inflation
and $g \lae 0.05$ for D-term inflation.
