  We discuss the important role played during inflation by one of the soft
supersymmetry breaking terms in the inflationary potential of supersymmetric
hybrid inflation models. With minimal Kaehler potential, the inclusion of this
term allows the prediction for the scalar spectral index to agree with the
value n_s = 0.963^{+0.014}_{-0.015} found by WMAP5. In the absence of this soft
term, and by taking into account only radiative and supergravity corrections,
it is well known that n_s >= 0.985. This same soft term has previously been
shown to play a key role in resolving the MSSM mu problem. The tensor to scalar
ratio r is quite small in these models, taking on values r <= 10^{-5} in the
WMAP5 2-sigma range of n_s.
