  We reconsider a class of well motivated supersymmetric models in which
inflation is associated with the breaking of a gauge symmetry G to H, with the
symmetry breaking scale M~10^16 GeV. Starting with a renormalizable
superpotential, we include both radiative and supergravity corrections to
derive the inflationary potential. The scalar spectral index n_s can exceed
unity in some cases, and it cannot be smaller than 0.98 if the number of
e-foldings corresponding to the present horizon scale is around 60. Two
distinct variations of this scenario are discussed in which non-renormalizable
terms allowed by the symmetries are included in the superpotential, and one
finds n_s>=0.97.
  The models discussed feature a tensor to scalar ratio r<~10^-4, while
dn_s/dlnk<~10^-3. If G corresponds to SO(10) or one of its rank five subgroups,
the observed baryon asymmetry is naturally explained via leptogenesis.
