  We consider a simplified version of supersymmetric smooth hybrid inflation
which contains a single ultraviolet cutoff m_P = 2.4 x 10^{18} GeV, instead of
the two cutoffs m_P and M_* ~ few x 10^{17} GeV that are normally employed.
With global supersymmetry the scalar spectral index n_s ~ 0.97, which is in
very good agreement with the WMAP observations. With a non-minimal Kahler
potential, the supergravity version of the model is compatible with the current
central values of n_s and also yields potentially observable gravity waves
(tensor to scalar ratio r <~ 0.02).
