  We propose a new version of the hybrid inflation scenario that produces a
significantly tilted n>1 spectrum of curvature perturbations. This may happen
in supersymmetric models where the inflaton field acquires a mass proportional
to the Hubble constant, and in the models where this field non-minimally
couples to gravity. A large tilt of the spectrum in this scenario is often
accompanied by a considerable contribution of tensor perturbations to the
temperature anisotropies. We also show that under certain conditions the
spectrum of density perturbations in this scenario may have a minimum on an
intermediate length scale.
