  We have proposed a new class of inflationary scenarios in which the first
stage of expansion is driven by "old" false vacuum inflation. This ends by
nucleation of a bubble, which then further inflates. Unlike the standard
slow-roll scenarios the "clock" ending the second inflationary phase is not a
local order parameter, but rather the average value of an oscillating scalar
field, which locks the system at a saddle point of the potential in a temporary
inflationary state. Inflation ends when the amplitude drops below a certain
critical point and liberates the system from the false vacuum state. The second
stage of inflation has only about 50 e-foldings, a number which is determined
entirely by the ratio of the fundamental mass scales, such as the Planck/string
scale and the supersymmetry breaking scale. The density perturbations are
generated due to fluctuations of moduli-dependent Yukawa couplings. In this
note we explore the observable imprints in the fluctuation spectrum of generic
cross-couplings in the superpotential and in the Kahler potential. We show that
in the presence of generic non-renormalizable interactions in the
superpotential between the fluctuating modulus and the oscillating inflaton,
the amplitude of the density perturbations is exponentially cut-off for
sufficiently large wavelengths. With reasonable choices of scales and
interactions, this long wavelength cutoff can occur at approximately the
current horizon size. The perturbative corrections in the K\"ahler potential
give non-trivial potentially observable tilt and a running of the spectral
index which is different from the standard inflationary models.
