  Inverted hybrid inflation (in which the inflaton field slowly rolls away from
the origin, giving a spectral index $n\lsim 1$) is an appealing variant of the
more usually studied hybrid model. Analysing the model alongside the ordinary
hybrid case, we show that, in order to provide the correct density
perturbations consistent with the COBE measurements, the dimensionless coupling
constants of the inverted hybrid potential must be very small indeed. For
example, the quartic coupling in a typical such potential is found to be $\lsim
10^{-12}$. A supersymmetric model of inverted hybrid inflation, which does not
involve the troublesome quartic coupling is found to lead to a potential which
is unbounded from below.
