  Nonminimally coupled inflation models based on a nonminimal coupling $\xi
\phi^{2} R$ and a $\phi^{4}$ potential are in excellent agreement with the
scalar spectral index observed by Planck. Here we consider the modification of
these models by a conformal factor with a zero. This enables a nonminimally
coupled model to have a Planck-scale potential energy density at large values
of the inflaton field, which can account for the smooth, potential-dominated
volume that is necessary for inflation to start. We show that models with a
conformal factor zero generally predict a correlated increase of the spectral
index $n_{s}$ and tensor-to-scalar ratio $r$. For values of $n_{s}$ that are
within the present $2-\sigma$ bounds from Planck, modification by $\Delta r$ as
large as 0.0013 is possible, which is large enough to be measured by next
generation cosmic microwave background polarization satellites.
