Nonminimally coupled inflation models based on a nonminimal coupling xi phi R-2 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.