  We consider D-term hybrid inflation in the framework of superconformal
supergravity. In part of the parameter space, inflation continues for
subcritical inflaton field value. Consequently, a new type of inflation
emerges, which gives predictions for the scalar spectral index and the
tensor-to-scalar ratio that are consistent with the Planck 2015 results. The
potential in the subcritical regime is found to have a similar structure to one
in the simplest class of superconformal alpha attractors.
