  In this paper we present a simple argument that shows a non-singular bouncing
cosmology naturally yields an era of super-inflation which can precede the
phase of normal potential driven inflation. One of the consequences of a
super-inflation phase is that it might be able to account for suppressing the
low multipole in the amplitude of the cosmic microwave background radiation. We
are able to constrain the number of e-folds of super-inflation from the current
Planck data to be roughly 3 e-folds in a model independent way.
