  We study the interplay between graviton reggeization and double-logarithmic
in energy contributions to four-graviton scattering in theories with and
without supersymmetry. Predictions to all orders in the gravitational coupling
are given for these double-logarithms. As the number of supersymmetries grows
these terms generate a convergent behaviour for the amplitudes at very high
energies. At two-loop level, we find agreement with previous exact results for
N=8 supergravity and with those of Boucher-Veronneau and Dixon, who studied the
N=4,5,6 supergravities using a conjectured double-copy structure of gravity.
