  We examine the Regge (high energy) limit of 4-point scattering in both QCD
and gravity, using recently developed techniques to systematically compute all
corrections up to next-to-leading power in the exchanged momentum i.e. beyond
the eikonal approximation. We consider the situation of two scalar particles of
arbitrary mass, thus generalising previous calculations in the literature. In
QCD, our calculation describes power-suppressed corrections to the Reggeisation
of the gluon. In gravity, we confirm a previous conjecture that next-to-soft
corrections correspond to two independent deflection angles for the incoming
particles. Our calculations in QCD and gravity are consistent with the
well-known double copy relating amplitudes in the two theories.
