  We study bounds arising from the analyticity and unitarity of scattering
amplitudes in the context of effective field theories with massless particles.
We provide an approach that only uses dispersion relations away from the
forward limit. This is suitable to derive constraints in the presence of
gravity, in a way that is robust with respect to radiative corrections. Our
method not only allows us to avoid the Coulomb pole, but also the singularities
associated with calculable loop effects, which would otherwise diverge.
