  We show how calculable IR loop effects impact positivity bounds in Effective
Field Theories with causal and unitary UV completions. We identify infrared
singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the
massless limit, they weaken two-sided bounds based on crossing symmetry, such
as the lower bound on the amplitude for Galileon scattering. For amplitudes
that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we
propose a new simple analytic approach to dispersive bounds, which are instead
insensitive to the singularities, and explicitly compute the finite
contributions from loops. Finally we show that the singularity do not affect
the bounds based on smearing in impact parameter.
