  We study the high-energy limit of $2 \to 2$ one-loop string amplitudes at
fixed momentum transfer. For the closed string, the high-energy behaviour of
the amplitudes can be determined from Regge theory just like in field theory,
as was first discussed by Amati, Ciafaloni and Veneziano. However, field theory
intuition partially breaks down for the open-string amplitude, where amplitudes
can exhibit surprising asymptotics in the high-energy limit depending on the
topology of the diagram. We call this phenomenon Regge attenuation. We extract
Regge limits by a combination of unitarity cuts and saddle-point analysis. We
show that the leading contribution of the planar open-string amplitude is
sufficiently simple that we can extract it at any loop order. This allows us to
resum the genus expansion in a certain limit and demonstrate that the leading
Regge trajectory remains linear in that limit.
