  The high-energy factorization of gauge theory scattering amplitudes in terms
of universal impact factors and a Reggeized exchange in the $t$-channel,
corresponding to a Regge pole in the angular momentum plane, is know to
conflict with the structure of soft anomalous dimensions starting at the
two-loop level. We explore the implications of this violation of factorization
for two- and three-loop QCD amplitudes: first we propose criteria to organize
the amplitudes into factorizing and non-factorizing terms, then we test them by
recovering a known result for non-logarithmic terms at two loops. Finally we
predict the precise value of the leading non-factorizing energy logarithms at
three loops, and we uncover a set of all-order identities constraining infrared
finite terms in quark and gluon amplitudes.
