  We calculate the order alpha_s^2 and order alpha_s^3 QCD contributions to
colour-singlet exchange in the leading log s approximation. We implement the
resulting amplitude at the hadronic level and thus construct the QCD pomeron
and odderon to this order of perturbation theory. We show that the structure of
the hadronic form factors provides a natural mechanism through which the
odderon gets suppressed at t=0 whereas it dominates the elastic cross section
at large t. We also demonstrate that the inclusion of nonperturbative effects
through a modification of the gluon propagator accelerates greatly the
convergence of the log s expansion, although not enough to provide agreement
with the data.
