  We study QCD hard processes at scales of order k^2 > Lambda^2 in the limit in
which the beta-function coefficient - b is taken to be small, but alphas(k) is
kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this
limit, making it possible to define purely perturbative high-energy Green's
functions. The hard Pomeron exponent acquires diffusion and running coupling
corrections which can be expanded in the b parameter and turn out to be
dependent on the effective coupling b alphas^2 Y. We provide a general setup
for this b-expansion and we calculate the first few terms both analytically and
numerically.
