  We resum the recently calculated second order kernel of the BFKL equation.
That kernel can be viewed as the sum of a conformally invariant part and a
running coupling part. The conformally invariant part leads to a corrected BFKL
intercept as found earlier. The running coupling part of the kernel leads to a
non-Regge term in the energy dependence of high energy hard scattering, as well
as a $Q^2-$dependent intercept.
