  We investigate the sensitivity of the discrete BFKL spectrum, which appears
in the gluon Green function when the running coupling is considered, to a lower
cut-off in the relative rapidities of the emitted particles. We find that the
eigenvalues associated to each of the discrete eigenfunctions decrease with the
size of the rapidity veto. The effect is stronger on the lowest eigenfunctions.
The net result is a reduction of the growth with energy for the Green function
together with a suppression in the regions with small transverse momentum.
