  On the basis of previous work by Fadin, Lipatov, and collaborators, and of
our group, we extract the "irreducible" part of the next-to-leading (NL) BFKL
kernel, we compute its (IR finite) eigenvalue function, and we discuss its
implications for small-x structure functions. We find consistent running
coupling effects and sizable NL corrections to the Pomeron intercept and to the
gluon anomalous dimension. The qualitative effect of such corrections is to
smooth out the small-x rise of structure functions at low values of Q2. A more
quantitative analysis will be possible after the extraction of some additional,
energy-scale dependent contributions to the kernel, which are not treated here.
