  This talk reviews some recent results on the NLL resummed small-x gluon
splitting function, as determined including renormalisation-group improvements.
It also discusses the observation that the LO, NLO, NNLO, etc. hierarchy for
the gluon splitting function breaks down not when (alpha_s log 1/x) is of order
one but rather for (alpha_s log^2 1/x) of order one.
