  We propose an improvement of the splitting functions at small x which
overcomes the apparent problems encountered by the BFKL approach. We obtain a
stable expansion for the x-evolution function chi(M) near M=0 by including in
it a sequence of terms derived from the one- and two-loop anomalous dimension
gamma. The requirement of momentum conservation is always satisfied. The
residual ambiguity on the splitting functions is effectively parameterized in
terms of the value of lambda, which fixes the small x asymptotic behaviour
x^-lambda of the singlet parton distributions. We derive from this improved
evolution function an expansion of the splitting function which leads to good
apparent convergence, and to a description of scaling violations valid both at
large and small x.
