The contributions to the deep inelastic scattering structure function
which arise from emission of zero, one, two or three resolvable gluons
and any number of unresolvable ones are computed to order <(alpha)ove
r bar>(3)(s). Coherence effects are taken into account via angular ord
ering and are demonstrated to yield (at the leading logarithm level) t
he identical results to those obtained assuming the multi-Regge kinema
tics of BFKL. (C) 1998 Elsevier Science B.V. All rights reserved.