QCD coherence and jet rates in small x deep inelastic scattering

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 ${\bar{\alpha }}_S^3$. Coherence effects are taken into account via angular ordering and are demonstrated to yield (at the leading logarithm level) the identical results to those obtained assuming the multi-Regge kinematics of BFKL.