  We present first calculations of QCD matrix-elements in perturbation theory
at finite Nc beyond 2 loops in the eikonal approximation for e+ e- annihilation
processes. For the emission of n soft energy-ordered gluons we solve both the
colour and kinematic structures at a given order in perturbation theory by
means of a Mathematica program that relies solely on a recently developed
Mathematica code, ColorMath, that evaluates the trace of products of colour
matrices. At large Nc, our squared amplitudes reduce to those already known in
the literature.
