  At future electron-positron colliders, one of the largest irreducible
backgrounds to top searches in the channel `4 jets + lepton + missing energy'
comes from QCD events of order $\alpha_s^2$. We compute here such processes
exactly at the parton level by resorting to 2 -> 6 matrix elements exploiting
helicity amplitude techniques. We adopt a typical selection procedure based on
the tagging of a high momentum and separated lepton. We finally outline
kinematic differences between signal and background events that can be
exploited to further reduce such a QCD noise.
