  We reexamine the improved effective vector boson approximation which is based
on two-vector-boson luminosities $\mathrm{\mathbf{L}}_{\rm pol}$ for the
computation of weak gauge-boson hard scattering subprocesses $V_1 V_2\to {\cal
W}$ in high-energy hadron-hadron or $e^-e^+$ collisions. We calculate these
luminosities for the nine combinations of the transverse and longitudinal
polarizations of $V_1$ and $V_2$ in the unitary and axial gauge. For these two
gauge choices the quality of this approach is investigated for the reactions
$e^-e^+ \to W^- W^+ \nu_e {\bar\nu}_e$ and $e^-e^+ \to t {\bar t} \nu_e
{\bar\nu}_e$ using appropriate phase-space cuts.
