  A method to embed models of strong $WW$ scattering in unitary gauge
amplitudes is presented that eliminates the need for the effective $W$
approximation (EWA) in the computation of cross sections at high energy
colliders.The cross sections obtained from the U-gauge amplitudes include the
distributions of the final state fermions in $ff \rightarrow ffWW$, which
cannot be obtained from the EWA. Since the U-gauge method preserves the
interference of the signal and the gauge sector background amplitudes, which is
neglected in the EWA, it is more accurate, especially if the latter is
comparable to or bigger than the signal, as occurs for instance at small angles
because of Coulomb singularities. The method is illustrated for on-shell
$W^+W^+ \rightarrow W^+W^+$ scattering and for $qq \rightarrow qqW^+W^+$.
