  We present the results of the first calculation of the logarithmic
corrections to the QCD contribution to same-sign $W$-pair production, $pp\to
e^\pm \nu_e \mu^\pm \nu_\mu jj$, for same-sign charged leptons. This includes
all leading logarithmic contributions which scale as $\alpha_W^4
\alpha_s^{2+k}\log^k(\hat s/p_\perp^2)$. This process is important for the
study of electroweak couplings and hence the QCD contributions are usually
suppressed through a choice of Vector Boson Scattering (VBS) cuts. These select
regions of phase space where logarithms in $\hat s/p_\perp^2$ are enhanced.
While the logarithmic corrections lead to a small change for the cross
sections, several distributions relevant for experimental studies are affected
more significantly.
