  The production of $W^{\pm}H$, $ZH$, $W^+W^-$, and $W^\pm Z$ pairs probes
non-Standard-Model interactions of quarks, gauge bosons, and the Higgs boson.
New effects can be parameterized in terms of an effective field theory (EFT)
where the Lagrangian is expanded in terms of higher-dimension operators
suppressed by increasing powers of a high scale $\Lambda$. We examine the
importance of including next-to-leading-order QCD corrections in global fits to
the coefficients of the EFT. The numerical implications on the fits due to
different approaches to enforcing the validity of the EFT are quantified. We
pay particular attention to the dependence of the fits on the expansion in
$1/\Lambda^2$ since the differences between results calculated at ${\cal
{O}}(1/\Lambda^2)$ and ${\cal{O}}(1/\Lambda^4)$ may give insight into the
possible significance of dimension-8 effects.
