  Novel contributions to the total inclusive cross section for Higgs-Strahlung
in the Standard Model at hadron colliders are evaluated. Although formally of
order $\alpha_s^2$, they have not been taken into account in previous NNLO
predictions. The terms under consideration are induced by Higgs radiation off
top-quark loops and thus proportional to the top-quark Yukawa coupling. At the
Tevatron, their effects to HW production are below 1% in the relevant Higgs
mass range, while for HZ production, we find corrections between about 1% and
2%. At the LHC, the contribution of the newly evaluated terms to the cross
section is typically of the order of 1%-3%. Based on these results, we provide
updated predictions for the total inclusive Higgs-Strahlung cross section at
the Tevatron and the LHC.
