  We extend the study of Higgs boson couplings in the "golden" $gg\to H \to
ZZ^\ast \to 4\ell$ channel in two important respects. First, we demonstrate the
importance of off-shell Higgs boson production ($gg\to H^\ast \to ZZ \to
4\ell$) in determining which operators contribute to the $HZZ$ vertex. Second,
we include the five operators of lowest non-trivial dimension, including the
$Z_\mu Z^\mu \Box H$ and $H Z_\mu \Box Z^\mu$ operators that are often
neglected. We point out that the former operator can be severely constrained by
the measurement of the off-shell $H^\ast \to ZZ$ rate and/or unitarity
considerations. We provide analytic expressions for the off-peak cross-sections
in the presence of these five operators. On-shell, the $Z_\mu Z^\mu \Box H$
operator is indistinguishable from its Standard Model counterpart $H Z_\mu
Z^\mu$, while the $H Z_\mu \Box Z^\mu$ operator can be probed, in particular,
by the $Z^\ast$ invariant mass distribution.
