  Parametrizing beyond Standard Model physics by the SU(3) x SU(2)_L x U(1)_Y
dimension-six effective Lagrangian, we study the impact of anomalous Higgs
couplings in angular asymmetries of the crossing-symmetric processes H -->
Zl+l- and e+e- --> HZ. In the light of present bounds on d=6 couplings, we show
that some asymmetries can reveal BSM effects that would otherwise be hidden in
other observables. The d=6 HZgamma couplings as well as (to a lesser extent)
HZll contact interactions can generate asymmetries at the several percent
level, albeit having less significant effects on the di-lepton invariant mass
spectrum of the decay H --> Zl+l-. The higher di-lepton invariant mass probed
in e+e- --> HZ can lead to complementary anomalous coupling searches at e+e-
colliders.
