  We compute the helicity amplitudes for boson-boson scattering at high energy
due to the operators $\O_{B\Phi}$, $\O_{W\Phi}$ and $\O_{UB}$, and we derive
the corresponding unitarity bounds. Thus, we provide relations between the
couplings of these operators and the corresponding New Physics thresholds,
where either unitarity is saturated or new degrees of freedom are excited. We
compare the results with those previously obtained for the operators $\O_W$ and
$\O_{UW}$ and we discuss their implications for direct and indirect tests at
present and future colliders. The present treatment completes the study of the
unitarity constraints for all blind bosonic operators.
