  The rare decays $B\to K^{(*)}\ell^+\ell^-$, $B\to K^{(*)}\nu\bar\nu$ and
$B_s\to\mu^+\mu^-$ are analyzed in a generic scenario where New Physics effects
enter predominantly via $Z$ penguin contributions. We show that this
possibility is well motivated on theoretical grounds, as the $\bar sbZ$ vertex
is particularly susceptible to non-standard dynamics. In addition, such a
framework is also interesting phenomenologically since the $\bar sbZ$ coupling
is rather poorly constrained by present data. The characteristic features of
this scenario for the relevant decay rates and distributions are investigated.
We emphasize that both sign and magnitude of the forward-backward asymmetry of
the decay leptons in $\bar B\to \bar K^*\ell^+\ell^-$, ${\cal A}^{(\bar
B)}_{FB}$, carry sensitive information on New Physics. The observable ${\cal
A}^{(\bar B)}_{FB}+{\cal A}^{(B)}_{FB}$ is proposed as a useful probe of
non-standard CP violation in $\bar sbZ$ couplings.
