  With the wealth of new data from the B-factories, b -> d penguin decays
become available for study, in addition to their b -> s counterparts that have
proven an indespensable tool for the exploration of new-physics effects in
flavour physics. A prominent example of the b -> d penguin transitions is $\bar
B^0_d \to K^0 \bar K^0$. We show that this decay can be charaterized in the
Standard Model by a surface in the observable space of the direct and
mixing-induced CP asymmetries and the branching ratio. The form of this
surface, which is theoretically clean, implies a lower bound for the branching
ratio that has recently been confirmed experimentally. If future measurements
of the CP asymmetries yield a point away from the SM surface, this would be an
interesting signal of new physics. We point out that the hadronic parameters in
$\bar B^0_d \to K^0 \bar K^0$ that parameterize the position on the SM surface
are related to hadronic parameters in the B -> pi K system. The fact that the
branching ratio of $\bar B^0_d \to K^0 \bar K^0$ is very close to its lower
bound yields interesting implications for B -> pi K even without knowledge of
the CP asymmetries of $\bar B^0_d \to K^0 \bar K^0$. The mechanism that
produces the lower bound for $\bar B^0_d \to K^0 \bar K^0$ is actually much
more general; we derive lower bounds for various other b -> d penguin-induced
processes, including B -> rho gamma and $B^\pm \to K^{(\ast)\pm} K^{(\ast)}$.
Some of these theoretical lower bounds are very close to the current
experimental upper bounds.
