  The CP asymmetries of the decay B_d^0 -> K^0 \bar K^0, which originates from
\bar b -> \bar d s \bar s flavour-changing neutral-current processes, and its
CP-averaged branching ratio BR(B_d -> K^0 \bar K^0) offer interesting avenues
to explore flavour physics. We show that we may characterize this channel,
within the Standard Model, in a theoretically clean manner through a surface in
observable space. In order to extract the relevant information from BR(B_d ->
K^0 \bar K^0), further information is required, which is provided by the B ->
pi pi system and the SU(3) flavour symmetry, where we include the leading
factorizable SU(3)-breaking corrections and discuss how experimental insights
into non-factorizable effects can be obtained. We point out that the Standard
Model implies a lower bound for BR(B_d -> K^0 \bar K^0), which is very close to
its current experimental upper bound, thereby suggesting that this decay should
soon be observed. Moreover, we explore the implications for ``colour
suppression'' in the B -> pi pi system, and convert the data for these modes
into a peculiar Standard-Model pattern for the CP-violating B_d^0 -> K^0 \bar
K^0 observables.
