  For the exploration of flavour physics, b -> d penguin processes are an
important aspect, with the prominent example of \bar B^0_d -> K^0 \bar K^0. We
recently derived lower bounds for the CP-averaged branching ratio of this
channel in the Standard Model; they were found to be very close to the
corresponding experimental upper limits, thereby suggesting that \bar B^0_d ->
K^0 \bar K^0 should soon be observed. In fact, the BaBar collaboration
subsequently announced the first signals of this transition. Here we point out
that it is also possible to derive lower bounds for \bar B -> \rho \gamma
decays, which are again surprisingly close to the current experimental upper
limits. We show that these bounds are realizations of a general bound that
holds within the Standard Model for b -> d penguin processes, allowing further
applications to decays of the kind B^\pm -> K^{(\ast)\pm} K^{(\ast)} and B^\pm
-> \pi^\pm \ell^+ \ell^-, \rho^\pm \ell^+ \ell^-.
