  In models with partially composite quarks, the couplings of quarks to the Z
boson generically receive non-universal corrections that are not only
constrained by electroweak precision tests but also lead to flavour-changing
neutral currents at tree level. The impact of these flavour-changing couplings
on rare K and B decays is studied in two-site models for three scenarios: an
anarchic strong sector with two different choices of fermion representations
both leading to a custodial protection of the Z->bb coupling, and for a strong
sector invariant under a U(2)^3 flavour symmetry. In the complete numerical
analysis, all relevant constraints from Delta(F)=2 processes are taken into
account. In all scenarios, visible effects in rare K and B decays like K->pi nu
anti-nu, B(s)->mu+mu- and B->K*mu+mu- are possible that can be scrutinized
experimentally in the near future. Characteristic correlations between
observables allow to distinguish the different cases. To sample the large
parameter space of the anarchic models, a new method is presented that allows
larger statistics than conventional approaches.
