Interference between amplitudes producing-eta and eta'-mesons via their strange and nonstrange components give relative suppression factors of an order of magnitude in certain diagrams and can be used to identify penguin contributions to B --> K-eta and B --> K eta'-decays as well as annihilation diagram contributions to corresponding D decays. Similar suppression factors also arise in D(O) --> pi-0-eta and D(O) --> pi-O-eta'-decays and in charmonium decays to K + K- eta and K + K- eta'.