Achieving self-consistent simultaneous interpretations of pions and kaons as bound states of quark and antiquark and as the (almost) massless boson states related, according to Goldstone's theorem, to the dynamical, and explicit, breakdown of the chiral symmetries of QCD still represents a major challenge. Applying inversion techniques to conveniently simplified versions of the homogeneous Bethe--Salpeter equation, governing bound states in quantum field theory, enables us to get along a straightforward route a qualitative idea of how the underlying effective interaction might look like.