With the experimental observation of several credible candidates for multiquark hadrons, the latter states re-entered the focus of interest of theoretical strong-interaction physics. Proper treatment of hadronic bound states by quantum chromodynamics, QCD, the quantum field theory governing all strong interactions, necessitates a nonperturbative approach. A well-established framework of this kind is provided by QCD sum rules relating hadron features to the parameters of QCD. Conceptual reconsideration, however, reveals that, in order to really match the peculiarities of multiquarks, the long-standing conventional QCD sum-rule techniques evidently must be subjected to considerable modification. The so far overlooked necessity for such adaptations is most easily demonstrated for the case of least complexity, that is, for tetraquarks, bound states of two quarks and two antiquarks.