Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large-[Formula: see text] limit of QCD, the subleading diagrams that involve, in the s-channel of meson-meson scattering amplitudes, two-quark-two-antiquark intermediate states. The latter contribute, together with gluon exchanges, to the formation, at the hadronic level, of two-meson and tetraquark intermediate states. It is shown that the two-meson contributions, which are predictable, in general, from leading-order [Formula: see text]-behaviors, consistently satisfy the constraints resulting from the [Formula: see text] expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from [Formula: see text]-subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of [Formula: see text]. For the particular case of exotic tetraquarks, involving four different quark flavors, two different types of tetraquark are needed, each having a preferred decay channel, to satisfy the consistency constraints.