Co-crystallization of the push-pull nitriles NCNR2 (R-2 = Me-2 1, C4H8 2, C5H10 3, and C4H8O 4) with iodo-substituted perfluorobenzenes (1,4-diiodotetrafluorobenzene - 1,4-FIB and 1,3,5-triiodotrifluorobenzene - 1,3,5-FIB) gave cocrystals 1<middle dot>1,3,5-FIB, 2<middle dot>1,3,5-FIB, 3<middle dot>1/2(1,4-FIB), 4<middle dot>1/2(1,4-FIB), and 4<middle dot>2(1,3,5-FIB), which were studied by single-crystal X-ray diffractometry (XRD). The structure-directing I<middle dot><middle dot><middle dot>sp-N-nitrile halogen bond (HaB) in all cocrystals was identified based on the consideration of the XRD geometrical (bond length and angles) parameters and also by Hirshfeld surface analysis, whereupon the observed HaBs were analyzed theoretically. The HaB-accepting role of the push-pulling dialkylcyanamides NCNR2 and conventional nitriles NCR (R = Alk) was examined and compared in detail using, as model examples, the structures of cocrystals 3<middle dot>1/2(1,4-FIB) (this work) and AdCN<middle dot>1/2(1,4-FIB) (CSD refcode: KIHROL). These two cocrystals, which display similar supramolecular organization, were studied by several quantum chemistry methods including molecular electrostatic potential surface analysis, the natural bond orbital analysis, the quantum theory of atoms in molecules combined with the NCIPlot approach, and also by the Kitaura-Morokuma energy decomposition approach. While AdCN is a slightly poorer sp-N electron donor than the push-pull nitrile 3, HaBs in the cocrystals exhibit similar interaction energies. Although in the covalent chemistry the two types of nitriles often exhibit strikingly different reactivity patterns, the sigma-hole-based I<middle dot><middle dot><middle dot>sp-N-nitrile noncovalent interaction provided the leveling effect, resulting in significant similarities between the HaB situations for both nitrile species.