Copper–organic compounds have gained momentum as potent antitumor drug candidates largely due to their ability to generate an oxidative burst upon the transition of Cu2+ to Cu1+ triggered by the exogenous-reducing agents. We have reported the differential potencies of a series of Cu(II)–organic complexes that produce reactive oxygen species (ROS) and cell death after incubation with N-acetylcysteine (NAC). To get insight into the structural prerequisites for optimization of the organic ligands, we herein investigated the electrochemical properties and the cytotoxicity of Cu(II) complexes with pyridylmethylenethiohydantoins, pyridylbenzothiazole, pyridylbenzimidazole, thiosemicarbazones and porphyrins. We demonstrate that the ability of the complexes to kill cells in combination with NAC is determined by the potential of the Cu+2 → Cu+1 redox transition rather than by the spatial structure of the organic ligand. For cell sensitization to the copper–organic complex, the electrochemical potential of the metal reduction should be lower than the oxidation potential of the reducing agent. Generally, the structural optimization of copper–organic complexes for combinations with the reducing agents should include uncharged organic ligands that carry hard electronegative inorganic moieties.