The complete binding cascade of human hemoglobin consists of eight partially ligated intermediates and 16 binding constants. Each intermediate binding constant can be evaluated via dimer-tetramer assembly when ligand configurations within the tetramer are fixed through the use of hemesite analogs. The Zn/Fe analog, in which the nonbinding Zn2+ heme substitutes for deoxy Fe2+ heme, also permits direct measurement of O2 binding to the remaining Fe2+ hemesites within the symmetrically ligated Hb tetramers. Measurement of O2 binding over a range of Zn/Fe Hb concentrations to both alpha-subunits (species 23) or to both beta-subunits (species 24) shows noncooperative binding and incomplete saturation of the available Fe2+ hemesites. In contrast, the asymmetrically ligated Zn/FeO2 species 21, in which both oxygens are bound to one of the dimers within the tetramer, exhibits positive cooperativity and >90% ligation under atmospheric conditions. These properties are confirmed in the present study by measurement of the rate constant for tetramer dissociation to free dimer. The binding constants thus derived for these partially ligated intermediates are consistent with the stoichiometric constants measured for native hemoglobin by standard O2 binding techniques, providing additional evidence that Zn2+-heme substitution provides an excellent deoxy hemoglobin analog. There is no evidence that Zn-substitution stabilizes a low-affinity form of the tetramer, as previously suggested. These characterizations demonstrate distinct, nonadditive physical properties of the doubly ligated tetrameric species, yielding an asymmetric distribution of cooperativity within the cascade of O2 binding by human hemoglobin.