Precise oxygen equilibria for carp hemoglobin had been measured from about 1% to 99% saturation at 15 degrees C. The determinations were made in 2,2-bis(hydroxymethyl)-2,2',2"-nitrilotriethanol buffer and in phosphate buffer in the presence and absence of P6-inositol (IHP). At the highest cooperativity, carp hemoglobin has a maximum Hill coefficient, n, of 2.3 and free energy of interaction, delta GI, of 2100 cal/site; addition of IHP decreases these values to 1.6 and 1640 cal/site, respectively. NaCl at 0.1 M or 0.2 M increases both delta GI and n. Intrinsic association constants, ki, were estimated by nonlinear least square fit of Hill plots; their values are more sensitive to pH than normal adult human hemoglobin (HbA). Identical values of nmax and ki were obtained with either one of the two major components of carp hemoglobin as with the hemolysate under the same conditions. IHP, whose effect on carp hemoglobin is much smaller than that on HbA, alters all ki values rather indiscriminately. Since IHP affects k4, it binds to Hb(O2)3 as well as the lower oxygenated species. The same is true for inorganic phosphate at pH < 8.3; however, above this pH, the phosphate ion is apparently expelled when the third heme is oxygenated since addition of PO(3-)4 does not change k4. From the intrinsic association constants, one concludes that carp hemoglobin in the cooperative regime undergoes allosteric transition after oxygenation of the third heme. Lowering of cooperativity by pH changes seems to shift conformational transitions to earlier stages of oxygenation. Parameters of the Monod, Wyman, and Changeux model were estimated by a similar nonlinear least square procedure. In the phosphate system, values of KR, c, and L are found to be 8.2 mm Hg-1, 1.3 x 10(-2), and 4.2 x 10(6) at pH 7.20. Changes of pH in either direction increases the values of KR and L and decreases the c value negating assumptions for pH-independent T and R quaternary structures.