Much is known about how allosteric effectors influence the equilibrium between the relaxed (R) and tense (T) states of hemoglobin (Hb), but little is known about how and to what extent the effectors lower the intrinsic O2 affinity of each allosteric state, especially the R‐state. Here, we provide a thorough characterization of the O2 equilibria of effector‐bound and unbound R‐quaternary form crystals of horse Hb without a quaternary structural switching. In the absence of effectors, R crystals of horse Hb were shown to bind O2 noncooperatively with a very high affinity virtually identical to that of R crystals of human Hb. We found that the effector bezafibrate (BZF) and its derivative L35 lower the overall O2 affinity of R crystals by approximately a factor of 3 and 2, respectively, while both maintaining noncooperative oxygenation. These effects are observed regardless of whether the effectors are co‐crystallized or soaked into the effector‐free protein crystals with a different lattice, confirming that the observed affinity reduction is induced by the BZF derivatives and not by crystal packing forces. Our findings, combined with available co‐crystal structural data, suggest that the BZF derivatives lower the O2 affinity of the R‐quaternary structure of Hb through structural constraints imposed by a quaternary shift slightly toward T. Additionally, since no co‐crystal of R‐state Hb with the effector inositol hexakisphosphate (IHP) is available, we only present an IHP‐soaking experiment showing little change in O2 affinity, and poor IHP binding to the R crystal structure of horse Hb is suggested.