Background Along with high affinity binding of epibatidine (Kd1≈10 pM) to α4β2 nicotinic acetylcholine receptor (nAChR), low affinity binding of epibatidine (Kd2≈1-10 nM) to an independent binding site has been reported. Studying this low affinity binding is important because it might contribute understanding about the structure and synthesis of α4β2 nAChR. The binding behavior of epibatidine and α4β2 AChR raises a question about interpreting binding data from two independent sites with ligand depletion and nonspecific binding, both of which can affect equilibrium binding of [3H]epibatidine and α4β2 nAChR. If modeled incorrectly, ligand depletion and nonspecific binding lead to inaccurate estimates of binding constants. Fitting total equilibrium binding as a function of total ligand accurately characterizes a single site with ligand depletion and nonspecific binding. The goal of this study was to determine whether this approach is sufficient with two independent high and low affinity sites. Results Computer simulations of binding revealed complexities beyond fitting total binding for characterizing the second, low affinity site of α4β2 nAChR. First, distinguishing low-affinity specific binding from nonspecific binding was a potential problem with saturation data. Varying the maximum concentration of [3H]epibatidine, simultaneously fitting independently measured nonspecific binding, and varying α4β2 nAChR concentration were effective remedies. Second, ligand depletion helped identify the low affinity site when nonspecific binding was significant in saturation or competition data, contrary to a common belief that ligand depletion always is detrimental. Third, measuring nonspecific binding without α4β2 nAChR distinguished better between nonspecific binding and low-affinity specific binding under some circumstances of competitive binding than did presuming nonspecific binding to be residual [3H]epibatidine binding after adding a large concentration of cold competitor. Fourth, nonspecific binding of a heterologous competitor changed estimates of high and low inhibition constants but did not change the ratio of those estimates. Conclusions Investigating the low affinity site of α4β2 nAChR with equilibrium binding when ligand depletion and nonspecific binding are present likely needs special attention to experimental design and data interpretation beyond fitting total binding data. Manipulation of maximum ligand and receptor concentrations and intentionally increasing ligand depletion are potentially helpful approaches.