Data exploring a wide range of fractional occupancies of both binding sites help identify the low affinity binding site with homologous competition data with zero NSB. A. The p-values comparing one site modeltotal and two sites modeltotal depend on the maximum S/N in the homologous competition data. With R1T = 0.13 nM, single concentrations of [3H]EB with ([3H]EB = 0.013 nM; □; average log(p), short dashed line) or without ([3H]EB = 20 nM;∇; average log(p), long dashed line) ligand depletion require highly precise data (maximum S/N > 300) to consistently achieve p < 0.05 (p = 0.05, dotted line). When [3H]EB and R1T are 20 nM (Δ; average log(p), dash-dot line) and ligand depletion is significant, less precise data are needed to consistently achieve p < 0.05. With the same number of data points (114 points), simultaneous fitting of data from concentrations of [3H]EB at 0.013, 0.3, and 20 nM with R1T = 0.13 nM (●; average log(p), solid line) also needs less precise data to consistently achieve p < 0.05. Number of trials at each concentration and S/N value was 5. Estimates of dissociation constants and binding site concentrations are not significantly different from true values when S/N = 50. The CIs of Kd1 (9.6 - 13.8 pM; mean = 11.5 pM) and Kd2 (1.9-22.0 nM; mean = 6.5 nM) and CIs of R1T (0.126-0.131; mean = 0.128) and R2T (0.0198-0.0315; mean = 0.0256) (n = 5 for each CI) included the true values. B, C, D, and E. The two sites modelfree generated noisy homologous competition data sets with R1T = 0.13 nM; [3H]EB = 0.013 (●), 0.3 (○), and 20 nM (▼); and maximum S/N = 100 (B), 50 (C), 25 (D), and 15 (E). Fitting the one site modeltotal and two sites modeltotal to these types of data sets produced p values in A. Lines shown are fits of two sites modeltotal.