Binding expressions are derived and analytical procedures developed for the quantitative characterization of inhibitor binding that is only partially competitive with the interaction between an acceptor and the ligand that is being monitored. Two such situations are considered: (i) that in which the partial competition reflects binding of inhibitor to fewer acceptor sites than available to ligand; and (ii) that in which the partial competition reflects binding of inhibitor to acceptor sites in addition to those occupiable by ligand. The potential efficacy of the suggested analyses is then explored by their application to simulated data that span the likely range of experimental behavior. Quantitative analysis of the displacement of [3H]nitrobenzylthioinosine from cultured leukemic cells by an adduct of 5'-S-(2-amino-ethyl)-N6-(4-nitrobenzyl)-5'-thioadenosine with fluorescein-5-isothiocyanate is used to establish that the cells possess 6% fewer sites (150,000 cf. 159,000 sites/cell) for the fluorescent adduct than for the tritiated ligand, and that the binding is 10-fold weaker (binding constant of 0.28 cf. 2.8 nM-1). Corresponding analysis of results obtained with bovine aorta endothelial cells indicates that a 3-fold weaker interaction (binding constant of 1.1 cf. 3.3 nM-1) occurs between the fluorescent adduct and 79% of the cell sites accessible to the tritiated ligand. The present analytical procedures extend the utility of competitive binding assays for the quantitative screening of potential inhibitors by removing the inherent limitation of existing analyses that all acceptor sites be accessible to both the competing solute and the indicator ligand.