The EPA-recommended toxicity equivalence factor (TEF) approach to estimating the lifetime incremental cancer risks for dioxins does not address (a) differences in the severity of toxicity according to the composition of chemical mixture and (b) potentials for modification of tissue-level doses of congeners in mixtures and consequently the cancer risk estimates. Our earlier efforts to model the binding of congeners to the Ah receptor in the low-dose range and to develop quantitative estimates for the formation of fractions of Ah receptor-congener complexes resulted in the definition of a unique parameter, defined as competitive binding ratio (CBR), to adjust tissue-level doses for mixture exposure. We made an effort to incorporate CBR values in the dose-response analysis and risk characterization of congeners in two distinct exposure scenarios. The modified approach to estimating tissue-level doses of congeners in mixtures by the use of a competitive binding model indicated that (a) the Ah receptor affinity is an important criterion in the determination of tissue-level dose of congeners, (b) the TEF doses calculated by using the model algorithms modified the tissue-level doses for congeners in mixture exposures, and (c) the combined lifetime incremental cancer risks for all congeners were generally lower when model algorithms were used in the dose-response analysis. However, the percentage contribution of toxic congeners was significantly higher when model algorithms were used. The percentage contribution of higher congeners with low toxicity was considerably reduced when model algorithms were used.(ABSTRACT TRUNCATED AT 250 WORDS)