Benchmark Dose Model software (BMDS), developed by the U.S. Environmental Protection Agency, involves a growing suite of models and decision rules now widely applied to assess noncancer and cancer risk, yet its statistical performance has never been examined systematically. As typically applied, BMDS also ignores the possibility of reduced risk at low doses (“hormesis”). A simpler, proposed Generic Hockey-Stick (GHS) model also estimates benchmark dose and potency, and additionally characterizes and tests objectively for hormetic trend. Using 100 simulated dichotomous-data sets (5 dose groups, 50 animals/group), sampled from each of seven risk functions, GHS estimators performed about as well or better than BMDS estimators, and a surprising observation was that BMDS mis-specified all of six non-hormetic sampled risk functions most or all of the time. When applied to data on rodent tumors induced by the genotoxic chemical carcinogen anthraquinone (AQ), the GHS model yielded significantly negative estimates of net potency exhibited by the combined rodent data, suggesting that—consistent with the anti-leukemogenic properties of AQ and structurally similar quinones—environmental AQ exposures do not likely increase net cancer risk. In addition to its simplicity and flexibility, the GHS approach offers a unified, consistent approach to quantifying environmental chemical risk.