The usual method for establishing allowable daily intake (ADI) for a chemical involves determining a no-observed-effect level (NOEL) and applying a safety factor. Even though this method has been used for many years, there appear to be no general guidelines or rules for defining a NOEL. The determination of a NOEL is particularly uncertain for lesions which occur naturally in untreated animals. NOELs also have shortcomings in that smaller experiments tend to give larger values (this should be reversed because larger experiments can provide greater evidence of safety) and that the steepness of the dose response in the dose range where effects occur plays little or no role in the determination of a NOEL. This paper proposes and illustrates the use of a "benchmark dose" (BD) as an alternative to a NOEL. A BD is a statistical lower confidence limit to a dose producing some predetermined increase in response rate such as 0.01 or 0.1. The BD is calculated using a mathematical dose-response model. This approach makes appropriate use of sample size and the shape of the dose-response curve. The BD normally will not depend strongly upon the mathematical model used because the method does not involve extrapolation far below the experimental range. Thus the method sidesteps much of the model dependency often associated with extrapolation of carcinogenicity data to low doses. The method can be applied to either "quantal" data in which only the presence or absence of an effect is recorded, or "continuous" data in which the severity of the effect is also noted.