Genetic toxicity testing has traditionally been used for hazard identification, with dichotomous classification of test results serving to identify genotoxic agents. However, the utility of genotoxicity data can be augmented by employing dose–response analysis and point of departure determination. Via interpolation from a fitted dose–response model, the benchmark dose (BMD) approach estimates the dose that elicits a specified (small) effect size. BMD metrics and their confidence intervals can be used for compound potency ranking within an endpoint, as well as potency comparisons across other factors such as cell line or exposure duration. A recently developed computational method, the BMD covariate approach, permits combined analysis of multiple dose–response data sets that are differentiated by covariates such as compound, cell type or exposure regime. The approach provides increased BMD precision for effective potency rankings across compounds and other covariates that pertain to a hypothesised mode of action (MOA). To illustrate these applications, the covariate approach was applied to the analysis of published in vitro micronucleus frequency dose–response data for ionising radiations, a set of aneugens, two mutagenic azo compounds and a topoisomerase II inhibitor. The ionising radiation results show that the precision of BMD estimates can be improved by employing the covariate method. The aneugen analysis provided potency groupings based on the BMD confidence intervals, and analyses of azo compound data from cells lines with differing metabolic capacity confirmed the influence of endogenous metabolism on genotoxic potency. This work, which is the first of a two-part series, shows that BMD-derived potency rankings can be employed to support MOA evaluations as well as facilitate read across to expedite chemical evaluations and regulatory decision-making. The follow-up (Part II) employs the combined covariate approach to analyse in vivo genetic toxicity dose–response data focussing on how improvements in BMD precision can impact the reduction and refinement of animal use in toxicological research.