The minimal detection limit and the conditions of maximal sensitivity of a one-step solid-phase inhibition radioimmunoassay for human immunoglobulin A have been determined by application of statistical methods of experimental optimization. The choice of the optimal combination of qualitative variables, such as the origin of the antibody and the nature of the solid phase, was made by the study of a covariable under non-optimal conditions of the quantitative variables, such as the amount of antibody. The covariable was the avidity of the antibody, which is expected to have a large influence on the sensitivity. Only the difference in avidity between two immunosorbents with cellulose or Sepharose as solid-phase material proved to be statistically significant, and further study was done with cellulose. The experimental optimization of the sensitivity as a function of five quantitative variables yielded a reduction of the detection limit by a factor 5.6 (from 23.5 to 4.2 ng IgA). The variables determining the amount of insolubilized antibody in the assay had the largest influence on the value of the detection limit. The conditions of optimal sensitivity did agree with the predictions by a physical model of radioimmunoassay. The results are discussed in relation to the assay parameters such as the amount and the avidity of the insolubilized antibody and the initial percentage of binding, and in relation with theoretical optimization of the sensitivity.