Limiting dilution (LD) analyses of polyclonally activated T cells yielded results suggesting the existence of multiple paired populations of effector and suppressor precursors for a number of different T cell functions and specificities analyzed. These populations occur at graded frequencies and suppression occurs within a pair but not between pairs. In this paper, we establish the mathematical basis for the interpretation of these multi-component limiting dilution results. First, we derive equations for a number of mathematical models and identify one model that both makes biological sense and can be used to reproduce experimental data. Second, within this model, we identify parameters such as the frequency of suppressive cells and the number of suppressive cells required for suppression. The results suggest that within each paired population, suppressor precursors are 20 times more frequent that effector precursors. Furthermore, a similar but variable excess of suppressor cells is required for suppression to become effective. Together with the high frequency (1/50-1/500) of most effector T cell precursors previously reported, the results suggest that up to 40% of the T cells can become involved in suppression of an antigen-specific effector T cell population. These studies may provide exact estimates for predictions to be tested in experiments on immune regulation.