An analysis is presented of a continuous-culture technique named "Brown and Oliver Interactive-Continuous Selection" (BOICS; Brown and Oliver, 1982), that was devised for the selection of microbial mutants tolerant to extreme environmental stress. The case in which the stress is due to a growth inhibitor is considered. The possible steady outcomes of competition between mutants in BOICS are analyzed under the assumption that the specific growth rates of the competing mutants depend only on the inhibitor concentration. The analysis indicates that BOICS selects mutants that sustain a given specific growth rate (equal to the dilution rate in the selection experiment) at an increased concentration of the inhibitor. Simulation results support the steady-state analysis. Further simulation results show that BOICS may fail if the specific growth rate of a mutant has to be considered to depend on a factor beside the inhibitor concentration. The choice of experimental conditions that promote the success of BOICS is discussed. An interpretation of BOICS emerges from the analysis. Namely, that BOICS implements (at least approximately) a strategy for the selection of tolerant mutants in which (1) all factors in the growth environment, beside the stress of interest (inhibitor concentration) are maintained constant, and (2) the stress is adjusted as the culture evolves so that it is always maximized subject to a specified minimum value of the mea n specific-growth rate being maintained. This interpretation suggests new (possibly improved) ways of implementing essentially the same selection technique. It is noted that a chemostat implements the same strategy in the case that the stress is due to the lack of a growth-rate-limiting nutrient. The outcome of selection for inhibitor tolerant mutants in chemostats, turbidostats, and in BOICS is compared. Only BOICS selects specifically for mutants tolerant to extreme concentrations of the inhibitor.