Selective stopping paradigms address selectivity in controlled behavior, as subjects stop certain responses or responses to certain stimuli. The literature has discussed 2 strategies for selective stopping. First, selective stopping may prolong the stop process by adding a discrimination stage (Independent Discriminate then Stop). Second, selective stopping may involve stopping nonselectively and then restarting the response if the signal is an ignore signal (Stop then Discriminate). We discovered a variant of the first strategy that occurred often in our experiments and previously published experiments: The requirement to discriminate stop and ignore signals may interact with the go process, invalidating the independent race model (Dependent Discriminate then Stop). Our experiments focused on stimulus selective stopping, in which subjects stop to one signal and ignore another. When stop and ignore signals were equally likely, some subjects used the Stop then Discriminate strategy and others used the Dependent Discriminate then Stop strategy. When stop signals were more frequent than ignore signals, most subjects used the Stop then Discriminate strategy; when ignore signals were more frequent than stop signals, most subjects used the Dependent Discriminate then Stop strategy. The commonly accepted Independent Discriminate then Stop strategy was seldom implemented. Selective stopping was either not selective (Stop then Discriminate), or interacted with going (Dependent Discriminate then Stop). Implications for the cognitive science, lifespan development, clinical science, and neuroscience of selective stopping are discussed.