How does one control an inappropriate tendency? Many studies have investigated this question by measuring the speed with which subjects stop an initiated response. Yet the rapid stopping of an initiated response is apparently underpinned by a neurocognitive mechanism that has global effects on multiple tendencies. This limits such studies as models of cognitive control because they do not explain the selectivity of control over particular tendencies that is apparent in everyday life. We hypothesized that subjects employ a selective stopping mechanism when they have foreknowledge of which response to stop, but employ a global stopping mechanism when they do not have such foreknowledge. Comparing foreknowledge and no-foreknowledge conditions, we show that when subjects have foreknowledge, stopping is indeed more selective, as evidenced by less of an effect on the concurrent execution of an alternative response; however, stopping is also slower when subjects have foreknowledge. Thus, selective and global mechanisms of stopping can be dissociated. We suggest that the selective mechanism is used when people maintain the goal of controlling particular responses, whereas the global mechanism is used when it is essential to stop quickly.