Cognitive control is the functional backbone of intelligent behavior, because it allows to act according to one's intentions, even when the environment elicits opposed behaviors. Recently, it has been shown that reactions under urgency in a cognitive control task are dominated by stimulus-driven information and goal-directed actions are overpowered, as reflected by a temporary drop in performance below chance level in conflict situations. This effect was shown for eye movements as well as manual cognitive control tasks. Crucially, most previous studies used tasks that involved a natural processing asymmetry between the stimulus-driven information and the goal-directed information, leaving it unclear whether urgency affects cognitive control in general. Here, we investigated whether urgency also impacts performance in tasks that evoke a stimulus-stimulus conflict between similarly processed stimuli. Therefore, urgency was applied to two Eriksen flanker tasks, one using color stimuli, the other one using letter stimuli. In both experiments, urgency did not lead to a drop in performance below chance level in conflict situations, meaning that goal-directed behavior could be maintained. In a third experiment, an Eriksen flanker task with letter stimuli and a stimulus-onset asynchrony (SOA) of 120 ms between the appearance of the flanker stimuli and the target stimulus, urgency evoked a large drop in performance below chance level. These results reveal that the effect of urgency on cognitive control is based on an amplification of cognitive processing asymmetries induced by urgency and is thus specific for tasks involving processing asymmetries, thereby evoking early-onset cognitive conflicts.