When people make decisions they often face opposing demands for response speed and response accuracy, a process likely mediated by response thresholds. According to the striatal hypothesis, people decrease response thresholds by increasing activation from cortex to striatum, releasing the brain from inhibition. According to the STN hypothesis, people decrease response thresholds by decreasing activation from cortex to subthalamic nucleus (STN); a decrease in STN activity is likewise thought to release the brain from inhibition and result in responses that are fast but error-prone. To test these hypotheses – both of which may be true – we conducted two experiments on perceptual decision making in which we used cues to vary the demands for speed vs. accuracy. In both experiments, behavioral data and mathematical model analyses confirmed that instruction from the cue selectively affected the setting of response thresholds. In the first experiment, we used ultra high-resolution 7T structural magnetic resonance imaging (MRI) to locate the STN precisely. We then used 3T structural MRI and probabilistic tractography to quantify the connectivity between the relevant brain areas. The results showed that participants who flexibly change response thresholds (as quantified by the mathematical model) have strong structural connections between pre-supplementary motor area and striatum. This result was confirmed in an independent second experiment. In general, these findings show that individual differences in elementary cognitive tasks are partly driven by structural differences in brain connectivity. Specifically, these findings support a cortico-striatal control account of how the brain implements adaptive switches between cautious and risky behavior.