Why do humans make errors on seemingly trivial perceptual decisions? It has been shown that such errors occur in part because the decision process (evidence accumulation) is initiated before selective attention has isolated the relevant sensory information from salient distractors. Nevertheless, it is typically assumed that subjects increase accuracy by prolonging the decision process rather than delaying decision onset. To date it has not been tested whether humans can strategically delay decision onset to increase response accuracy. To address this question we measured the time course of selective attention in a motion interference task using a novel variant of the response signal paradigm. Based on these measurements we estimated time-dependent drift rate and showed that subjects should in principle be able trade speed for accuracy very effectively by delaying decision onset. Using the time-dependent estimate of drift rate we show that subjects indeed delay decision onset in addition to raising response threshold when asked to stress accuracy over speed in a free reaction version of the same motion-interference task. These findings show that decision onset is a critical aspect of the decision process that can be adjusted to effectively improve decision accuracy.