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While cognitive neuroscientists have uncovered principles of perceptual decision-making by analyzing choices and neuronal firing across thousands of trials, we do not yet know the behavioral or neuronal dynamics underlying one SINGLE choice. For instance, why might a subject judge a given stimulus in category A 70% of the time but in category B 30%? Until we can work out precisely what determines single-decisions – this choice, right now – the mechanisms of real-world decision-making will remain unknown. In tactile psychophysical tasks with rats and humans, we are trying to sort out factors that explain the variability in judgments (across trials) to the identical stimulus input. We identify four factors: (i) trial-to-trial fluctuations in sensory coding, (ii) temporal context, namely, the history of preceding stimuli and choices, (iii) attention, and (iv) bias (predictions originating in beliefs about the environment’s probabilistic structure). The strategy is to bring these factors under experimental control, rather than leaving them to vary according to uninterrogated states within the subject. Psychophysics from rats and humans show that large chunks of variability are accounted for by these factors; evidence from cortical neuronal populations in rats provides some mechanistic grounding.