Gradual accumulation of evidence is thought to be a fundamental component of decision-making. Over the last 16 years, research in non-human primates has revealed neural correlates of evidence accumulation in parietal and frontal cortices, and other brain areas . However, the circuit mechanisms underlying these neural correlates remains unknown. Reasoning that a rodent model of evidence accumulation would allow a greater number of experimental subjects, and therefore experiments, as well as facilitate the use of molecular tools, we developed a rat accumulation of evidence task, the “Poisson Clicks” task. In this task, sensory evidence is delivered in pulses whose precisely-controlled timing varies widely within and across trials. The resulting data are analyzed with models of evidence accumulation that use the richly detailed information of each trial’s pulse timing to distinguish between different decision mechanisms. The method provides great statistical power, allowing us to: (1) provide compelling evidence that rats are indeed capable of gradually accumulating evidence for decision-making; (2) accurately estimate multiple parameters of the decision-making process from behavioral data; and (3) measure, for the first time, the diffusion constant of the evidence accumulator, which we show to be optimal (i.e., equal to zero). In addition, the method provides a trial-by-trial, moment-by-moment estimate of the value of the accumulator, which can then be compared in awake behaving electrophysiology experiments to trial-by-trial, moment-by-moment neural firing rate measures. Based on such a comparison, we describe data and a novel analysis approach that reveals differences between parietal and frontal cortices in the neural encoding of accumulating evidence. Finally, using semi-automated training methods to produce tens of rats trained in the Poisson Clicks accumulation of evidence task, we have also used pharmacological inactivation to ask, for the first time, whether parietal and frontal cortices are required for accumulation of evidence, and we are using optogenetic methods to rapidly and transiently inactivate brain regions so as to establish precisely when, during each decision-making trial, it is that each brain region’s activity is necessary for performance of the task.