There has been progress in both psychological modeling and neurophysiology in attempting to understand simple decision processes. The kinds of models used are sequential sampling models of the class of diffusion processes. We present a leaky accumulator model with negatively correlated starting points and discuss how it accounts for standard RT phenomena including accuracy, correct and error RTs and their distributions. This model assumes evidence is accumulated in two separate accumulators to separate decision criteria. We then show how simulated paths in the two accumulators mimic neural firing rate data recorded from buildup cells in the superior colliculus of rhesus monkeys in a brightness discrimination task. I will focus on the criteria for behavioral modeling, including fitting RT distributions and error RTs. Much work in the neurophysiology domain corrently ignores these dependent variables, but in the psychological domain, they have proved decisive in deciding among models.