We describe a leaky competing accumulator (LCA) model of the lexical decision task that can be used as a response/decision module for any computational model of word recognition. The LCA model uses evidence for a word, operationalized as some measure of lexical activity, as input to the "YES" decision node. Input to the "NO" decision node is simply a constant value minus evidence for a word. In this way, evidence for a nonword is a function of time from stimulus onset (as in standard deadline models) modulated by lexical activity via the competitive dynamics of the LCA. We propose a simple mechanism for determining the value of this constant online during the first trials of a lexical decision experiment, such that the model can rapidly optimize speed and accuracy in discriminating words from nonwords. Further optimization is achieved via trial-by-trial adjustments in response criteria as a function of task demands and list context. We show that the LCA model can simulate mean response times and response distributions for correct and incorrect "YES" and "NO" decisions for a number of benchmark experiments that have been shown to be fatal for deadline models of lexical decision. Finally, using lexical activity calculated by a computational model of word recognition as input to the LCA decision module, we provide the first item-level simulation of both word and nonword responses in a large-scale database. (Contains 3 tables, 7 figures and 4 footnotes.)