Many neurons that initially respond to a stimulus stop responding if the stimulus is presented repeatedly but recover their response if a different stimulus is presented. This phenomenon is referred to as stimulus-specific adaptation (SSA). SSA has been investigated extensively using oddball experiments, which measure the responses of a neuron to sequences of stimuli. Neurons that exhibit SSA respond less vigorously to common stimuli, and the metric typically used to quantify this difference is the SSA index (SI). This article presents the first detailed analysis of the SI metric by examining the question: How should a system (e.g., a neuron) respond to stochastic input if it is to maximize the SI of its output? Questions like this one are particularly relevant to those wishing to construct computational models of SSA. If an artificial neural network receives stimulus information at a particular rate and must respond within a fixed time, what is the highest SI one can reasonably expect? We demonstrate that the optimum, average SI is constrained by the information in the input source, the length and encoding of the memory, and the assumptions concerning how the task is decomposed.