Segmentation of target odorants from background odorants is a fundamental computational requirement for the olfactory system and is thought to be behaviorally mediated by olfactory habituation memory. Data from our laboratory have shown that odor-specific adaptation in piriform neurons, mediated at least partially by synaptic adaptation between the olfactory bulb outputs and piriform cortex pyramidal cells, is highly odor specific, while that observed at the synaptic level is specific only to certain odor features. Behavioral data show that odor habituation memory at short time constants corresponding to synaptic adaptation is also highly odor specific and is blocked by the same pharmacological agents as synaptic adaptation. Using previously developed computational models of the olfactory system we show here how synaptic adaptation and potentiation interact to create the observed specificity of response adaptation. The model analyzes the mechanisms underlying the odor specificity of habituation, the dependence on functioning cholinergic modulation, and makes predictions about connectivity to and within the piriform neural network. Predictions made by the model for the role of cholinergic modulation are supported by behavioral results.