This study used functional near-infrared spectroscopy (fNIRS) to measure aspects of the speech discrimination ability of sleeping infants. We examined the morphology of the fNIRS response to three different speech contrasts, namely "Tea/Ba," "Bee/Ba," and "Ga/Ba." Sixteen infants aged between 3 and 13 months old were included in this study and their fNIRS data were recorded during natural sleep. The stimuli were presented using a nonsilence baseline paradigm, where repeated standard stimuli were presented between the novel stimuli blocks without any silence periods. The morphology of fNIRS responses varied between speech contrasts. The data were fit with a model in which the responses were the sum of two independent and concurrent response mechanisms that were derived from previously published fNIRS detection responses. These independent components were an oxyhemoglobin (HbO)-positive early-latency response and an HbO-negative late latency response, hypothesized to be related to an auditory canonical response and a brain arousal response, respectively. The goodness of fit of the model with the data was high with median goodness of fit of 81%. The data showed that both response components had later latency when the left ear was the test ear ( < .05) compared to the right ear and that the negative component, due to brain arousal, was smallest for the most subtle contrast, "Ga/Ba" ( = .003).