The event-related potential (ERP) effect of mismatch negativity (MMN) was the first electrophysiological probe to evaluate cognitive processing (change detection) in newborn infants. Initial studies of MMN predicted clinical utility for this measure in identification of infants at risk for developmental cognitive deficits. These predictions have not been realized. We hypothesized that in sleeping newborn infants, measures derived from wavelet assessment of power in the MMN paradigm would be more robust markers of the brain’s response to stimulus change than the ERP-derived MMN. Consistent with this premise, we found increased power in response to unpredictable and infrequent tones compared to frequent tones. These increases were present at multiple locations on the scalp over a range of latencies and frequencies and occurred even in the absence of an ERP-derived MMN. There were two predominant effects. First, theta band power was elevated at middle and late latencies (200 to 600 ms), suggesting that neocortical theta rhythms that subserve working memory in adults are present at birth. Second, late latency (500 ms) increased power to the unpredictable and infrequent tones was observed in the beta and gamma bands, suggesting that oscillations involved in adult cognition are also present in the neonate. These findings support the expectation that frequency dependent measures, such as wavelet power, will improve the prospects for a clinically useful test of cortical function early in the postnatal period.