Recent studies have linked variability in near-threshold stimulus detection to fluctuations in the prestimulus EEG alpha power (α, ∼8-12 Hz). Typically, these studies rely on hit rate as a measure of detection performance and show that detection is enhanced when α power is low compared to when it is high. However, hit rates are determined by both sensitivity to the stimulus and the placement of the response criterion. Here, we investigated the relationships between prestimulus α power and variability in these two measures on a single-trial basis. We confirm earlier reports that detection is inversely related to power in the individual α-frequency band. However, our results show a stronger relationship between α power and response criterion than with sensitivity. Higher α power was related to a more conservative response criterion (i.e., more "no" responses). A response criterion that varies depending on α power might help to optimize performance in an excited state and protect against false positives in a relatively disengaged state.