Variability in the detection and discrimination of weak visual stimuli has been linked to prestimulus neural activity. In particular, the power of oscillatory activity in the alpha-band (8-12 Hz) has been shown to impact upon the objective likelihood of stimulus detection, as well as measures of subjective visibility, attention, and decision confidence. We aimed to clarify how prestimulus alpha influences performance and phenomenology, by recording simultaneous subjective measures of attention and confidence (Experiment 1), or attention and visibility (Experiment 2) on a trial-by-trial basis in a visual detection task. Across both experiments, prestimulus alpha power was negatively and linearly correlated with the intensity of subjective attention. In contrast to this linear relationship, we observed a quadratic relationship between the strength of prestimulus alpha power and subjective ratings of confidence and visibility. We find that this same quadratic relationship links prestimulus alpha power to the strength of stimulus evoked responses. Visibility and confidence judgements corresponded to the strength of evoked responses, but confidence, uniquely, incorporated information about attentional state. As such, our findings reveal distinct psychological and neural correlates of metacognitive judgements of attentional state, stimulus visibility, and decision confidence.