Several studies have demonstrated that prestimulus occipital alpha-band activity substantially influences subjective perception and discrimination of near-threshold or masked visual stimuli. Here, we studied the role of prestimulus power fluctuations in two visual phenomena called double-flash illusion (DFI) and fusion effect (FE), both consisting of suprathreshold stimuli. In both phenomena, human subjects' perception varies on a trial-by-trial basis between perceiving one or two visual stimuli, despite constant stimulation. In the FE, two stimuli correspond to veridical perception. In the DFI, two stimuli correspond to an illusory perception. This provides for a critical test of whether reduced alpha power indeed promotes veridical perception in general. We find that in both, DFI and FE, reduced prestimulus occipital alpha predicts the perception of two stimuli, regardless of whether this is veridical (FE) or illusory (DFI). Our results suggest that reduced alpha-band power does not always predict improved visual processing, but rather enhanced excitability. In addition, for the DFI, enhanced prestimulus occipital gamma-band power predicted the perception of two visual stimuli. These findings provide new insights into the role of prestimulus rhythmic activity for visual processing.