Accumulating evidence suggests that visual perception operates in an oscillatory fashion at an alpha frequency (around 10Hz). Moreover, visual attention also seems to operate rhythmically, albeit at a theta frequency (around 5 Hz). Both rhythms are often associated to "perceptual snapshots" taken at the favorable phases of these rhythms. However, less is known about the unfavorable phases: do they constitute "blind gaps," requiring the observer to guess, or is information sampled with re- duced precision insufficient for the task demands? As simple detection or discrimi- nation tasks cannot distinguish these options, we applied a continuous report task by asking for the exact orientation of a Landolt ring's gap to estimate separate model parameters for precision and the amount of guessing. We embedded this task in a well- established psychophysical protocol by densely sampling such reports across 20 cue- target stimulus onset asynchronies in a Posner- like cueing paradigm manipulat- ing involuntary spatial attention. Testing the resulting time courses of the guessing and precision parameters for rhythmicities using a fast Fourier transform, we found an alpha rhythm (9.6Hz) in precision for invalidly cued trials and a theta rhythm (4.8Hz) in the guess rate across validity conditions. These results suggest distinct roles of the perceptual alpha and the attentional theta rhythm. We speculate that both rhythms result in environmental sampling characterized by fluctuating spatial reso- lution, speaking against a strict succession of blind gaps and perceptual snapshots.