Attention has been found to sample visual information periodically, in a wide range of frequencies below 20 Hz. This periodicity may be supported by brain oscillations at corresponding frequencies. We propose that part of the discrepancy in periodic frequencies observed in the literature is due to differences in attentional demands, resulting from heterogeneity in tasks performed. To test this hypothesis, we used visual search and manipulated task complexity, i.e., target discriminability (high, medium, low) and number of distractors (set size), while electro-encephalography was simultaneously recorded. We replicated previous results showing that the phase of pre-stimulus low-frequency oscillations predicts search performance. Crucially, such effects were observed at increasing frequencies within the theta-alpha range (6–18 Hz) for decreasing target discriminability. In medium and low discriminability conditions, correct responses were further associated with higher post-stimulus phase-locking than incorrect ones, in increasing frequency and latency. Finally, the larger the set size, the later the post-stimulus effect peaked. Together, these results suggest that increased complexity (lower discriminability or larger set size) requires more attentional cycles to perform the task, partially explaining discrepancies between reports of attentional sampling. Low-frequency oscillations structure the temporal dynamics of neural activity and aid top-down, attentional control for efficient visual processing.