Recent research has related the orienting of selective attention to the lateralization of posterior EEG alpha power (∼8 to 12 Hz). Typically, alpha power decreases over the side of the head contralateral to the cued side of space. However, it is not clear how this lateralization affects behavior. We recorded EEG from 20 participants while they performed a cued visual discrimination task under three different response‐deadline conditions to investigate the effect of alpha‐power modulation on behavioral performance in more detail. Although all participants benefited from the cue behaviorally and adjusted their performance according to the response deadlines, we found the cue‐related alpha‐power modulation to depend on the general alpha‐power level at baseline: Only participants with high baseline alpha power showed significant cue‐related alpha‐power lateralization that was, however, strikingly similar across response‐deadline conditions. On the other hand, participants with low alpha power at baseline did not show any lateralization, but adjusted their alpha levels according to the response‐deadline instructions and, more importantly, showed a stronger influence of the task instructions on behavioral performance and adapted their response accuracies to the task requirements more flexibly. These findings challenge the often‐assumed role of alpha‐power lateralization for attentional deployment. While alpha power seems to be related to behavioral performance and the orienting of attention, this relationship is rather complex and, at least under the current task requirements, the general alpha‐power state seems to be more strongly related to behavioral performance (in our case, the flexible adjustment to task requirements) than the cue‐related lateralization.