Cognitive-processing demands can affect postural control processes. Traditional methods of analyzing postural control aggregate sway data, making it difficult to isolate specific influences of cognitive processes. In the present study, an event-related methodology is used during a cognitive dual task to explore how cognitive processes influence postural control processes. The dual task comprises a visual-vocal short-term memory task with a delayed vocal response and an auditory-manual reaction time (RT) task. We manipulated the stimulus onset asynchrony (SOA; 100 vs. 1,000 ms) between the stimuli (Experiment 1) and whether participants had to report or ignore the visual object (task load: ignore vs. report; Experiment 2). These were applied on a trial-by-trial basis or in blocks of predictable versus unpredictable task load (Experiment 3). RTs in the auditory-manual task were longer during short SOA compared to long SOA, suggesting a bottleneck caused by encoding the visual object for later report. This effect disappeared in predictable ignore-trials, when the visual object was never relevant. To assess postural correlates, we analyzed continuous force-plate data using cluster-based permutation analysis, providing a sensitive and precise approach. This analysis revealed no process-specific influence of SOA on postural control processes, but a reduction of sway variability after visual target onset in report but not in ignore trials. Moreover, a difference in sway variability over the course of a trial in report vs. ignore trials occurred in predictable blocks only. The data suggest a bottleneck between memory-consolidation processes and postural control adjustments.