Healthy young adults (n = 39) were asked to perform four different secondary cognitive tasks during quiet unperturbed stance, in order to investigate the influence of physiological arousal and attention distraction on the control of spontaneous postural sway. During each task, postural activity was quantified in terms of center-of-pressure displacement, leg-muscle activation, and ankle and hip rotation. Arousal was monitored via skin conductance, and questionnaires were used to assess state anxiety. Respiratory trunk movements were also recorded, to assess potential arousal-related destabilizing effects, but failed to show a strong association with the postural measures. The nature of the secondary task affected the postural responses in that subjects tended to lean slightly forward, and exhibited higher levels of activation in tibialis anterior, when performing a mental-arithmetic task. Although this task affected both attention and arousal, the leaning effect was limited to subjects who reported higher levels of anxiety-related autonomic or somatic symptoms during testing, and the degree of leaning was correlated with the level of physiological arousal. A secondary task that diverted attention but did not affect physiological arousal (listening to a spoken-word recording) failed to elicit changes in postural response. These findings suggest that the changes in leaning were associated with task-related changes in physiological arousal, and highlight the need to account for the potentially confounding influence of arousal when studying attentional effects. Given the potential influence on stability, the results also suggest that leaning should be monitored or controlled during balance assessment, particularly when dealing with individuals who may be anxious or afraid of falling.