We investigated the effect of performing a mental arithmetic task with two levels of difficulty on the regulation of centre of foot pressure (COP) displacements during bipedal quiet standing in young healthy individuals. There was also a control condition in which no concurrent task was required. A space-time-domain analysis showed decreased COP displacements, along the antero-posterior axis, when participants concurrently performed the most difficult mental arithmetic task. Frequency-domain and stabilogram-diffusion analyses further suggested these decreased COP displacements to be associated with an increased stiffness and a reduction of the exploratory behaviours in the short term, respectively.