A stochastic complexity analysis is applied to centre-of-pressure (COP) time series, by using different complexity features, namely the spectral entropy, the approximate entropy, and the singular value decomposition spectrum entropy. A principal component analysis allows an estimate of the overall signal complexity in terms of the ensemble complexity score; the difference in values between open-eyes (OE) and closed-eyes (CE) trials is used for clustering purposes. In experiments on healthy young adults, the complexity of the mediolateral component is shown not to depend on the manipulation of vision. Conversely, the increase of the anteroposterior complexity in OE conditions can be statistically significant, leading to a functional division of the subjects into two groups: the Romberg ratios (RRs), namely the ratios of the CE measure to the OE measure, are: RR = 1.19 +/- 0.15 (group 1 subjects), and RR = 1.05 +/- 0.14 (group 2 subjects). Multivariate statistical techniques are applied to the complexity features and the parameters of a postural sway model recently proposed; the results suggest that the complexity change is the sign of information-generating behaviours of postural fluctuations, in the presence of a control strategy which aims at loosening long-range correlation and decreasing stochastic activity when visual feedback is allowed.