We explored one of the unusual predictions of the concept of back-coupling within the theoretical scheme of the control of posture and movement with setting referent coordinates for the effectors. This concept implies slow drifts of referent coordinates toward actual coordinates leading to unintentional drift in performance. During standing, such slow drifts may lead to a protective step or even a fall and, therefore, corrections are expected leading to body sway at frequencies under 0.1 Hz. Young healthy subjects stood on the force platform quietly for 60 s under two single-task conditions, with eyes open and closed, and two double-task conditions, matching an irrelevant muscle activation signal to a target (MATCH) and performing a subtraction task. The latter was performed with eyes open and closed. The rambling-trembling decomposition was applied to the displacements of the center of pressure in the anterior-posterior direction. Spectral analysis was used to quantify power within typical ranges for Tr and Rm, as well as for a slow Rm component (under 0.1 Hz) addressed as Drift. Closing eyes led to a significant increase in Rm and Tr, but no effects on Drift. Drift increased significantly in the MATCH task with no changes in Rm and a drop in Tr. No effects of the subtraction task were seen on Drift. Overall, our findings suggest that unintentional slow drift of referent body orientation towards the actual body orientation leads to Drift, a specific example of back-coupling reflected in postural sway. This observation can be also seen as an example of physiological minimization of activity of motoneurons. Natural visual feedback is used to avoid the COP drift and/or correct it quickly and effectively; this ability is compromised when vision is used for an unrelated task.