Complexity (or its opposite, regularity) of heart period variability has been related to age and disease but never linked to a progressive shift of the sympatho-vagal balance. We compare several well-established estimates of complexity of heart period variability based on entropy rates (i.e. approximate entropy (ApEn), sample entropy (SampEn) and correct conditional entropy (CCE)) during an experimental protocol known to produce a gradual shift of the sympatho-vagal balance towards sympathetic activation and vagal withdrawal (i.e. the graded head-up tilt test). Complexity analysis was carried out in 17 healthy subjects over short heart period variability series (about 250 cardiac beats) derived from ECG recordings during head-up tilt with table inclination randomly chosen inside the set {0, 15, 30, 45, 60, 75, 90}. We found that: 1) ApEn does not change significantly during the protocol; 2) all indices measuring complexity based on entropy rates including ad-hoc corrections of the bias arising from their evaluation over short data sequences (i.e. corrected ApEn, SampEn, CCE) evidence a progressive decrease of complexity as a function of the tilt table inclination, thus indicating that complexity is under control of the autonomic nervous system; 3) corrected ApEn, SampEn and CCE provide global indices that can be helpful to monitor sympatho-vagal balance.