  An analysis of hadron abundances in heavy ion collisions from SPS to RHIC
energy within the statistical-thermal model is presented. Pb--Pb collisions at
40 A GeV are analysed for the first time here. Unlike stated in similar recent
studies, the data analysis rules out a complete strange chemical equilibrium in
full phase space. In fact, the use of multiplicities integrated in full phase
space or in a limited rapidity window at SPS energy gives rise to different
results for the extra-strangeness suppression parameter gamma_S while the
extracted values of temperature and baryon-chemical potential do not vary
significantly. This behaviour rises the question whether the observed hadronic
strangeness phase space saturation at RHIC within a small mid-rapidity window
would hold in a possible full phase space analysis.
