The recently proposed use of hydrogels for water desalination is based on the decrease of salt concentration in the gel upon compression. In the first experiments, desalination cycles using hydrogels involved an irreversible mixing step, which inevitably reduced the thermodynamic efficiency. This approach could become competitive with membrane-based desalination methods if it could work close to maximum thermodynamic efficiency. In this work, we develop a thermodynamic model for compression of weak polyelectrolyte hydrogels in open and closed systems. We use this model to design a fully reversible desalination cycle which can, in principle, achieve maximum thermodynamic efficiency. We also show that compressing weak polyelectrolyte hydrogels at low salinity decreases their ionization, thereby leading to a non-monotonic dependence of salt concentration on the gel compression. Therefore, our model shows how to redesign the desalination cycle when using weak polyelectrolytes at low salinities.