An electrodialysis process and apparatus is presented for improving the current efficiency of salty water desalination. The process includes reducing the osmotic and the electro-osmotic flow of water from diluate compartments to concentrate compartments, and between electrode compartments and adjacent compartments, by confinement and hydraulic isolation of their contents in constant volume compartments, so that the tendency of waters entering from diluate compartments to concentrate compartments leads to pressure buildup in the concentrate compartments, reducing the transfer of product desalinated water to the concentrate waste.