First and second stages are used in electrodeionization to purify water including calcium and carbon dioxide and its hydrates. The diluting flow channels of the first stage include only anion exchange material or cation exchange material, and thus remove either carbon dioxide and its hydrates (and other anions) or calcium (and other cations) but not the other. The diluting flow channels of the second stage receive the diluting channel effluent from the first stage and include the other type of exchange resin (or a mixed resin) and remove the oppositely charged ions. The brine effluent from the concentrating flow channels in the first stage is isolated from the second stage, and calcium and total inorganic carbon tend to be removed in different stages so as to deter calcium carbonate precipitation in any of the concentrating flow channels. Also the concentrating channels can include cation exchange material next to the anion membrane, with pH being lowered at the surface of the anion so as to limit calcium carbonate precipitation in the concentrating flow channel. Also disclosed are using countercurrent flow in the diluting flow channels and the concentrating flow channels and flowing the feed to the concentrating compartment first through a region that renders it substantially acidic before it enters a region that contains calcium.