The invention provides for the treatment of raw water having a pH of 2.5 to 9, an alkalinity of at most 50 mg/l expressed as calcium carbonate, a calcium content of at most 100 mg/l expressed as calcium carbonate, and a positive calcium carbonate dissolution potential. The process comprises separating part of the water from the remainder thereof and acidifying the part to increase its calcium carbonate dissolution potential. The acidified water is then fed through a bed of particles comprising calcium carbonate where the water consumes part of the calcium carbonate thereby increasing the calcium content and the alkalinity of the water which issues from the bed. The water issuing from the bed is then mixed with the remainder of the raw water to obtain an at least partially treated product water having a positive calcium carbonate dissolution potential which is at least 2 mg/l calcium carbonate less than that of the raw water.