We studied the physico-chemical and radioactive characteristics of four waters of subsurface origin. They were chosen for having the highest natural radioactivity levels of waters for human consumption in the Autonomous Community of Extremadura, Spain Their activity levels for alpha emitting radionuclides are between 120 and 19300 mBq L(-1), all exceeding the 100 mBq L(-1) threshold established in the European Union above which radioactive isotopes that are present in water should be investigated to determine which corrective action, if any, is needed. These waters were used to compare the efficiency in eliminating their uranium and radium content of two potabilization processes - one the standard chlorination-only process used by their respective municipalities, and the other a procedure consisting of coagulation, flocculation, settling, filtration, and chlorination stages, specifically designed to maximize the elimination of their natural radioactive content. The results showed the uranium and radium elimination efficiencies to depend strongly on the water's hydrogencarbonate, calcium, and magnesium ion concentrations. In particular, with increasing concentrations of any of these ions, the uranium elimination efficiency fell from 90% to 60% at its optimal working pH, pH=6, while the radium elimination efficiency rose from 50% to 90% at its optimal working pH, pH=10.