The main Cu-bearing mineral in copper concentrates consumed in smelters around the world is chalcopyrite (CuFeS2). Minor participation in this consumption is copper concentrates containing secondary copper minerals, such as chalcocite (Cu2S) and bornite (Cu5FeS4). The main issues concerning these copper concentrates are the amount of impurities, such as, fluoride and uranium. These impurities cause a lot of problems for smelters owners, such as equipment corrosion, gas treatment necessity and radionuclides residues generation, leading them to impose restrictions to buy fluoride and uranium copper concentrates. This study proposes a selective atmospheric sulfuric acid leaching process route to extract the maximum of fluoride and uranium and a minimum of copper from two types of copper concentrates, one having chalcocite/bornite as main Cu-bearing minerals, named as chalcocite/bornite concentrate, and another with chalcopyrite as the main Cu-bearing mineral, named as chalcopyrite concentrate. The results show that it is possible to reduce significantly the amount of fluoride and uranium in both samples. These two samples required the addition of sulfuric acid until reaching a pH of (3.5 ± 0.2), which means consumption of 23 kg and 9 kg of H2SO4 97.5 wt% per ton of chalcocite/bornite concentrate or chalcopyrite concentrate, respectively. The addition of aluminum sulfate increases the fluoride extraction, whereas it did not raise the uranium extraction. Chalcocite/bornite concentrate showed a slow kinetic to have fluoride leached, whereas chalcopyrite concentrate presented a fast kinetic to have uranium leached. It was possible to extract 60% of fluoride and 35% of uranium from chalcocite/bornite concentrate and around 10% of fluoride and 60% of uranium from chalcopyrite concentrate. As expected, the copper leached from chalcocite/bornite concentrate was higher (~4.5% of total Cu) than from chalcopyrite concentrate (~0.3% of total Cu). Moreover, it was proposed a complete process route to reduce the amount of fluoride and uranium comprising of acid leaching, copper recovery from the liquor by cementation with powder Fe and liquor treatment by raising the pH up to 9.0 by addition of calcium hydroxide pulp.