The present invention relates to a method and system for cleaning a process gas containing carbon dioxide and contaminants, by bringing the process gas into direct contact with an alkaline solution orslurry, and capturing in the alkaline solution or slurry at least a part of the contaminants of the process gas; and bringing the process gas, depleted in contaminants, into direct contact with a cooling liquid to form a cooled process gas; wherein said alkaline solution or slurry is separate from the cooling liquid.