A process for eliminating at least pollutants including polar compounds present in a first fluid, with said first fluid sent to a subsequent treatment, e.g., an etherification process: a) the first fluid containing pollutants is contacted with an auxiliary fluid such as a vapor phase, under operating conditions that are selected so as to obtain, at the end of this first stage, said first fluid that is purified and freed of, for the most part, pollutants, and a vapor phase that is loaded with pollutants, said vapor phase being produced during one phase of the process, and b) at least a portion of said first purified fluid is recycled to a subsequent treatment stage.