A process for adsorbing aromatic sulfur compounds, where an adsorbent is contacted with a C6-C20 aromatic and/or aliphatic stream which comprises a solution of (i) at least one benzothiophene compound, (ii) a solvent which comprises at least one C6-C16 aliphatic compound, and (iii) optionally at least one C6-C12 aromatic compound. In this process, the adsorbent is regenerated using an organic regenerant such as, but not limited to, toluene. Also disclosed is another process for adsorbing aromatic sulfur compounds. In this process, an adsorbent is contacted with a mixture comprising a model diesel feed comprising at least one benzothiophene compound. In this process, the adsorbent is regenerated using an organic regenerant such as, but not limited to, toluene.