A method of processing a hydrocarbon feed boiling in the range of 180°C to 450°C selected from straight run gas oil, a middle distillate fraction, or a diesel fraction, to reduce the concentration of undesired organosulfur compounds comprising: separating the hydrocarbon feed by aromatic extraction into an aromatic-lean fraction that contains labile heteroatom-containing compounds and an aromatic-rich fraction that contains refractory aromatic heteroatom-containing compounds; wherein separating the hydrocarbon feed into the aromatic-lean fraction and the aromatic-rich fraction is by subjecting the hydrocarbon feed and an effective quantity of an extraction solvent to an extraction zone to produce an extract containing a major proportion of the aromatic content of the hydrocarbon feed and a portion of the extraction solvent and a raffinate containing a major proportion of the non-aromatic content of the hydrocarbon feed and a portion of the extraction solvent; separating at least a proportion of the extraction solvent from the raffinate and retaining the aromatic-lean fraction; separating at least a portion of the extraction solvent from the extract and retaining the aromatic-rich fraction, wherein the exreaction solvent is selected from the group consisting of furfural, N-methyl-2-pyrrolodine, dimethylformamide and dimethylsulfoxide; introducing the aromatic-lean fraction to a first hydrotreating zone operating at mild hydrotreating conditions effective for reducing the sulfur content of the aromatic-lean fraction including hydrogen partial pressures of 40 bars and below and recovering a first hydrotreated effluent; and introducing the aromatic-rich fraction to a second hydrotreating zone operating at conditions effective for reducing the sulfur content of the aromatic-rich fraction including hydrogen partial pressures of 40 bars and above and recovering a second hydrotreated effluent; removing light gases from the second hydrotreated effluent to produce a hydrotreated liquid effluent; and introducing the hydrotreated liquid effluent to an aromatic hydrogenation zone and recovering a hydrogenated hydrocarbon product stream, in which at least one of the first and second hydrotreating zones comprise a layered catalyst bed containing at least a first and second layer of different catalyst compositions, and the catalysts are Co-Mo on alumina and Ni-Mo on alumina. separating the hydrocarbon feed by aromatic extraction into an aromatic-lean fraction that contains labile heteroatom-containing compounds and an aromatic-rich fraction that contains refractory aromatic heteroatom-containing compounds; wherein separating the hydrocarbon feed into the aromatic-lean fraction and the aromatic-rich fraction is by subjecting the hydrocarbon feed and an effective quantity of an extraction solvent to an extraction zone to produce an extract containing a major proportion of the aromatic content of the hydrocarbon feed and a portion of the extraction solvent and a raffinate containing a major proportion of the non-aromatic content of the hydrocarbon feed and a portion of the extraction solvent; separating at least a proportion of the extraction solvent from the raffinate and retaining the aromatic-lean fraction; separating at least a portion of the extraction solvent from the extract and retaining the aromatic-rich fraction, wherein the exreaction solvent is selected from the group consisting of furfural, N-methyl-2-pyrrolodine, dimethylformamide and dimethylsulfoxide; introducing the aromatic-lean fraction to a first hydrotreating zone operating at mild hydrotreating conditions effective for reducing the sulfur content of the aromatic-lean fraction including hydrogen partial pressures of 40 bars and below and recovering a first hydrotreated effluent; and introducing the aromatic-rich fraction to a second hydrotreating zone operating at conditions effective for reducing the sulfur content of the aromatic-rich fraction including hydrogen partial pressures of 40 bars and above and recovering a second hydrotreated effluent; removing light gases from the second hydrotreated effluent to produce a hydrotreated liquid effluent; and introducing the hydrotreated liquid effluent to an aromatic hydrogenation zone and recovering a hydrogenated hydrocarbon product stream, in which at least one of the first and second hydrotreating zones comprise a layered catalyst bed containing at least a first and second layer of different catalyst compositions, and the catalysts are Co-Mo on alumina and Ni-Mo on alumina.