A method providing for the selective hydroproces sing of cracked naphtha feedstock to make a low-sulfur gasoline blending component. The method includes the use of two catalytic distillation stages in combination with two stripping columns and two fixed-bed reactors integrated in a novel arrangement so as to provide for the treatment of cracked naphtha feedstock that has a high sulfur concentration to yield exceptionally low-sulfur light cracked naphtha and heavy cracked naphtha products. The desulfurized light and heavy cracked naphtha are produced with a minimal amount of hydrogenation of the olefin content and at may suitably be used as gasoline blending components.