A method providing for the selective hydroprocessing of cracked naphtha feedstock to make blending components for low-sulfur gasoline and either ultra-low sulfur diesel or ultra-low sulfur jet fuel. The method includes the use of two catalytic distillation stages in combination with three 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 and low-sulfur diesel or jet fuel. The desulfurized light and heavy cracked naphtha are produced with a minimal amount of hydrogenation of the olefin content and may suitably be used as gasoline, jet fuel, and diesel blending components.