Processes are provided herein for producing naphtha boiling range products with a desired sulfur content by reducing the mercaptan content of the naphtha boiling range products after the products exit a hydroprocessing stage. Due to mercaptan reversion, naphtha boiling range products that contain even small amounts of olefins can have a higher than expected sulfur content after hydroprocessing. In order to reduce or mitigate the effects of mercaptan reversion, microchannel reactors (or microreactors) can be placed in a processing system downstream of a reactor that produces a low sulfur naphtha product. The microreactors can include a coating of metals that have activity for hydrodesulfurization. By passing at least a portion of the naphtha product through the downstream microreactors, the mercaptans formed by reversion reactions can be reduced or eliminated, resulting in a naphtha product with possessing a very low sulfur content.