A method to cook thin chips in a continuous digester vessel including: introducing thin chips having a thickness of no more than 6 mm, into a chip bin; adding white (cooking) liquor to the chip bin or to a chip transport passage extending from the chip bin to an upper inlet of the continuous digester vessel; injecting medium pressure steam or another heated fluid to an upper region of the digester vessel to elevate a cooking temperature of the chips in the vessel to at least 130 degrees Celsius; cooking the chips in the vessel as the chips flow downward through the vessel without substantial extraction or introduction of liquor in the cooking section of the vessel; injecting wash liquid to a lower region of the vessel; extracting at least wash liquid through a wash liquid extraction screen in the lower region of the vessel and above the injection of the wash liquid, and discharging the cooked thin chips from the lower region of the vessel.