Abstract: A system for drilling a subsea well from a rig through a subsea wellhead below the rig includes a wellhead stack which is mounted on the subsea wellhead. The wellhead stack includes at least a subsea blowout preventer stack and a subsea diverter. A drill string extends from the rig through the wellhead stack into the well to conduct drilling fluid from the rig to a drill bit in the well. A riser which has one end coupled to the wellhead stack and another end coupled to the rig internally receives the drill string such that a riser annulus is defined between the drill string and the riser. A well annulus extends from the bottom of the well to the subsea diverter to conduct fluid away from the drill bit. A pump has a suction side in communication with the well annulus and a discharge side in communication with the rig and is operable to maintain a selected pressure gradient in the well annulus.