Abstract: A drilling riser for use at great sea depths for drilling of wells in the seabed using a drill string, with the drilling riser arranged to be connected between a wellhead at the seabed and a vessel, and arranged for use with a drilling fluid with sufficiently high density to balance the fluid pressure from the geological formations, with a sensor arranged to detect the level of the drilling fluid's level in the drilling riser, and a return riser pipe with an adjustable return riser pump. The return riser pipe extends up to the vessel, from an outlet on the riser, from a depth which is substantially below the sea surface, and at the same time at a height substantially above the seabed.