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. The riser mud return pump is arranged by the outlet and arranged to adjust the drilling fluid level to a predetermined level by or above the outlet and substantially deeper than the sea surface, and that the drilling fluid has considerably higher density than what would be sufficient to balance the same fluid pressure from the geological formations by using a drilling fluid column entirely up to the surface, or to the vessel.