A system for drilling subsea wells from a Mobile Offshore Drilling Unit (MODU), comprising a marine drilling riser arranged from the MODU to a seabed located Blow Out Preventer, a drill string arranged from the MODU through the marine drilling riser and BOP and further down a wellbore, at least one closing device (13, 15) arranged in the marine drilling riser, or in a high pressure part of the system below the marine drilling riser, such as integral with the BOP, the closing device (13, 15) being configured to close the annulus outside the drill string, characterised in that the system further comprises: at least one mud return outlet (29, 35) fluidly connected to the annulus, at a lower part of the riser or below the riser as well as below said closing device (13, 15), for flowing mud to a subsea lift pump that is configured to pump the received mud to above sea level, and a pipe that via at least one valve is fluidly connected to the subsea lift pump upstream of the subsea pump and downstream of the outlet (29, 35), and extending upwards from seabed or near seabed level to a level above sea level, providing a height between said levels for adjustment of a mud liquid level in said pipe in order to adjust and regulate the annular well pressure and keep a constant well bore pressure. a marine drilling riser arranged from the MODU to a seabed located Blow Out Preventer, a drill string arranged from the MODU through the marine drilling riser and BOP and further down a wellbore, at least one closing device (13, 15) arranged in the marine drilling riser, or in a high pressure part of the system below the marine drilling riser, such as integral with the BOP, the closing device (13, 15) being configured to close the annulus outside the drill string, characterised in that the system further comprises: at least one mud return outlet (29, 35) fluidly connected to the annulus, at a lower part of the riser or below the riser as well as below said closing device (13, 15), for flowing mud to a subsea lift pump that is configured to pump the received mud to above sea level, and a pipe that via at least one valve is fluidly connected to the subsea lift pump upstream of the subsea pump and downstream of the outlet (29, 35), and extending upwards from seabed or near seabed level to a level above sea level, providing a height between said levels for adjustment of a mud liquid level in said pipe in order to adjust and regulate the annular well pressure and keep a constant well bore pressure. at least one mud return outlet (29, 35) fluidly connected to the annulus, at a lower part of the riser or below the riser as well as below said closing device (13, 15), for flowing mud to a subsea lift pump that is configured to pump the received mud to above sea level, and a pipe that via at least one valve is fluidly connected to the subsea lift pump upstream of the subsea pump and downstream of the outlet (29, 35), and extending upwards from seabed or near seabed level to a level above sea level, providing a height between said levels for adjustment of a mud liquid level in said pipe in order to adjust and regulate the annular well pressure and keep a constant well bore pressure.