A completion method for completing a well having a top, comprising: - drilling a borehole below a first well tubular metal structure in the well, - circulating mud at least partly while drilling the borehole, - providing a second well tubular metal structure having at least one unexpanded annular barrier having a tubular part surrounded by an expandable metal sleeve, expandable by means of pressurised fluid from within the second well tubular metal structure through a valve assembly into an annular space between the tubular part and the expandable metal sleeve, the second well tubular metal structure having a first end closest to the top and a second end, the valve assembly having a first condition in which fluid communication between an inside of the second well tubular metal structure and the space is disconnected, and having a second condition allowing fluid communication between the inside of the second well tubular metal structure and the annular space, - running of the second well tubular metal structure into the well to a position at least partly below the first well tubular metal structure, - circulating cleaning fluid at a first pressure out through the second end to remove at least part of the mud, characterised by - displacing cement at a second pressure down through the second well tubular metal structure and out through the second end into an annulus between the second well tubular metal structure and a wall of the borehole, - pressurising the inside of the second well tubular metal structure to a third pressure above the first pressure and the second pressure breaking a breakable element in the valve assembly, which changes condition from the first condition to the second condition, and - further pressurising the inside of the second well tubular metal structure, expanding the expandable metal sleeve to abut the wall of the borehole. - drilling a borehole below a first well tubular metal structure in the well, - circulating mud at least partly while drilling the borehole, - providing a second well tubular metal structure having at least one unexpanded annular barrier having a tubular part surrounded by an expandable metal sleeve, expandable by means of pressurised fluid from within the second well tubular metal structure through a valve assembly into an annular space between the tubular part and the expandable metal sleeve, the second well tubular metal structure having a first end closest to the top and a second end, the valve assembly having a first condition in which fluid communication between an inside of the second well tubular metal structure and the space is disconnected, and having a second condition allowing fluid communication between the inside of the second well tubular metal structure and the annular space, - running of the second well tubular metal structure into the well to a position at least partly below the first well tubular metal structure, - circulating cleaning fluid at a first pressure out through the second end to remove at least part of the mud, - displacing cement at a second pressure down through the second well tubular metal structure and out through the second end into an annulus between the second well tubular metal structure and a wall of the borehole, - pressurising the inside of the second well tubular metal structure to a third pressure above the first pressure and the second pressure breaking a breakable element in the valve assembly, which changes condition from the first condition to the second condition, and - further pressurising the inside of the second well tubular metal structure, expanding the expandable metal sleeve to abut the wall of the borehole.