A multi-unit abutment aligning a dental implant and a screw-attached prosthesis with copings is disclosed. The multi-unit abutment has a threaded base post for attachment to the implant and a ball portion. A swivel post into the implant with the multi-unit assembly in a linear configuration. The swivel shell is then positioned and fixed at a desired tilt and azimuthal angle. The swivel shell has a mating surface for a coping. The lock screw remains accessible through an aperture in the coping when the prosthesis is positioned on the implant abutments. Different embodiments are disclosed for capturing the swivel shell on the ball. Methods for improving passive alignment of the prosthesis to the implants are described.