A dental attachment assembly has an abutment portion at the proximal end of a one-piece dental implant (an “abutment portion”), or is an abutment for attachment to a dental implant or to a bar joining two or more dental implants, and a two-part assembly including a metal cap for placement in/attachment to a dental appliance. The cap includes a flanged skirt that projects from the top surface of the cap. A second part, a plastic insert, snaps firmly inside the cap.