A method forms a non-circular socket in a jawbone of a patient for receiving a dental implant. A pilot hole is formed in the jawbone. A framework having one or more sets of opposing drill points configured to rotate along axes that are transverse to a vertical axis is directed along the pilot hole. The framework produces the non-circular socket, which may have a series of tiers. A dental implant is inserted into the socket. The dental implant may have a series of tiered sections shaped so that each tiered section conforms to a respective one of the tiers in the socket. An abutment may be securely fastened to the dental implant.