The specification describes one-piece dental implants comprising a threaded shaft, optionally a non-circular abutment and a head having a shape which is capable of accepting a keeper cap or an O-ring, or which is capable of accepting and retaining a dental wire. The implants have dimensions that permit their use in a non-surgical method of insertion into bone, and are useful in both prosthodontic and orthodontic applications. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.