Several embodiments of a wedgethread pipe connection are disclosed that have improved makeup, sealing, and non-loosening characteristics. In one embodiment, an open wedgethread is disclosed that has an included angle measured in the gap between the stab flank and the load flank to be not less than zero, so as to prevent premature wedging between mating flanks before the position of full makeup is reached, as does occur between trapped wedgethreads wherein the included angle is less than zero. The invention may be used for pipe threads large or small, as a flush joint, with collars, screwed into plates or it may even be used to reversibly connect such as solid posts to base members where a wide makeup torque range is desired. This Open wedgethread, as opposed to trapped wedgethreads, provides a threaded pipe connection that: is more cost-effective; can seal high pressure gas; can provide selectively a connection strength as high as the pipe strength; assures easy makeup to the desired position of full makeup within a wide torque range; may have a torque strength as high as the pipe torque strength; is easier to manufacture; is easier to gage; and is less subject to handling damage.