A compression connector for the end of a coaxial cable. The coaxial cable has a center conductor surrounded by a dielectric layer, the dielectric layer being surrounded by a conductive grounding sheath, and the conductive grounding sheath being surrounded by a protective outerjacket. The compression connector includes a body, a post and a compression member. The body and/or the compression member can have various shapes and orientations to enable the compression connector to readily accommodate coaxial cable having various thicknesses, due to, for example, being made by different manufacturers.