A compression connector for smooth walled, corrugated, and spiral corrugated coaxial cable includes an insulator disposed within the body, wherein the insulator contains a central opening therein which is dimensioned smaller than a collet portion which seizes a center conductor of the coaxial cable. The connector also includes a clamp disposed inside the body as well as a compression sleeve assembly. An intermediate connector element includes a transitional surface which interacts with the clamp. When an axial force is applied to the compression sleeve, the clamp is forced by the transitional surface into the body, causing the clamp to squeeze onto an outer conductor layer of the coaxial cable. At approximately the same time, the collet portion is forced through the central opening of the insulator, causing the collet portion to squeeze onto the center conductor.