A compression connector for connecting to a coaxial cable is provided. The compression connector is provided in a first state for fitting onto an end of the cable, after which it may be compressed to a second state, thereby joining the connector to the cable to make a coaxial cable assembly. The connector is comprised of a tubular connector body and a compression cap structured to slidably engage the second end of the tubular body. The connector is further internally configured with means for collapsing the first exposed corrugation of the outer conductor of the coaxial cable in the axial direction when the compression cap is compressed onto the tubular connector body.