This invention features an assembly that creates a strong bond connection between a conductive polymeric element of a cable, such as a polymeric conductive core or polymeric conductive shield layer, and an electrical connector. The invention features two components: a newly styled connector, and an intermediate sleeve. The newly styled connector is made of an inner, concave, bullet-shaped recess that fits within an outer, deformable shell. The intermediate sleeve joins the polymeric element of the cable and the electrical connector. The sleeve consists of two sections. The first section has a solid, convex, bullet-shaped nose portion that fits into the concave, bullet-shaped recess located in the connector. The two bullet-shaped male and female surfaces mate with each other; they are metallic, so that they are easily solderable. The second section of the sleeve is made of a hollow tube-like portion that fits over the polymeric element; this hollow tube-like portion is deformably crimped over the polymeric element, providing a strong mechanical bond. The first section of the sleeve is solderable to the connector after the outer shell of the connector has been fitted over the sleeve and crimped onto it. The double crimp between the connector and the sleeve, and between the sleeve and the polymeric element, provides a double mechanical bond between the polymeric element, the sleeve and the connector. Such double crimping, in combination with the soldered connection, provides a very strong mechanical bond.