The invention is an elongate intracorporeal member having a polymer jacket secured to a high strength shaft with the polymer jacket having an outer layer of polymeric material and an inner layer formed of polymeric adhesive. In one embodiment, a balloon catheter has a proximal high strength tubular section with a polymer jacket having an polymeric outer layer and an adhesive polymer inner layer. In another embodiment, a guidewire has an elongate core with polymer jacket disposed about at least a portion of the elongate core, wherein the polymer jacket comprises a polymeric outer layer an inner layer of polymeric adhesive disposed between and bonding the outer layer to the elongate core.