Abstract: A multilayer, heat shrinkable composite tube covering is provided for a cable joint structure in which intimately joined layers define a semiconductive inner or conductor shield, an insulation layer, and an outer or insulation shield for the joint. Furthermore, a highly resistive semiconducting layer is provided over the joint under the innermost layer of the composite tube, forming a dual layer conductor shield for the joint. In the preferred embodiment, the entire composite tube is pressure extruded in a common operation and all three layers are simultaneously chemically cured and cooled under pressure to provide the intimately joined layers of the composite tube. Subsequently, when the tube is shrunk over the joint, the three layers shrink as a unit, so that there is no possibility of trapping impurities or gas bubbles between layers.