Fibers may be intertwined to form cables for headsets and other structures. The cables may include wires. The wires may be surrounded by a jacket formed from intertwined fibers. The intertwined fibers may include fibers with different melting temperatures. The jacket may be heated to a temperature that is sufficient to melt some of the fibers in the jacket without melting other fibers in the jacket. The melted fibers may flow into spaces between the unmelted fibers and may serve as a binder that holds together the unmelted fibers. The intertwining process may be used to form a bifurcation for a headset. A dipping process may be used to cover the jacket with a coating. The coating may be formed over the entire length of the cable or may be formed in a particular portion of the cable such as the portion of the cable that includes the bifurcation.