My headphones had a loose connection. I could make the sound cut in and out of the right ear by bending the cable just above the audio plug. So I set about peeling back the insulation. I thought it would be as simple as soldering the broken wire back together. I was wrong for a couple of reasons. Inside the cable, I found three coloured wires: red, blue, and copper. The first complication was that these wires are very small; they didn't fit in my wire strippers, so I know that they are smaller than 32-gauge. Secondly, rather than having coloured plastic insulation with bare wire underneath, these wires appear to have no separate insulation. Instead, the strands themselves are coloured, and they are non-conducting. Is each individual strand coated in something that insulates it? After scraping at some of the wires with my fingernail, I was able to peel back some translucent white stuff that appeared to be holding the strands together, but the exposed strands themselves still don't conduct, and solder doesn't bond to them at all. It appears that it was not as smart an idea as I first thought it would be to undertake this repair. How do I work with this type of wire?