Like Joe suggested, I've also just soldered wires together and used heat shrink over the joint. I would just fan out the strands a bit, push the wires together and twist the strands, then run a little solder on. That keeps the joint just barely larger in diameter than the original. I try to be sparing on the heat so as not to let solder wick up the wires under the insulation, softening that and making the wire stiffer than it should be.
