Both of the those methods are close to what was outlined on this post before the pics went missing. I would ignore the "thin wire" wrapping. It's a pain, and pretty useless. The side-by-side method, which has the virtue of looking easy is deceptivly so. Holding the two wires parallel while working the iron and the solder requires 4 hands. I never have 4 hands available. Do this: Get the heat shrink wrapping. Prepare the two wires to be spliced by stripping and twisting them. Place the shrink wrapping on the wire and slide it out of the way. Place the two stripped ends side by side (like seen in the second method above). Now twist them together. If you had enough wire stripped out, it should hold it's self together. Grab the iron and solder. Heat and wick the solder in to the wire wrap so it gets between the wire twists. Let cool. Slide the wrap over top and heat. I tend to layer vinyl tape over top of the completed splice, but that is personal preferance.