I've never had too much fun connecting two wires, and finally looked on YouTube for suggestions. My normal connection technique has always been the pigtail (see diagram below): Strip the wires, hold them together and twist, and solder. Cover the result with electrical tape or shrink wrap. The result works but is not as nice as butt connections, and takes up more space in tight situations.
But butt connections are impossible for me, with only two hands and my fumble-fingers. Especially with small gauge wire.
YouTube provide a technique I really like. Sadly I've lost the link and can't credit the YouTube poster. First, don't forget to slide a piece of shrink wrap onto one of the wires. The idea is to start with a pig-tail, then bend it half-way, press, and solder. Then bend at the bottom and press against one of the insulated wires, and slip the shrink-wrap over the connection. After the shrink-wrap is shrunk, f you can pull the connection apart you're either the Hulk, or you need to be careful around Kryptonite. This method is illustrated at the bottom of the following diagram.
What's really nice about this technique is that the result is very much like butt connections in terms of compactness and esthetics.
The following photo sequence shows this method: The pig-tail connection with the strands twisted together; the middle bend; a bit of solder applied; the base bend down against the gray wire; and the shrink-tube slipped over the connection, prepared for a blast from the heat gun.
