Expose about 1/2 inch of wire on each wire to be joined. Line up the bared ends of each wired so that they are side by side and use your finger tips to twist them together to form a tight group. Now with the very light gauge stuff, I roll the bare copper into a tight, compact ball before heat shrinking.
The heavier type wire that has been joined by twisting, just needs to be folded so it lays lengthwise with the wire it has now joined, then heat shrunk.
Go ahead and give your work a test tug to see how well it is connected, I don't bother with the test tug, this method has never failed.
The green heat shrink that is sold by Dubro works well.
The key to success is to have a light touch when scoring the insulation to strip the wire. Just barely score it by rolling the wire in your fingertips against a #11 blade. It might take a little practice, it isn't hard to get to where you harm 0% of the strands.