Absolutely nothing makes a better, lower-resistance splice than the wrapped connection known as a "Western Union" splice. About 2" of insulation is stripped off the main conductor, and the wire that taps off of it is applied around it with 10-15 TIGHT wraps. It gives more copper-to-copper contact area than any sort of butt splice or other connection method. The connection can be insulated with shrink tubing, self-vulcanizing rubber tape, or plain old electrician's tape. Soldering the joint if desired is a bit of overkill, but it strengthens the connection.
Jerry
