Here is an example of a Western Union connection that I made using 18 ga solid copper wire and 18 ga stranded wire. I lightly tinned the stranded wire and it behaved just like the solid copper wire.
The advantage of this connection is that it does not increase the diameter of the wires that much and the splice is stronger than the breaking strength of the wire itself.
The sharp ends of the wires are trimmed, if needed.
Then an insulating jacket of heat shrink tubing will make this splice very effective.
Mark