The result of the above join:
Just pull the covering back down and good to go.
An even slicker method would be to cut small bits of heat shrink plastic sleeve and feed it over the wire prior to soldering, and slide it over the joint when done. I got about 3/4 of the way through this job before I realised, oh well, next time...
This is the shape of the solder tip I am using. It is about 5mm across the tip, no one of those pointy Les, they have trouble getting enough heat in to the joint.
Notice how dirty it is. Another Reston that your soldering might not be going well. You can have like steel wool near the job, and rub the tip in it after each join. To clean up from here I simply hit it with a file, remember that it is still hot!