I'm late to the party. I have no advise that hasn't already been given.
I use a Weller SPG40 soldering station. I can't find a link so I guess they don't make them anymore. It's a 40 watt iron, I have it set at 4 1/2 on the dial and I have no problem soldering (or unsoldering) the back of pots or just about anything else. I do have to turn it all the way up to solder pickup covers and even then it's not quite enough, but I can make it work if I hold my tongue just right. I don't use the big fat wide tip or the pencil point tip, I use the in between one. Like the one laying on the sponge in this pic...