This is a rather interesting guide to solving the usual troubles. The writer effectively remove the whole capacitor before the soldering iron is ever applied.
Since I have lost traces while desoldering the little buggers in the past, I think I might well try this method next time around.
Seems like a decent way of doing it, providing you don't slip with your pliers and ruin the logicboard. I find it amusing that he replaced the old round cap with an equally cheap capacitor instead of a good tantalum one!