Pat's got it right. Especially when working with ground planes. The trick is not to remove solder, but to add more! I add solder to the joint (new flux), heat it up for a second or two, then pull that leg of the resistor out with a tiny pliers. Other side is then easier. Lots of solder will keep everything heated up and you won't pull or break traces. The added flux is very important.
With a lot of practice, I don't even use the pliers anymore. Just put iron under that little loop of exposed leg, heat up, and lift.
Only after part is removed do you remove solder. That's when the braid or vacuum pump comes in.
jh