I've found that desoldering wick has great affinity for solder. It removes solder it isn't even touching because as the solder it actually touches flows into it, adjacent solder gets pulled in by sufrace tension as well. The stuff works like a miracle. Don't give up until you have tried it. I use Chemtronics wick but some others I have used work just as well. Make sure it says it is a fluxed wick.