I know it's been covered but these DOA4 stick buttons are a pain in the

I’m trying to desolder the DOA4 buttons from the XBox360 stick so I can remove the PCB. I was hoping to save the buttons for now until I decide what I want to do with them. I tried using my 15 watt iron with desoldering braid but it doesn’t seem to want to desolder jack.

Should I get a special desoldering iron? Will it burn hotter than the 15 watt I’ve got or am I doing it wrong. What I’m doing is: letting the iron heat for about 20 minutes, applying braid to the solder, applying the iron to the braid then…waiting. And waiting. And NOTHING.

Any suggestions? Anyone been through this before? I just want to remove the PCB so I can begin the next phase of my project…(insert evil newbie laugh here).