Which soldering iron is good to work on iphones?

I need to work on the battery connector on my iphone 4. The one that I have heats up pretty good but can't seem to get the solder melted at the tip. Any help?

You don't want a really powerful one; that is delicate work. Perhaps you could apply a touch of rosin core solder to the connection while you are heating it. Sometimes that will get the old solder to melt.