I don't know if what I do is a good idea, but I've found that I can't always get all the solder clear of the pins in my first shot with the soldapullt.
1. Brush on a little bit of flux on the solder side of the board.
2. Heat up the iron so it's between 700F and 800F
3. Work with the board solder side up and desolder all of the pins using my $6 soldapullt. I try to work in a cross-hatch pattern to minimize the risk of over heating the chip, maybe? Top left to bottom right then top right to bottom left and repeat.
4. Flip the board over and inspect the top side, is all of the solder off the pins? Can I easily wiggle the legs with gentle pressure from a toothpick or blunt small flat head screwdriver?
5. If yes, slowly and carefully work the chip out of the board with said screwdriver, making sure not to scrape the traces.
6. If no, I'll mount the board in a vice so it stands vertically, then give it another 5 minutes to cool off.
7. Soldapullt in one hand and iron in the other, I'll put the soldapullt over whatever pin needs more solder removed (solder side) then I'll very briefly touch the top side of that same pin with the iron, making sure to also make contact with the top side through hole, no more than 2 or 3 seconds.
8. Activate the soldapullt and pull the iron off the pin, if done quickly and carefully, to any "stuck" pins, you should be able to literally pull the chip off the board with your fingers with almost no force.
I've had very good luck with this process, that being said, anyone is welcome to chime in and tell me I'm ruining chips and boards, this is just my two cents worth of info.