For very-difficult de-soldering, I use a variation on the Chip-Quik idea. I take a hunk of Cerrobend 158 fusible alloy and a file and make a small pile of powder from it. I then pack the powder around the pins of the IC to remove and heat the area using the light from a 75 watt PAR-38 halogen reflector lamp. (apply from the reverse side of the PCB). In very little time, the area of the board heats up enough to melt the cerrobend and it fuses with the solder. The part can then be easily removed (SMT stuff just slides off). Since the board never even gets to 100C, everything else stays in place and you don't burn the board or lift traces. Clean up with a toothbrush. Discard the fused metal. I suppose that instead of the lamp, you could use a hot-air rework tool set low.
Anyway, that's what I do. --Chuck