You can also try carefully applying a soldering iron to screw head. Maybe someone decided to put some loctite on it before you had it. I also own a set of precision stripped screw removers but they aren't the best as they are handheld (not enough torque or downward pressure as when using a power drill) and expensive. Good luck.
Thanks, forgot about the soldering iron.
Sometimes, a straightblade of the right width will get enough bite in a rounded out crosspoint screw to turn it out.