If they are a wood screw you might be able to use a tool called an easy out.
you have to drill a hole into the broken screw and depending what type of easy out you have (square or round) the square type you bang it into the hole you drilled in the screw and then turn it anti clockwise and the screw comes out. the round type have a left hand self taping thread, you just screw it in and keep turning it until the screw comes out.

i dont know if you will get one small enough though.