Make a stack! Use a scrap piece of 1/4" plywood. Using blue painters tape, tape the edges of the two boards together. The thicker stack will give you better control of your work piece. You can use two or three layers of the same ply, you can make more than one piece at a time. If you don't need multiple copies, than just use scrap ply, then toss it when you are done.
I never cut anything thinner than 1/4". If I need thinner, I always make a stack.