IIRC, the local Plexiglas shop has some drill bits intended for
Plexiglas. They look like high speed steel bits, but they have a smaller
tip angle (sharper point).

Backing the piece with a block of wood is still a good idea.

--
Paul Hovnanian
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Karate is a form of martial arts in which people who have had
years and years of training can, using only their hands and feet,
make some of the worst movies in the history of the world.
-- Dave Barry