Drilling alabaster

Quoted text begins.In using a drill press, the toughest part for me has been to hold the
piece
still. (Anybody have any suggestions on that?) I've improvised various
types of jigs and contraptions for each piece - always takes a lot of time
and many trips to the hardware store.
End of quote.

The easiest way I've seen to hold a delicate piece for work such as drilling
is to place the piece in a suitable wood box after wrapping it in a plastic
bag(keep the opening at the top).You then fill the box with expanding foam
like is used for insulating.The foam encases and cushions the piece and the
box gives you something square w/flat sides to either grip in a clamp or
bolt to a bench.After the work is done just pull the sides off the
box,carefully peel the foam away and unwrap the piece which was kept clean
by the plastic bag.
Hope this helps.

BTW-You hit it when you said to drill first if at all possible.

Bob