Thanks so much for the suggestions so far. To be clear, the holes are
only about 3-4" in diameter, but let me recap to make sure I understand
the suggestions.

Take a narrow, wide piece of wood and position over the hole(s). Secure
in place (through the ceiling?) with drywall screws. Adhere the filler
pieces to the wood with joint compound. (Is securing the piece with
drywall screws necessary for such a small piece?)

Let dry. Tape over seams and apply joint compound. Let dry. Apply
another layer of joint compound. Let dry. Sand, sponge, smooth to get a
blended effect. Repeat as necessary.

To address Joey's suggestion clips - it sounds like an interesting
idea, although I'm worried about the clip splitting the drywall around
the edges of the hole. I'll stop by Home Depot and ask them about it,
though, as I'll need to get some tape and adhesive.

Thanks again to everyone's help - I'm breaking new ground here patching
my ceiling. :-)

--charlie