There's a post floating around with plastic ornaments engraved with a dremel. They are beautiful. These--are not. For starters, she managed to find plastic ornaments that are white underneath. All of the ones I had in my stash were made of gray plastic. I also only have one engraving tip size for my dremel--but I figured I'd give it a whirl.
It's really hard to get anything resembling a smooth line. The dremel wants to shoot right off of the ornament. After ruining a couple red ones, I was left with some small gold and silver balls. I opted for a quick starburst/asterisk design as I thought I could manage it given how excitable the dremel was on the surface of the ornament. The starburst was easy enough and would probably look good no matter what color the plastic is underneath the paint. Just be sure to work on a covered surface to catch all the little paint/plastic filings.