I want to drill a hole or 8 in my computer case. I don't want to short out my motherboard or anything. There are a host of problems with this -- mainly throwing slivers of metal in several directions. Is there any great way to avoid throwing shards of metal everywhere or contain them?

Edit: The holes aren't actually near any components, I just don't want to accidentally throw metal shavings into the electronics 3-6 inches away