Dinged LCD Screen -- Suggestions for Fixing?

I've got myself a shiny new aluminum 20" Apple display. Sadly, I also now have myself a 1mm ding in the bottom right quadrent of it, though I have no idea how I did it (no, wasn't there when I bought it, so it's my fault).

Does anybody have any suggestions for polishing out/otherwise removing dings in that beautiful but soft plastic? It'd sure be nice to at least reduce how visible it is...

mklos said:

This is the only problem with the aluminum, while it looks very nice, it looks like crap in a hurry if it gets scratch and dinged up.

Click to expand...

Sorry, guess I wasn't clear in my question. The ding is on the plastic screen itself, not the aluminum case. The case, I'd feel comfortable tapping on or maybe polishing with some fine-grit sandpaper, but the plastic screen I'm not nearly so confident about messing with without making the blemish much worse.

Hence my asking for tips...