git-rm'ing all dead files

I couldn't find an easy way to remove all "dead" files from the index, i.e., call git-rm on all files that are missing from the working copy.

Here's the scenario: I moved/added/removed a lot of files using a GUI tool; now I need to reflect those changes in git. Using git-commit -a isn't the best choice because there are local modifications I don't want to commit. I can use "git add ." to automatically stage all new files, but how to the same for removed files?

-- Pazu