Renaming doubled file names?

Let's say I've got a user's system with a folder tree full of files that all happen to be named like this:

filename.txt.txt
othername.txt.txt
somename.txt.txt

I want to rename them using the DOS rename command. The following does NOT work:

rename *.txt.txt *.txt

Anyone know the correct way to fix this?

Never mind, found it:

rename *.txt *.