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If you (preferably on a copy) right-/ctrl-click on Mail.app, there's an option to "Show package Contents". In there you find a Contents folder, in that go into Resources, find the annoying sound (No Mail.aiff?) and replace that with another, less annoying, aiff file with the same name...
 
Any chance you could talk a newbie step by step thru finding a better sound file, and how I go about changing it in this situation? Thanks
 
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