Does anyone know of any site that lets you find out what the cheapest flight for a given itenerary (either on a specific airline or on all airlines the site surveys) is REGARDLESS of class (ie, one where a cheaper first class or business class price would show up automatically, and be identified somehow as first class or business class)?

Many sites make you choose the class on the very first page, then you make other choices on later pages, so it's a lot of re-specifiying you need to do if you're going to manully check one class after another.