I was thinking of "Quick Search" but "Simple Search" might be better. Or "Overly Simple Search" (okay, that's a bit too much). The word "Super" might also be confusing because "Advanced" is the term commonly used elsewhere.

With that said, why not just have the current "Search" call "Super Search" with the default settings? Then it would be a "Quick Super Search", which could be shortened to "Quick Search".

Update: Fixed typos and reworded the "Advanced" sentence.