FOR THE LOVE OF EVERLOVING MIKE!!! GODDAMMIT, THERE ARE NOT VARYING DEGREES OF UNIQUENESS. SOMETHING IS EITHER UNIQUE OR IT ISN'T. UNIQUE IS SINGULAR AND IN FACT IS A SYNONYM.
*pant, pant, pant*
The word you're searching for is uncommon, or unusual, or rare, etc. So, please, the next time you start to type the words, "his (voice/playing/driving/cooking/etc.) is very, very" just stop right there. Think, about what you want to really say and choose any words other than unique or singular.