"Rather quite" or "quite rather"?

I'm a bit confused about this. They both sound correct to me.

• Quite rather weird
• Rather quite weird

Which of the two is correct?

Rather quite sounds much better to me (American English speaker) than quite rather, but they both sound strange.

In fact, there seems to be a whole class of adverbs like this - rather, quite, somewhat, fairly - which you can't stack on top of one another. Not sure what to call this phenomenon, but all combinations of the above sound wrong to me: somewhat quite weird, rather fairly weird, fairly somewhat weird, etc.

Although both strike me as odd, and both are very infrequent, quite rather is less common that rather quite. See http://books.google.com/ngrams/graph?content=rather+quite%2C+quite+rather&year_start=1800&year_end=2000&corpus=0&smoothing=3