Looking on the internet deeply has found these results:

a fair bit small is the most popular phrase on the web.

a fair bit small decrease 10 results on the web	a fair bit small 13 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	fitting�... ... one of the ride attendants took this photo for us, which turned out extremely well and increased my appreciation for Alton Towers a fair bit (small things matter !)�... Heads up on merchandise: the shirts run a fair bit small. I would order at least one size bigger than you normally do if you prefer loose Mar 5, 2016 ... [�]kinectking 2 points3 points4 points 12 days ago (6 children). fuuuuuck its a fair bit small for my hand but that price is so damn goooooood.

a fair bit small decrease

10 results on the web

a fair bit small

13 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

fitting�...
... one of the ride attendants took this photo for us, which turned out extremely well and increased my appreciation for Alton Towers a fair bit (small things matter !)�...
Heads up on merchandise: the shirts run a fair bit small. I would order at least one size bigger than you normally do if you prefer loose
Mar 5, 2016 ... [�]kinectking 2 points3 points4 points 12 days ago (6 children). fuuuuuck its a fair bit small for my hand but that price is so damn goooooood.