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.