https://forums.overclockers.co.uk/showthread.php?t=18766061
Cheap, you'll be able to wind the fan right down and still have good cooling.
Edit: missed the height requirement. It's 159mm so might be too big.
I stuck one of these on the wifes G3420 and it keeps it nice and cool while being very quiet at the same time. Her case is the compact Sharkoon CA-M Micro ATX Case so airflow is limited but the cooler does a fine job. She uses the cpu's onboard gpu as well.
My basket at Overclockers UK:
- 1 x Arctic Alpine 11 Pro Rev.2 CPU Cooler= £8.99
Total: £15.01
(includes shipping: £6.02)