Thicker fans do 2 things. They increase airflow and increase static pressure when compared with thinner fans of the same design and RPM.
A number of things can be done to improve airflow:
1. Increase RPM
2. Increase fan depth
3. Direct airflow to the hot parts of the computer. Some people produce getto baffles from ceriel packets - but be careful it doesn't get hot enough to set anything on fire!
4. Choose a fan better at airflow for a given level of noise/backpressure
5. Remove backpressure normally done by cutting away un-needed metal from the case that the resticts airflow - be very careful of sharp edges, make sure you have safety equipment e.g. hand, eye, breathing and ear protection
For case fans I would expect low backpressure (unless the case has a very restrictive mesh covering the intake). For case fans I would consider scythe's very impressive slipstream series of fans which are poor at handling backpressure but produce a large amount of airflow in unrestricted environments for a given level of noise.
I know this doesn't help the OP who has already purchased a fan, but others may find this useful.
