The tight around the cheeks thing is something to be wary of. I thought it'd be no big deal. What ends up happening is you bite the insides of your cheeks. Had this problem with a helmet I used for go-karting last weekend. See if another brand in the same size feels different. Some brands just don't fit people well.
My friend Jay had to try all sorts of different brands before settling on one. His big head (due to intelligence, i'm sure) made it tough to find a helmet that fit right.
Tighter is better. As long as it's tight in a good way. I have problems with helmets being too tight around the ears since my ears are pretty big and stick out from my head more than the usual shmoe. I didn't shop around much and luckily my Bell seems to fit okay, but could be better in the ear department. After I pull the helmet down, I have to slide my hand inside the helmet to unfold my ears. Once I unfold my ears, the helmet fits nice. Maybe I should roll my ear lips?
I recall a good way to test helmet loose fitment is to put it on and secure the chinstrap as you normally would. If you can pull the helmet down in front and it covers your eyes? It's too loose. Too tight is obvious- it just doesn't fit.