I've got a few compression tops that I wear boxing sometimes but when ever I run in them I get terrible chaffing so have opted for proper running kit that is tight-ish but still allows to breathe and vent. The compression tops are great for not sweating though, it just evaporates.
The first time I ever tried on a compression top I was in a sports store in America, I put it on and looked in the mirror and I thought the T-shirt had some weird padding around the waist so I took it off and tried another which was the same.
It turns out it was me causing the "padding"

I was very shocked as I had a very flat stomach at the time and I'd never seen love handles before in a mirror. My friend and wife thought it was funny as hell. You've been warned.
Darren