I want to get a small 8x20 binocular that will fit in a shirt pocket. I have no experience with small glasses and would appreciate suggestions. Thanks!

In a 20mm objective quality of optic has a great deal to do with whether or not you'll get strain and eye fatigue.
I'd suggest a Zeiss, Leica or even Swarovski.
The Leica Trinovids are excellent and aren't too crazy expensive.
What price range were you looking for?
In a lower priced unit a Steiner would be a good option

I have used a pair of Leupold 9x20s for years and been entirely satisfied. The optical quality is excellent.

Why not look at 8x25 roof prisms? They give a bit more light and ease of seeing the full view with specs on but are half the weight of 8x30s.

Lou, my Zeiss 10x25 BTs are on the way.