First property! How to shop the rate?

[Allison Shea]

It's a 3-bedroom investment property (can't have it classify as second home since I don't own current place). Worth noting: only 3/12 units within the building are owner-occupied, so either I get a higher rate or I do a 25% down in order to avoid a review (will do latter). 

I've got 2 rates in hand: 4.5%, and 5.75% - I'd like to get to low 4s or below. What are my next steps? I can continue to shop around, but it's a credit ding each time. I've heard about credit unions but not sure that's a possibility given property out of state.