Trying to Refi SFH, fully occupied LTR... having trouble.

[Travis Moe]

I'm trying to refi a SFR in Jax and I'm running into difficulty. I've been using conventional lenders but I'm getting pushback because the amount is under $200K.

I owe about $162K on a property worth maybe as much as $250K. My current payment is 895/m and PITI is 1375.62/m. Current rate is 5.625%. I felt I could definitely beat that and drop my monthly payment by quite a bit, but so far the best I'm getting approved is only a $75/m reduction. That just doesn't feel worth all the fees.

Rates probably aren't going to get any lower any time soon. I'm seeing refi rates as much as 1% lower than my current rate, which I would think would render a lower payment. I must be missing something. 

Any lenders out there able to refi something like this for a more substantial monthly payment reduction?