Generally speaking your bank might give you some discount

If you have been a long term good customer with good amount of money in either saving or checking account. I do not know about other banks, I know BOA has three tiers of memberships: gold (3 month average $25K-$50K in your account), platinum ($50K to 100K), forgot the last one. You get 0.125% rate deduction for gold, 0.25% deduction for platinum and more for next tier, along with some savings from closing. That is the bank I have been using. So check with your bank about this, also should always compare at least three lenders.

Good luck!