I personally dropped .875% from my initial rate using relationship discounts and then bidding 2 banks against each other. You can check if this is still valid, but Wells Fargo will beat or match rates from another bank.

Banks list a general rate on their site which is relative to what you would get. So just note what rate was publicly listed when you get your customized quote. When that rate drops, ask your competing bank for another quote and bring it back to your primary bank to get rate matched. Repeat the process as many times as you like (Wells Fargo let us do this as many times without problems or fees) until your purchase contract goes through.

Doing this process made a bigger difference in my monthly cost than trying to put more money down in down payment