I always believed that there is not much negotiating with big banks. You ask the bank for a loan and get a good deal assuming your credit is perfect, your profit is great, you make a lot of money and have enough money for downpayment.
In my recent experience I first got a letter of commitment Wells Fargo for 7.85% and I believed it was a good deal. Then Bank of America contacted me and offered 6.4% with the same conditions. When Wells Fargo learned that they suddenly could do something what was never possible before (lock the rate, lower the interest rate spread). The only thing which let them offer a decent deal was the feeling of competition.
Always contact more banks and let them compete for your deal! You can save a lot of money!