Be specific about the loan you want. The more precise you are, the easier it will be for a loan officer or mortgage broker to find the best rate. For example, do you want a 15-year or 30-year mortgage? Do you need a "jumbo" mortgage (more than $333,700)? Are you willing to pay points to reduce the interest rate? The answers to these questions will depend on several factors, including when you plan to sell the house and how soon you want to retire your debt. Only you know the answers, but the sooner you know them, the better.
If your new mortgage rate seems too good to be true then it probably is. Check for hidden fees in your mortgage that will make up that suspicious difference.
When you do a cash-out refinance you are leveraging the equity in your home in order to receive a lump sum of cash at closing. Many individuals and families use this type of loan if they want to remodel their home, or they have kids that are attending college soon. Veterans and other military personnel can now take advantage of a 100% cashout refinance thanks to the Veterans Benefits Improvement Act of 2008.
You have a legal right to a good faith estimate. Get a copy of this document and go over it with a fine tooth comb, it will reveal where there is a real problem.