Most New Jersey mortgage lenders will allow for a “Float Down” of your interest rate once the initial rate lock is set. That said, there is usually some kind of cost. Generally, the lender may charge 1/4-3/8 points in fee for the privilege of floating down or may simply float your rate down to the current market rate + 1/8%. This is due to the fact that the agencies of Fannie Mae and Freddie Mac charge for this privilege, so this fee is generally a pass-through from them.