Just call your current mortgage company. Ask if they have refinance options available. The problem with refinancing is that they get to re-write the mortgage note (they don't just change the interest rate on the existing mortgage). You don't have as much hassle to go thru as you originally did when you got the mortgage. However, things like the plot plan, lien search, etc (along with all the charges) can usually be built into the new loan.
I've refinanced a number of times, and usually your current mortgage holder will allow a refinance, especially if you tell them that you'll go to someone else and you are just giving them 1st refusal.
Like I said, they re-write the note, so make sure you compare it to your existing mortgage note. They tend to add/delete sections to the new loan that may cause problems. Ex. Won't finance a home with underground oil tank; difficult to finance a home that has asbestos shingles or covered pipes; no refund of overpaid interest; not allow assumption of mortgage, etc. Of course, it depends on where you live, and they will add the cost of getting these type problems resolved into the new loan.