I am in the process of refinancing as well, we are basically in the same situation as you are, we had a 30 year 3.75% fixed rate, and when rates dropped it finally made sense. We had been aggressively pre-paying our loan, so at the rate we were paying it off, the 30 year would have been knocked out in 15 years. I know 3.75% was a low rate, but we just didn't like the debt. We were able to refinance initially at a 2.75% for 15 years at like 0.8 points or something like that, and when he gave me the stats of the points for the loan, it actually made sense for us to pay some points and go even lower, so we are at 2.25% for 2.8 points or something like that, I forget. So it added more to closing costs that we will roll into the loan, but over the life of the loan if we now pay it off over 15 years it will save us a lot of money for refinancing from a 30 year and just putting the extra money in the market.
First, I would make sure that if you are refinancing that you get multiple offers, we got a few and finally 2 of the big companies had to compete for business. When they have to compete you will only better your situation. If they are pulling your credit then you have like 45 days for others to pull it at no extra ding to your credit. I love the Karl's Mortgage calculator website/app, as you can play around w/the numbers and see what pre-paying does, what the total savings, interest, total amount paid, etc. I ran every single scenario based on the break even point of closing costs and the loan reduction, so you should probably run all of those scenario's and do the calculations and see what makes sense.
Also, make sure that you are refinancing that you are going to stay in the house at least until the break even point. I plan on living here for the next 20 years or so at least, so it makes sense for us and our break even point was like 8 years w/the extra costs for refinance/closing. So do the math and see what the break even point is, if it's cheaper to keep the same loan at your terms and just pre-pay or pay down the PMI (not sure if you can do that). But some simple online mortgage calculators will tell you if it makes sense to refinance or not. Good luck!
