Really, when you refinance, your choices are pretty much the 15 or 30 year loan (ARM or fixed), so unless your loan has 15 or 30 years remaining, you are either going to extend your loan terms or shorten it by paying more per month with the 15 year loan. Either way, you should have chipped down your principal at least a tad by paying it over the past four years, so even though your new loan was back to 30 years, it should have been a slightly lower monthly payment even before taking the lower rate into account.
Good on you for paying more principal up front. A word of caution - a lot of people don't really understand how this process works - especially about paying extra into principal each month. When you took out your new loan, say it was for $200K at 4% for simplicity, the bank reverse engineers the numbers assuming you are going to pay it down over 30 years, and are going to pay 4% interest on the balance yearly. In other words, you are going to pay $8K interest the first year, $7.8K interest the second year, $7.5K interest the third year - all divided by 12 months of course - or something similar to that as your overal principal decreases over the years. This math is reverse engineered assuming your principal is going down by the scheduled amount over 30 years. The "scheduled amount" gets all fucked up when you start paying extra and chipping down principal ahead of schedule. Paying down principal, of course, should favor you, but a lot of times the bank rigs the rules to favor them.
It looks like you are going to plop down an extra $3K in principal each year, but the bank is still going to charge you interest according to the original payback schedule. Usually, all they do is take off payments at the end of the loan, which greatly favors them. It just changes your pay-off date, not the yearly interest paid, which is based on the old, higher amount of principal.
In other words, say, for simplicity that you came across $100K and paid that in addition to your next payment. The numbers were originally crunched for you to pay 4% of a $200K balance the first year, 4% of a $198K balance the second year, 4% of $195K the third year, or whatever - hence my example interest numbers above of paying about $8K interest per year. If you paid the extra principal, $100K in this example, you should only be paying like $4K interest in the first year, $3.8K in the second year, $3.5K in the third year, etc. But your monthly overall payment and monthly interest payment will not change. Your loan will simply be paid off earlier, depending on how much extra you had pre-paid over the years. In other words, you are paying interest on a principal amount that is actually higher than the principal amount that you actually owe. Total robbery.
The way around it is that you have to periodically tell your bank to re-crunch the numbers, known as amortizing the numbers. I believe my bank calls it "re-characterizing" the loan, as I remember seeing that small blurb on page 69 of my stack of 150 pages of mortgage documents we went through on closing day. Most banks charge a $50 - $100 fee for the trouble of hitting the refresh button on their Excel program after typing in the new amount of principal that you actually owe. Not sure if you want to pay $100 to re-crunch your loan each year after paying it down $3K extra per year, but you will have to do it periodically if you want your extra principal payments to lower the overall amount of interest that you pay over the loan (which is the goal).
Some banks might automatically recalculate/reamoritize it for you with each additional payment, but I know a lot of banks don't.