You can "buy down" your interest rate thru paying "discount points". The cost vs. drop in rate differs depending on how long your rate is fixed for. I.E., the most expensive loan to "buy down" is a 30-year fixed, since you are lowering your rate for the entire term of the loan. You usually get a bigger decrease in your rate when you "buy down" an adjustable rate mortgage, since you are only insuring that your rate is fixed for, let's say, 3, 5, or 7 years.
Discount points are considered prepaid interest, so if you are paying them for your primary residence, you can write them off on your taxes. Consult you tax advisor for more details.
Paying points to lower your rate does not always make sense, so look at it like an investment. Here's how to make sense of it:
Let's say that you have a loan of $100,000 with a zero point rate. By paying two points (2% of the loan amount=$2000) you can knock one percent off of your rate. By doing so, you are lowering your monthly payment by $100. Divide your monthly savings ($100) into the cost ($2000) and you'll come up with a monthly break-even rate. In this instance, you would break-even in 20 months or less. I say "or less" because the fact that it's tax-deductible could shorten your break-even period for the better.
If it's going to cost you $2000 to save $50 a month, this increases your timeline of breaking even out to 40 months. This may not make sense depending on a) how long you plan on staying in the home, and b) if you refinance before then, you've lost out.
Hope this is helpful!
Executive Mortgage Banker