Is my credit good enough for mortgage refinance?

Since I obtained my mortgage, I have had some credit problems. Due to circumstances beyond my control, I made some slow payments on my credit card bills and other monthly obligations. Mortgage rates are lower now than they were when I purchased my home. If I would qualify for a lower interest rate, I would save thousands of dollars over the life of my mortgage loan. I just don’t know if I will qualify for today’s low rates or not. Is my credit good enough for mortgage refinance? Or will credit problems keep me from getting a lower interest loan?