birth control recommendations??

My major motivation for starting birth control is cramp relief, but of course getting pregnant is NOT on the agenda. During h**l week my cramps are so bad it's difficult to move and I often can't bring myself to get out of the house. Of course I try using Midol and other over the counter pain meds, but nothing seems to work. I've heard that birth control is effective in stopping or minimizing periods and period symptoms, but because of my family history I have a high chance of getting breast cancer and I've read that the hormones in bc can increase that chance. Does anyone know a safe, low hormone, EFFECTIVE birth control that helps with or stops periods or period symptoms?