usually, the rear brake adjustment will decrease the amount of travel of the hand brake, if it is adj. properly. 1st, loosen cable you just tightened, adjust your rear brakes, make sure all cables, linkages, and pivots are free and not binding, then check cable adjustment. I feel if you have to have the rears dragging to make the handbrake work, something else is not right. (like streched cable, poor adj. of shoes, worn shoes etc.etc.)