Problem: You've got an old shrub that's a woody, tangled mess.
Do give the plant an overhaul by thinning out the old wood over the course of three years, making room for all new growth. Starting at the base of the shrub, eliminate the centermost branches, taking out no more than one-third of the shrub's total mass. New growth from the base should follow the next growing season. Remove another third of the old wood at the base in each of years two and three. By the end of year three, the shrub should be made up of entirely new, vigorous growth.
Don't remove more than one-third of the shrub's branches at any one time. This preserves enough foliage that the plant can make sufficient food (through photosynthesis) to stay robust and generate new growth quickly.