We have 3 grapevines growing on our backyard fence. Two of them are vigorous and bear green/yellow grapes every year.

The third one has always been weak, and bears only a few purple grapes each year. Last year, the few canes that grew on it are all thin - less than 1/4" in diameter. When we prune it this spring, should we cut off all those thin canes, and cut the older growth back closer to the ground to stimulate new, thicker canes to grow?

Also, what should we do to help this grapevine to be more vigorous?