How much can I safely prune off a Rhus tree?

Like most trees, if you remove a huge amount the shock can set it back or even kill it. We cut down several rhus last winter, removing all the growth over six feet. Do this when it's dormant in the late winter. New growth will come in the spring.
We found that by doing this however, it encouraged even more suckering than before!

I would say prune all of it! . It suckers a lot and pops up here there and every where. Both our neighbours have done away with Rhus trees. I notice that even though our neighbour, at the side, cut down and poisoned his Rhus. There were about 10 suckers growing out of his lawn yesterday. They are away and the Rhus is making a comeback.

I wonder if I've done the wrong thing by growing ailanthus (tree of Heaven) from seed. This is a different type of sumach but has the same annoying habit. I've planted a whole line of them at the end of the vegetable bed and I'm already pulling out the suckers by the handful. The only Rhus we have is planted in the worst place in the worst soil I could find, and it's still a bit of a vandal.

Thanks Bertie and Dorjac!