We have a Bodark tree in our front yard that was pruned of dead limbs about 18 months ago. In the past few months it has produced "suckers" - some from where limbs were removed, and others from out of the bark of trunk and other limbs. We have been told to cut all of the suckers off the tree. My question is: aren't some of these suckers needed to re-grow new limbs and help keep the tree alive and growing well?

Picture is here: http://hortiplex.gardenweb.com/plants/jour/p/98/gw1024898/471271022365961.jpeg

Here is a link that might be useful: