I have this little tree that I ordered from Wayside Gardens catalog several years ago. I like it very much. It's a Fuji cherry, small, and fits the spot allotted for it perfectly.

The thing is, it suckers...a lot. I don't have a huge front yard and I have suckers coming up all over the place, even many feet from the tree. What can I do about the suckers? I can't dig them out because they would be too hard. Would putting something on them to kill them also kill the tree? Is taking the tree down the only solution about the suckering?