Pruning is what keeps a tree from becoming a removal.
Most of the trees that come down could have stayed up. They got heavy on one side, nobody took the dead wood out, and then one wet winter settled it.
Taking weight off a canopy does two jobs at once: the tree stops dropping things on whatever is underneath it, and it stops leaning on the half of itself that is already under strain.
It is also the cheaper half of this trade by a wide margin, which is the honest reason to ask about it before you ask about taking the tree out.
One limb, or the whole canopy?
Describe what is hanging over what, and go from there.