Sometimes people have bits of bone that are not pretty or that interfere with function (bone spurs or bony tunnels that are too restrictive as in carpal tunnel syndrome). In this case, to be able to locally remove bone without reducing the strength of the remaining structure would be a good thing. I would bet that surgeons who do reconstructive surgery have to deal with these kinds of issues and have developed tricks to trigger the body's natural bone resorption mechanisms. Bone reduction is a healthy, normal part of bone growth and maintenance. At the very local level, bone is removed to accommodate the growth of blood vessels into a bone or across its surface, in response to the growth of tissues bounded by bone (brain growth in the infant causes the skull to enlarge by stimulating osteoclastic activity in the inner table of the skull bones and osteogenic activity in the outer table, muscles and tendons shape the bone beneath them, etc.). And in a very generalized fashion, the process of bone growth requires that bone be removed. In the shafts of long bones, the medullary cavity must be steadily enlarged at the same time as the outer cortex is added to by appositional growth. The same process of integrated bone removal and bone growth is going on in the cancelous bone of the heads of long bones and in the centre of flat bones (the diploe of the skull for example) as growth occurs. Bone remodelling (growth and reduction simultaneously) is essential to fracture healing. It also must occur for the trabeculae in the head of a long bone to realign to take altered forces if a joint is used differently in weight-bearing activities. The trick here is to sequence and balance the regulatory mechanisms which trigger and control these two competing processes. The physical forces to which a bone is exposed are critical here as anybody who has had braces knows. Bone responds to pressure at right angles to its long axis by resorbing (for example, the erosion of ribs that occurs to accommodate enlarged intercostal arteries that result from stenosis of the aorta and increased blood flow routed through the intercostals, also witness the bone erosion that occurs in the cranial vault to accommodate an enlarging brain tumor adjacent to the skull). Bone responds to compressive forces along its long axis by becoming more heavily mineralized (increased density) and laying down more collagen fibrils in the bony matrix. It responds to tensile forces by protruding and becoming stronger as well.
I would guess that there are a variety of complexly interacting forces at play to achieve this normally well integrated and functional balance. This will involve generalized hormone release (thyroxine, growth hormone, testosterone and estrogens, and calcitonin in states of generalized bone growth (growing, working out heavily) and parathormone in cases of bone resorption (low calcium intake, lowered activity levels and strength demands).
The regulation of the contradictory processes at the local level is less well understood. TGF-beta appears to be an important osteoblast stimulator. I don't know anything about the osteoclast stimulators. A major regulator appears to be the pisoelectric forces that get generated in bone by the lines of force at work within the bone itself and due to the external forces it is made to bear. Electrical stimulation of bone that is slow to heal is used in the old and in pathological fractures. But these are osteogenic applications. Here's where the young entrepreneur/scientist might like to investigate. If one could reproduce the electrical forces associated with lessened load and focus these on the portion of bone of interest (say my unattractively large schnoz), then one could do gradual bone reduction without having to resort to cruder, more generalized controls (parathormone for example) that lead to bone demineralization and loss of strength (and would lead to breaking my nose when I sneezed). I suspect that artificially reproducing the balance of controls is going to be the tricky bit!
Another reference: Hill, PA, Bone remodelling. Br J Orthod, 1998 May; 25(2):101-7.