Sometimes the source of the problem can be altered to either eliminate the problem or direct it to another part of the product where it can more easily be treated.
For example, you are designing the structural elements of a forklift. Loads being passed to the structure near the lifting motors are very high; designing for them will require thick, heavy components that will dangerously raise the centre of gravity, and interfere with the operation of the forklift. The problem is not that stresses are too high in your components, but that the load is being directed at your components. Can the geometry of the forklift be altered to give loads a path to the axles (they shall inevitably end up there, right?) that avoids the components you are concerned with?
Another example: the cost of refining oil sands, like the Alberta tar sands1), into gasoline is very high in large part because of the viscosity of the sands once they've been mined and moved to a refinery. A group of researchers have patented a method of lowering the viscosity of the bitumen in the oil sands, in essence starting the refinement process before the oil sands are moved to the refinery. In this case, the source of the problem was changed from having to move the oil and the sand to the refinery, to (partially) refining the stuff before moving them.