Genrich Altschuller's Theory of Inventive Problem Solving (aka TRIZ - pronounced trees) is a brilliant framework that designers and engineers should all be familiar with.
One of the many tools included in the TRIZ methodology is an approach called trimming. Basically it involves arbitrarily removing one element from a design, then trying to make the system perform all the necessary functions without that piece.
I put together this little flowchart to help explain how Trimming works. To quote John Hodgeman, you're welcome.