It depends on what you mean by "design", but sometimes the best way to figure out what your options are is to throw something together and see how it feels. Could be UI, could be API design, could be a form of test-driven design.

If the problem isn't well-understood, you probably don't want to put code down -- you're better served going to the customer and scoping a problem to start from.

If the solution isn't well-understood, you probably don't want to commit to any code -- but there's no reason you can't use the development process to drive out some candidate solutions.