My solution is to produce a design in my head, and figure out its limitations. Then I ask for each limitation if this limitation will be a problem. If it is, then I figure out how to iterate the design to eliminate that limitation. Once I don't know of any unverified limits, then I start explaining my design, and explain how I know it will perform to spec.

This is also a good way to approach system design in the real world. Don't simply go with the first solution that looks like it might work. Also don't add on nice looking features on general principle. Instead sketch out the simplest thing which works in your head, figure out the limitations, check whether each is OK, and then improve my design if it doesn't work yet.