NonEmpty() and that all-important second parameter

Here's a question which comes up all the time - it was asked at Mosha's MDX seminar last week, and a friend of mine asked me about it recently too - what does the NonEmpty function do if you don't specify the second parameter?

Let's take a look at some example queries. I think everyone knows that you can use NON EMPTY before an axis definition to remove all the empty tuples on that axis, as with: