What's in a tail?

Yesterday, walking out of Whole Foods as I was walking in, two men addressed Luci like this:

"Oh, what a fine dog you are!" one squatted to tell her. 

"And," the other added, "You have such an important tail." 

I've heard Luci's tail called a lot of things--my previous favorite being "resplendent, which it is.  A long shaggy tail on such a little dog is definitely noteworthy, and it's often noted, but I'd never have thought of it as important. 

I love this so much that if I were a writer of children's stories, I'd write one about a fine dog with an important tail!