Why does 'You're So Vain' have that "I had a dream they were clouds in my coffee" lyric in what is otherwise a quite sensible song?

From Carly Simon's official site:

Clouds In My Coffee

Can you tell me what the meaning of the phrase "clouds in my coffee" has in the context of your song "You're So Vain"? I can't quite pin down the metaphor. What are the "clouds" in your coffee? Samantha - Dearborn, MI

"Clouds in my coffee" are the confusing aspects of life and love. That which you can't see through, and yet seems alluring...until. Like a mirage that turns into a dry patch. Perhaps there is something in the bottom of the coffee cup that you could read if you could (like tea leaves or coffee grinds). Carly Simon 5/17/01