Why is Z the letter of sleep?

Where did the phrase "catch some zzz's" come from?  Who decided the letter Z sounds like people sleeping?  I've heard some weird snores, but I've never heard anyone who sounded like a buzzing bee while sleeping...

When I Googled it, the most interesting theory I came across was this:

"I've been looking into this, and as far as I can tell, it entered common use through a comic in the 50's, though I haven't found which one. Recently, though, I've been reading a book called Mao, in which there is some discussion about a spy who played a critical role in the Battle of Shanghai in 1937. What's interesting about him is that he was a sleeper spy who had been planted by the Russians in the CCP army years before he was stationed in Shanghai--and his initials were ZZZ. Whether he is related to the use of "zzz" to mean sleep, I don't know, but I found it very interesting."

Read more here.

Also, BullyH's answer on Yahoo! Answers just made me chuckle:

"If most were like me at school, by the time I got through reciting the alphabet, I would have been asleep. So I guess when I got to the letter Z, I would have been catching up with my sleep. How much quicker would it be to say, I'm going to catch some Zs. Three words actually."

So the common consensus seems to be that "catch some zzz's" became popular slang over 50 years ago when it started to appear in cartoons, but I'm still curious as to why the letter Z was chosen.  In my opinion, snoring sounds more like ffffrghhgghhhnntthhgghfff...