Drunk as a skunk

Why is it 'drunk as a skunk'? Or rather: where are the origins?

Except that it's quite a nice alliteration I don't see much sense in the phrase.

I've heard and used the phrase since I was old enough to hold a glass -- that is, a glass containing an alcoholic beverage. I've never heard anything to indicate that its source is anything but the rhyme. That's reason enough, isn't it?
SS