Fag-paper?

Which is preferred?
She was fast asleep!
or
She was sound asleep!
We have divided opinions here and would appreciate any and all input.

I hadn't thought of this before but I think, "fast asleep" is that she's fully asleep.

"Sound asleep" implies she's in a deep sleep.

The difference if there is any is very slight so I'd think either way of saying it would do.

I haven't given it any thought until now either. I am not sure, but I think I probably use them very much interchangeably - no doubt I will now be shown to be unspeakably sloppy!

'fast' is used in the sense of 'tightly' or 'resolutely' (think 'fastened') - and 'sound' is being used in the sense of 'solid' or 'reliable' - there is not a fag-paper of difference between the usages when applied to sleep (IMO).
both are entirely acceptable meaning completely asleep.
I like 'comatose' myself.

zzzzzz.

What is the meaning and origin of that? It sounds derogatory.