wind died down/out/away

Could you help me with this question: Are all three die phrases fine with this sentence?
The wind died away/down/out to a faint breeze.

I think "died away" and "died out" suggest that the wind went away completely, leaving nothing at all. "Died down" suggests that it weakened so it would make sense for there to be faint breeze remaining afterwards.

"Died away" sounds odd to me.

Died away sounds fine to me, though not in this context- died down is the one I'd use here.