Strange, fine fairy story is indescribable (9)

I believe the answer is:

ineffable

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'is indescribable' is the definition.
(synonyms)

'strange fine fairy story' is the wordplay.
'strange' indicates anagramming the letters.
'fairy story' becomes 'fable' (fable is a kind of story. I am not sure about the 'fairy' bit.).
'fine' is an anagram of 'inef'.
'inef'+'fable'='INEFFABLE'

Can you help me to learn more?

(Other definitions for ineffable that I've seen before include "impossible to describe" , "Inexpressible" , "Defying description" , "Unable to be described in words" , "Too sacred to be uttered" .)

I've seen this clue in the Sydney Morning Herald.

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