Rather small bird having a funny fight in it (5,3)

I believe the answer is:

tight fit

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'rather small bird' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'a funny fight in it' is the wordplay.
'a funny' indicates an anagram.
'in' indicates putting letters inside.
'it' becomes 'tit' (I can't explain this - if you can you should believe this answer much more).
'fight' with letters rearranged gives 'ghtfi'.
'ghtfi' inserted within 'tit' is 'TIGHT FIT'.

'having' acts as a link.

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I've seen this clue in the Evening Standard.

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