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

'rather small bird' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.

'a funny fight in it' is the wordplay.
'a funny' indicates anagramming the letters.
'in' is an insertion indicator.
'it' becomes 'tit' (I can't explain this - if you can you should give a lot more credence to this answer).
'fight' with letters rearranged gives 'ightf'.
'ightf' inserted inside 'tit' is 'TIGHT FIT'.

'having' acts as a link.

Can you help me to learn more?