Tiny parasites in the public eye (4)

I believe the answer is:

lice

I'm a little stuck... Click here to teach me more about this clue!

'tiny parasites' is the definition.
'lice' can be an answer for 'parasites' (I've seen this before). I'm not sure about the 'tiny' bit.

'in the public eye' is the wordplay.
'in' says the answer is hidden in the clue.
'LICE' can be found hidden inside 'public eye'.

Can you help me to learn more?

(Other definitions for lice that I've seen before include "Bloodsucking insects" , "Wingless bloodsucking parasites" , "Crawlers" , "Bloodsucking parasitic insect" , "Parasitic insects" .)

I've seen this clue in the Irish Times and the Irish Times (Crosaire).

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