Barely deserved (4)
I believe the answer is:
just
I believe this clue is a double definition.
'barely' is the first definition.
('just' can be a synonym of 'barely')
'deserved' is the second definition.
(thesaurus)
(Other definitions for just that I've seen before include "Barely - deserved" , "Barely honest?" , "Barely; right and fair" , "legal?" , "Fair - precisely" .)