Slightly sooner (6)
I believe the answer is:
rather
I believe this is a double definition.
'slightly' is the first definition.
(thesaurus)
'sooner' is the second definition.
(I know that sooner can be written as rather)
(Other definitions for rather that I've seen before include "More willingly, by preference" , "More precisely; instead of" , "On the contrary; more precisely" , "To a certain extent" , "Preferably, instead" .)