In small segments, give out last message — fine, in fact (4,4)
I believe the answer is:
drip feed
'in small segments give out' is the definition.
(to drip feed is to give out in small amounts)
'last message fine in fact' is the wordplay.
'last message' becomes 'rip' (abbreviation for Rest in Peace).
'fine' becomes 'f' (abbreviation).
'in' means one lot of letters goes inside another.
'fact' becomes 'deed'.
'rip'+'f'='ripf'
'ripf' going within 'deed' is 'DRIP-FEED'.
(Other definitions for drip feed that I've seen before include "supply in small instalments" , "Drop supplies" .)