Some 'C' baggage is over 4k in size by itself.
"C baggage" usually comes from treating a small micro as a 'PC'. e.g. printf has no place when coding for a restricted memory size.

if the C code is 27k and you need to cut it to 4k there are two possibilities:
a) the C was coded by a "REAL C coder" with no concept of 'small' and you have a slim chance.
b) the C was coded by someone that understood 'small' and you will not be able to squeeze it into 4k, let alone 8 or 16

Erik