I am making a project with several modules and libraries involved. I just tested the SD lib example, and got a binary at ~14KB - way too much. I'd like the SD bits to go below 8KB, since it's just for logging from an NFC and RTC module. I notice some 'stabs' debug bits in my Makefile, and wonder if I could do something with that. Besides that, perhaps the experts here can recommend a smaller library for my SD bits, so I won't exceed my ~27KB flash capacity. I am using the SD example for creating/deleting files. Ask me to clarify if needed.
For AVR + SDCard you should check FatFs from Chang. It is widely used and proven C library. You can tweak the configuration file to get minimal size (8K shall be easy). Check wrapper library for Arduino here (6K with default options).
There is also even smaller version called Petit FAT (2-4K) but it doesn't support file delete feature.
If you would like to get smallest possible code, there is option to use Atmel Studio for programming Arduino boards, but you will loose the convenience of Arduino libraries (re-implement the libraries or find AVR versions of them, work with registers directly etc).