Compression – How low can you go?

Good day !

I’ve tried a few compression programs ( PKZIP, WINRAR to name a couple ), but I’m finding that the larger the file size, the less the compression is. Is there a compression program that can compact large file sizes ( around 8mb )
without simply splitting them up into 1.4 MB diskette sizes? ( example: can 8mb be compressed to 2MB or even 1MB? )

Let me know what your findings are and thanks once more for your help,

Kelly