Ultra-efficient compression
Solution 1:
lzma (aka xz) should do notably better than bzip2, but will take a bit longer.
paq (aka zp) will do quite a bit better yet, but will take ages to compress and just as long to decompress.
Both are available for Windows and *nix environments (most *nix systems have packages available)
A quick test on a smartd log:
Original 3900K
GZip 208K 0.11s
BZip2 71K 3.07s
XZ 13K 1.76s*
ZP 6K 25.68s*
*I've got -O3 compiled ports for xz and zp. The gzip and bzip2 binaries were precompiled with no optimization.