A sysadmin would use the logging facility (if traditional syslog) or simply awk/sed to process the logs into different files that are similar to each other (such as different levels of INFO/WARN/ERROR); then, increase the size of the DEFLATE dictionary used for compression until you get better compression.

See for instance this discussion of creating a custom DEFLATE dictionary: https://blog.cloudflare.com/improving-compression-with-prese...