compressed logfiles

logrotate (<- needed)
rsyslog (optional)

uncomment "#compress" in /etc/logrotate.conf

run to test it: logrotate /etc/logrotate.conf -f

optional define olddir in logrotate.conf
eg: olddir /var/log/old
or define it per file.. its up to you.

check if any files missed and create commands in /etc/logrotate.d/ for them..