Firt: avi is a container format so there's no such thing as avi compressor
Second: any video editor would be able to output avi files - the key for compressing video is using the correct codec (encoding-decoding algorythm) in the right way.
I reccomend Virtual Dub, it's free and one of the most advanced softwares out there - not as fancy as some Adobe or other studio but when it comes to pure conversion it's hard to beat the classic.
http://www.virtualdub.org/d/l - on the site.
However I don't recommend the latest DivX version - use 5.05 or 5.01 not the latest 5.1 versions. - the simple would do, the professional doesn't offer much more and it installs spyware.
The other option is Xvid - it's a free opensource alternate.
Xvid is more tricky but gives you more control then the DivX user interface. - Read up on it before encoding.
Both of those codecs support multiple-pass (or 2 pass) encoding. This is a must be nowadays - it will create a lot smaller files with better quality.
