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you can't "compress" avi's... you'll have to re-encode.
And re-encoding will take a lot of time to learn how to keep the quality up while lowering filesize, plus the actual reencode time (probably 3-4 hrs per 25min. episode). It's a pain in the ass.
i sometimes re-encode avi files into mp4 files (for an ipod) which makes them much smaller yet still great quality (at the right setting). that could be an option. the program i use is for a mac, so doubt you can use it.
i would encode them into mpeg format. that is dvd quality but without the large avi file size.
MPEG is a video format and AVI is just a file wrapper. Hell, MPEG4 is used in some .avi files (Ever hear of H.264?) even...
I would just buy a dual layer DVD and be done with it. Compressing anything twice makes it look crappy, and it would be too much of a pain to trim out the unwanted portions of the video... well, it can be made easy, but I wont get into that cause you should just be buying the legit DVDs