I think that there was a program that you could take avi and make it into a dvd and it would make shrink and burn it on a 4.7 g disk. Also there was a program that decrypt a dvd and then shrink and burn on a 4.7 disk. Could it bee the same program? I think it was freeware.
There are lots of different programs that can convert avi to dvd. Look at FAVC, Avi2DVD, DVDFlick, ConvertXtoDVD, etc. Of those, only ConvertXtoDVD is not free to use. You can set the output to fit onto a single layer dvd in each of those programs.
DVDShrink was the program that could decrypt and compress your dvd to fit a dvdr. It is basically obsolete as a decryption program—for anything that has more than simple CSS protection. It is still a good transcoder though. Use it in combination with a commercial program called AnyDVD, or rip first with DVDFab HD Decrypter, which is free to use.
Edit: And for a modern equivalent to DVDShrink, look at DVDFab Platinum. It has more capabilities, like converting dvds to mpeg4, as well as compressing dvds, but it is not free. It is up to date on decryption.