Avi files grow 5X to DVD in Nero & Cucusoft

I am amazed and frustrated by why my AVI files, when I attempt to make a DVD out of them, expand in size by a factor of approximately 5X. This occurs whether I use Nero or Cucusoft.
I had thought that AVI files were rather large and if anything would have gotten smaller in the DVD -Mpeg 2 format.
My research said to expect a small increase in size but this is ridiculous.
Am I doing something terribly wrong?
Thank you for taking the time to consider my problem.

This is perfectly normal, assuming that the AVI files were compressed with a codec like Xvid or Divx.

Thank you Tim, I appreciate your response.